A rigid copper tank, initially containing 1 m3 of air at

A laser Doppler velocimeter measures a velocity of 8 m/s as water flows in an open channel. The channel has a rectangular cross section of 0.5 m by 0.2 m in the flow direction. If the water density is a constant \(998 \mathrm{~kg} / \mathrm{m}^{3}\), determine the mass flow rate, in kg/s.

Refrigerant 134a exits a heat exchanger through 0.75-in.- diameter tubing with a mass flow rate of 0.9 lb/s. The temperature and quality of the refrigerant are \(-15^{\circ} \mathrm{F}\) and 0.05, respectively. Determine the velocity of the refrigerant, in m/s.

Steam enters a 1.6-cm-diameter pipe at 80 bar and \(600^{\circ} \mathrm{C}\) with a velocity of 150 m/s. Determine the mass flow rate, in kg/s.

Air modeled as an ideal gas enters a combustion chamber at \(20 \mathrm{lbf} / \mathrm{in}^{2}\) and \(70^{\circ} \mathrm{F}\) through a rectangular duct, 5 ft by 4 ft. If the mass flow rate of the air is 830,000 lb/h, determine the velocity, in ft/s.

Air exits a turbine at 200 kPa and \(150^{\circ} \mathrm{C}\) with a volumetric flow rate of 7000 liters/s. Modeling air as an ideal gas, determine the mass flow rate, in kg/s.

If a kitchen-sink water tap leaks one drop per second, how many gallons of water are wasted annually? What is the mass of the wasted water, in lb? Assume that there are 46,000 drops per gallon and that the density of water is \(62.3 \mathrm{lb} / \mathrm{ft}^{3}\).

Figure P4.7 provides data for water entering and exiting a tank. At the inlet and exit of the tank, determine the mass flow rate, each in kg/s. Also find the time rate of change of mass contained within the tank, in kg/s.

Figure P4.8 shows a mixing tank initially containing 2000 lb of liquid water. The tank is fitted with two inlet pipes, one delivering hot water at a mass flow rate of 0.8 lb/s and the other delivering cold water at a mass flow rate of 1.2 lb/s. Water exits through a single exit pipe at a mass flow rate of 2.5 lb/s. Determine the amount of water, in lb, in the tank after one hour.

A 380-L tank contains steam, initially at \(400^{\circ} \mathrm{C}\), 3 bar. A valve is opened, and steam flows out of the tank at a constant mass flow rate of 0.005 kg/s. During steam removal, a heater maintains the temperature within the tank constant. Determine the time, in s, at which 75% of the initial mass remains in the tank; also determine the specific volume, in \(100 \mathrm{m}^{3} / \mathrm{kg}\), and pressure, in bar, in the tank at that time

Data are provided for the crude oil storage tank shown in Fig. P4.10. The tank initially contains \(1000 \mathrm{m}^{3}\) of crude oil. Oil is pumped into the tank through a pipe at a rate of \(2 \mathrm{~m}^{3} / \mathrm{min}\) and out of the tank at a velocity of 1.5 m/s through another pipe having a diameter of 0.15 m. The crude oil has a specific volume of \(0.0015 \mathrm{~m}^{3} / \mathrm{kg}\). Determine (a) the mass of oil in the tank, in kg, after 24 hours, and (b) the volume of oil in the tank, in m3, at that time.

An \(8-\mathrm{ft}^{3}\) tank contains air at an initial temperature of \(80^{\circ} \mathrm{F}\) and initial pressure of \(100 \mathrm{lbf} / \mathrm{in}^{2}\) The tank develops a small hole, and air leaks from the tank at a constant rate of 0.03 lb/s for 90 s until the pressure of the air remaining in the tank is \(30 \mathrm{lbf} / \mathrm{in}^{2}\) Employing the ideal gas model, determine the final temperature, in 8F, of the air remaining in the tank.

Liquid propane enters an initially empty cylindrical storage tank at a mass flow rate of 10 kg/s. Flow continues until the tank is filled with propane at \(20^{\circ} \mathrm{C}\), 9 bar. The tank is 25 m long and has a 4-m diameter. Determine the time, in minutes, to fill the tank.

As shown in Fig. P4.13, river water used to irrigate a field is controlled by a gate. When the gate is raised, water flows steadily with a velocity of 75 ft/s through an opening 8 ft by 3 ft. If the gate is raised for 24 hours, determine the volume of water, in gallons, provided for irrigation. Assume the density of river water is \(62.3 \mathrm{lb} / \mathrm{ft}^{3}\).

Figure P4.14 shows a two-tier fountain operating with basins A and B. Both basins are initially empty. When the fountain is turned on, water flows with a constant mass flow rate of 10 kg/s into basin A. Water overflows from basin A into basin B. Thereafter, water drains from basin B at a rate of \(5 L_{\mathrm{B}}\) kg/s, where \(L_{\mathrm{B}}\) is the height of the water in basin B, in m. Dimensions of the basins are indicated on the figure. Determine the variation of water height in each basin as a function of time. The density of water is constant at \(1000 \mathrm{kg} / \mathrm{m}^{3}.

Liquid water flows isothermally at \(20^{\circ} \mathrm{C}\) through a one-inlet, one-exit duct operating at steady state. The duct’s inlet and exit diameters are 0.02 m and 0.04 m, respectively. At the inlet, the velocity is 40 m/s and pressure is 1 bar. At the exit, determine the mass flow rate, in kg/s, and velocity, in m/s.

Air enters a one-inlet, one-exit control volume at 6 bar, 500 K, and 30 m/s through a flow area of \(28 \mathrm{~cm}^{2}\). At the exit, the pressure is 3 bar, the temperature is 456.5 K, and the velocity is 300 m/s. The air behaves as an ideal gas. For steady-state operation, determine (a) the mass flow rate, in kg/s. (b) the exit flow area, in \(\mathrm{cm}^{2}\).

As shown in Fig. P4.17, air with a volumetric flow rate of \(15,000 \mathrm{ft}^{3} / \mathrm{min}\) enters an air-handling unit at \(35^{\circ} \mathrm{F}\), 1 atm. The air-handling unit delivers air at \(80^{\circ} \mathrm{F}\), 1 atm to a duct system with three branches consisting of two 26-in.-diameter ducts and one 50-in. duct. The velocity in each 26-in. duct is 10 ft/s. Assuming ideal gas behavior for the air, determine at steady state (a) the mass flow rate of air entering the air-handling unit, in lb/s. (b) the volumetric flow rate in each 26-in. duct, in ft3/min. (c) the velocity in the 50-in. duct, in ft/s.

Refrigerant 134a enters the evaporator of a refrigeration system operating at steady state at \(24^{\circ} \mathrm{C}\) and quality of 20% at a velocity of 7 m/s. At the exit, the refrigerant is a saturated vapor at a temperature of \(24^{\circ} \mathrm{C}\). The evaporator flow channel has constant diameter. If the mass flow rate of the entering refrigerant is 0.1 kg/s, determine (a) the diameter of the evaporator flow channel, in cm. (b) the velocity at the exit, in m/s.

As shown in Fig. P4.19, steam at 80 bar, \(440^{\circ} \mathrm{C}\), enters a turbine operating at steady state with a volumetric flow rate of \(236 \mathrm{~m}^{3} / \mathrm{min}\). Twenty percent of the entering mass flow exits through a diameter of 0.25 m at 60 bar, \(400^{\circ} \mathrm{C}\). The rest exits through a diameter of 1.5 m with a pressure of 0.7 bar and a quality of 90%. Determine the velocity at each exit duct, in m/s.

Figure P4.20 provides steady-state data for water vapor flowing through a piping configuration. At each exit, the volumetric flow rate, pressure, and temperature are equal. Determine the mass flow rate at the inlet and exits, each in kg/s.

Air enters a compressor operating at steady state with a pressure of \(14.7 \mathrm{lbf} / \text { in. }^{2}\) and a volumetric flow rate of 8 ft3/s. The air velocity in the exit pipe is 225 ft/s and the exit pressure is \(150 \mathrm{lbf} / \mathrm{in}^{2}\) If each unit mass of air passing from inlet to exit undergoes a process described by \(p v^{1.3}=\) constant, determine the diameter of the exit pipe, in inches.

Ammonia enters a control volume operating at steady state at \(p_{1}=16 \text { bar, } T_{1}=32^{\circ} \mathrm{C}\), with a mass flow rate of 1.5 kg/s. Saturated vapor at 6 bar leaves through one exit and saturated liquid at 6 bar leaves through a second exit with a volumetric flow rate of \(0.10 \mathrm{~m}^{3} / \mathrm{min}\). Determine (a) the minimum diameter of the inlet pipe, in cm, so the ammonia velocity at the inlet does not exceed 18 m/s. (b) the volumetric flow rate of the exiting saturated vapor, in \(0.10 \mathrm{~m}^{3} / \mathrm{min}\).

Figure P4.23 provides steady-state data for air flowing through a rectangular duct. Assuming ideal gas behavior for the air, determine the inlet volumetric flow rate, in ft3/s, and inlet mass flow rate, in kg/s. If you can determine the volumetric flow rate and mass flow rate at the exit, evaluate them. If not, explain.

Refrigerant 134a enters a horizontal pipe operating at steady state at \(40^{\circ} \mathrm{C}\), 300 kPa, and a velocity of 40 m/s. At the exit, the temperature is \(50^{\circ} \mathrm{C}\) and the pressure is 240 kPa. The pipe diameter is 0.04 m. Determine (a) the mass flow rate of the refrigerant, in kg/s, (b) the velocity at the exit, in m/s, and (c) the rate of heat transfer between the pipe and its surroundings, in kW.

As shown in Fig. P4.25, air enters a pipe at \(25^{\circ} \mathrm{C}\), 100 kPa with a volumetric flow rate of \(23 \mathrm{~m}^{3} / \mathrm{h}\). On the outer pipe surface is an electrical resistor covered with insulation. With a voltage of 120 V, the resistor draws a current of 4 amps. Assuming the ideal gas model with \(c_{p}=1.005 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\) for air and ignoring kinetic and potential energy effects, determine (a) the mass flow rate of the air, in kg/h, and (b) the temperature of the air at the exit, in \({ }^{\circ} \mathrm{C}\).

Air enters a horizontal, constant-diameter heating duct operating at steady state at 290 K, 1 bar, with a volumetric flow rate of \(0.25 \mathrm{~m}^{3} / \mathrm{s}\), and exits at 325 K, 0.95 bar. The flow area is \(0.04 \mathrm{~m}^{2}\). Assuming the ideal gas model with k = 1.4 for the air, determine (a) the mass flow rate, in kg/s, (b) the velocity at the inlet and exit, each in m/s, and (c) the rate of heat transfer, in kW.

Air at 600 kPa, 330 K enters a well-insulated, horizontal pipe having a diameter of 1.2 cm and exits at 120 kPa, 300 K. Applying the ideal gas model for air, determine at steady state (a) the inlet and exit velocities, each in m/s, and (b) the mass flow rate, in kg/s.

At steady state, air at 200 kPa, 325 K, and mass flow rate of 0.5 kg/s enters an insulated duct having differing inlet and exit cross-sectional areas. The inlet cross-sectional area is \(6 \mathrm{cm}^{2}\). At the duct exit, the pressure of the air is 100 kPa and the velocity is 250 m/s. Neglecting potential energy effects and modeling air as an ideal gas with constant \(c_{p}=1.008 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\), determine (a) the velocity of the air at the inlet, in m/s. (b) the temperature of the air at the exit, in K. (c) the exit cross-sectional area, in \(\mathrm{cm}^{2}\).

Refrigerant 134a flows at steady state through a horizontal tube having an inside diameter of 0.05 m. The refrigerant enters the tube with a quality of 0.1, temperature of \(36^{\circ} \mathrm{C}\), and velocity of 10 m/s. The refrigerant exits the tube at 9 bar as a saturated liquid. Determine (a) the mass flow rate of the refrigerant, in kg/s. (b) the velocity of the refrigerant at the exit, in m/s. (c) the rate of heat transfer, in kW, and its associated direction with respect to the refrigerant.

As shown in Fig. P4.30, electronic components mounted on a flat plate are cooled by convection to the surroundings and by liquid water circulating through a U-tube bonded to the plate. At steady state, water enters the tube at \(20^{\circ} \mathrm{C}\) and a velocity of 0.4 m/s and exits at \(24^{\circ} \mathrm{C}\) with a negligible change in pressure. The electrical components receive 0.5 kW of electrical power. The rate of energy transfer by convection from the plate-mounted electronics is estimated to be 0.08 kW. Kinetic and potential energy effects can be ignored. Determine the tube diameter, in cm.

Steam enters a nozzle operating at steady state at 20 bar, \(280^{\circ} \mathrm{C}\), with a velocity of 80 m/s. The exit pressure and temperature are 7 bar and \(180^{\circ} \mathrm{C}\), respectively. The mass flow rate is 1.5 kg/s. Neglecting heat transfer and potential energy, determine (a) the exit velocity, in m/s. (b) the inlet and exit flow areas, in \(\mathrm{cm}^{2}\).

Refrigerant 134a enters a well-insulated nozzle at \(200 \mathrm{lbf} / \mathrm{in}^{2}\), \(220^{\circ} \mathrm{F}\), with a velocity of 120 ft/s and exits at \(20 \mathrm{lbf} / \mathrm{in}^{2}\) with a velocity of 1500 ft/s. For steady-state operation, and neglecting potential energy effects, determine the exit temperature, in \({ }^{\circ} \mathrm{F}\).

Air enters a nozzle operating at steady state at \(720^{\circ} \mathrm{R}\) with negligible velocity and exits the nozzle at \(500^{\circ} \mathrm{R}\) with a velocity of 1450 ft/s. Assuming ideal gas behavior and neglecting potential energy effects, determine the heat transfer in Btu per lb of air flowing.

Air with a mass flow rate of 2.3 kg/s enters a horizontal nozzle operating at steady state at 450 K, 350 kPa, and velocity of 3 m/s. At the exit, the temperature is 300 K and the velocity is 460 m/s. Using the ideal gas model for air with constant \(c_{p}=1.011 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\), determine (a) the area at the inlet, in \(\mathrm{m}^{2}\). (b) the heat transfer between the nozzle at its surroundings, in kW. Specify whether the heat transfer is to or from the air.

Helium gas flows through a well-insulated nozzle at steady state. The temperature and velocity at the inlet are \(550^{\circ} \mathrm{R}\) and 150 ft/s, respectively. At the exit, the temperature is \(400^{\circ} \mathrm{R}\) and the pressure is \(40 \mathrm{lbf} / \mathrm{in}^{2}\) The area of the exit is \(0.0085 \mathrm{ft}^{2}\). Using the ideal gas model with k = 1.67, and neglecting potential energy effects, determine the mass flow rate, in lb/s, through the nozzle.

Nitrogen, modeled as an ideal gas, flows at a rate of 3 kg/s through a well-insulated horizontal nozzle operating at steady state. The nitrogen enters the nozzle with a velocity of 20 m/s at 340 K, 400 kPa and exits the nozzle at 100 kPa. To achieve an exit velocity of 478.8 m/s, determine (a) the exit temperature, in K. (b) the exit area, in \(\mathrm{m}^{2}\).

As shown in Fig. P4.37, air enters the diffuser of a jet engine operating at steady state at 18 kPa, 216 K and a velocity of 265 m/s, all data corresponding to high-altitude flight. The air flows adiabatically through the diffuser and achieves a temperature of 250 K at the diffuser exit. Using the ideal gas model for air, determine the velocity of the air at the diffuser exit, in m/s.

Air enters a diffuser operating at steady state at \(540^{\circ} \mathrm{R}\), \(15 \mathrm{lbf} / \mathrm{in}^{2}\), with a velocity of 600 ft/s, and exits with a velocity of 60 ft/s. The ratio of the exit area to the inlet area is 8. Assuming the ideal gas model for the air and ignoring heat transfer, determine the temperature, in \({ }^{\circ} \mathrm{R}\), and pressure, in \(\mathrm{lbf} / \mathrm{in}^{2}\), at the exit.

Refrigerant 134a enters an insulated diffuser as a saturated vapor at \(80^{\circ} \mathrm{F}\) with a velocity of 1453.4 ft/s. At the exit, the temperature is \(280^{\circ} \mathrm{F}\) and the velocity is negligible. The diffuser operates at steady state and potential energy effects can be neglected. Determine the exit pressure, in \(\mathrm{lbf} / \mathrm{in}^{2}\)

Oxygen gas enters a well-insulated diffuser at \(30 \mathrm{lbf} / \mathrm{in}^{2}\), \(440^{\circ} \mathrm{R}\), with a velocity of 950 ft/s through a flow area of \(2.0 \mathrm{in}^{2}\) At the exit, the flow area is 15 times the inlet area, and the velocity is 25 ft/s. The potential energy change from inlet to exit is negligible. Assuming ideal gas behavior for the oxygen and steady-state operation of the diffuser, determine the exit temperature, in \({ }^{\circ} \mathrm{R}\), the exit pressure, in \(\mathrm{lbf} / \mathrm{in}^{2}\), and the mass flow rate, in lb/s.

Air modeled as an ideal gas enters a well-insulated diffuser operating at steady state at 270 K with a velocity of 180 m/s and exits with a velocity of 48.4 m/s. For negligible potential energy effects, determine the exit temperature, in K.

Steam enters a well-insulated turbine operating at steady state at 4 MPa with a specific enthalpy of 3015.4 kJ/kg and a velocity of 10 m/s. The steam expands to the turbine exit where the pressure is 0.07 MPa, specific enthalpy is 2431.7 kJ/kg, and the velocity is 90 m/s. The mass flow rate is 11.95 kg/s. Neglecting potential energy effects, determine the power developed by the turbine, in kW.

Air expands through a turbine from 8 bar, 960 K to 1 bar, 450 K. The inlet velocity is small compared to the exit velocity of 90 m/s. The turbine operates at steady state and develops a power output of 2500 kW. Heat transfer between the turbine and its surroundings and potential energy effects are negligible. Modeling air as an ideal gas, calculate the mass flow rate of air, in kg/s, and the exit area, in \(m^{2}\).

Air expands through a turbine operating at steady state. At the inlet,\(p_{1}=150 \mathrm{lbf} / \mathrm{in}^{2}, T_{1}=1400^{\circ} \mathrm{R}\), and at the exit, \(p_{2}=14.8 \mathrm{lbf} / \mathrm{in.}^{2}, T_{2}=700^{\circ} \mathrm{R}\). The mass flow rate of air entering the turbine is 11 lb/s, and 65,000 Btu/h of energy is rejected by heat transfer. Neglecting kinetic and potential energy effects, determine the power developed, in hp.

Steam enters a turbine operating at steady state at \(700^{\circ} \mathrm{F}\) and \(450 \mathrm{lbf} / \mathrm{in}^{2}\) and leaves as a saturated vapor at \(1.2 \mathrm{lbf} / \mathrm{in}^{2}\) The turbine develops 12,000 hp, and heat transfer from the turbine to the surroundings occurs at a rate of \(2 \times 10^{6} \mathrm{Btu} / \mathrm{h}\). Neglecting kinetic and potential energy changes from inlet to exit, determine the volumetric flow rate of the steam at the inlet, in \(\mathrm{ft}^{3} / \mathrm{s}\).

A well-insulated turbine operating at steady state develops 28.75 MW of power for a steam flow rate of 50 kg/s. The steam enters at 25 bar with a velocity of 61 m/s and exits as saturated vapor at 0.06 bar with a velocity of 130 m/s. Neglecting potential energy effects, determine the inlet temperature, in \({ }^{\circ} \mathrm{C}\).

Steam enters a turbine operating at steady state with a mass flow of 10 kg/min, a specific enthalpy of 3100 kJ/kg, and a velocity of 30 m/s. At the exit, the specific enthalpy is 2300 kJ/kg and the velocity is 45 m/s. The elevation of the inlet is 3 m higher than at the exit. Heat transfer from the turbine to its surroundings occurs at a rate of 1.1 kJ per kg of steam flowing. Let \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\). Determine the power developed by the turbine, in kW.

Steam enters a turbine operating at steady state at 2 MPa, \(360^{\circ} \mathrm{C}\) with a velocity of 100 m/s. Saturated vapor exits at 0.1 MPa and a velocity of 50 m/s. The elevation of the inlet is 3 m higher than at the exit. The mass flow rate of the steam is 15 kg/s, and the power developed is 7 MW. Let \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\). Determine (a) the area at the inlet, in \(\mathrm{m}^{2}\), and (b) the rate of heat transfer between the turbine and its surroundings, in kW.

Water vapor enters a turbine operating at steady state at 5008C, 40 bar, with a velocity of 200 m/s, and expands adiabatically to the exit, where it is saturated vapor at 0.8 bar, with a velocity of 150 m/s and a volumetric flow rate of \(9.48 \mathrm{~m}^{3} / \mathrm{s}\). The power developed by the turbine, in kW, is approximately (a) 3500, (b) 3540, (c) 3580, (d) 7470.

Steam enters the first-stage turbine shown in Fig. P4.50 at 40 bar and \(500^{\circ} \mathrm{C}\) with a volumetric flow rate of \(90 \mathrm{~m}^{3} / \mathrm{min}\). Steam exits the turbine at 20 bar and \(400^{\circ} \mathrm{C}\). The steam is then reheated at constant pressure to \(500^{\circ} \mathrm{C}\) before entering the second-stage turbine. Steam leaves the second stage as saturated vapor at 0.6 bar. For operation at steady state, and ignoring stray heat transfer and kinetic and potential energy effects, determine the (a) mass flow rate of the steam, in kg/h. (b) total power produced by the two stages of the turbine, in kW. (c) rate of heat transfer to the steam flowing through the reheater, in kW.

Steam at \(1800 \mathrm{lbf} / \mathrm{in} .^{2}\) and \(1100^{\circ} \mathrm{F}\) enters a turbine operating at steady state. As shown in Fig. P4.51, 20% of the entering mass flow is extracted at \(600 \mathrm{lbf} / \text { in. }^{2} \text { and } 500^{\circ} \mathrm{F}\). The rest of the steam exits as a saturated vapor at \(1 \mathrm{lbf} / \mathrm{in}^{2}\) The turbine develops a power output of \(6.8 \times 10^{6} \mathrm{Btu} / \mathrm{h}\). Heat transfer from the turbine to the surroundings occurs at a rate of \(5 \times 10^{4} \mathrm{Btu} / \mathrm{h}\). Neglecting kinetic and potential energy effects, determine the mass flow rate of the steam entering the turbine, in lb/s.

Hot combustion gases, modeled as air behaving as an ideal gas, enter a turbine at \(145 \mathrm{lbf} / \mathrm{in}^{2}\), \(2700^{\circ} \mathrm{R}\) with a mass flow rate of 0.22 lb/s and exit at \(29 \mathrm{lbf} / \mathrm{in}^{2}\) and \(1620^{\circ} \mathrm{R}\). If heat transfer from the turbine to its surroundings occurs at a rate of 14 Btu/s, determine the power output of the turbine, in hp.

Air enters a compressor operating at steady state at 1.05 bar, 300 K, with a volumetric flow rate of \(12 \mathrm{~m}^{3} / \mathrm{min}\) and exits at 12 bar, 400 K. Heat transfer occurs at a rate of 2 kW from the compressor to its surroundings. Assuming the ideal gas model for air and neglecting kinetic and potential energy effects, determine the power input, in kW.

Nitrogen is compressed in an axial-flow compressor operating at steady state from a pressure of \(15 \mathrm{lbf} / \mathrm{in}^{2}\) and a temperature of \(50^{\circ} \mathrm{F}\) to a pressure \(60 \mathrm{lbf} / \mathrm{in}^{2}\) The gas enters the compressor through a 6-in.-diameter duct with a velocity of 30 ft/s and exits at \(198^{\circ} \mathrm{F}\) with a velocity of 80 ft/s. Using the ideal gas model, and neglecting stray heat transfer and potential energy effects, determine the compressor power input, in hp.

Refrigerant 134a enters a compressor operating at steady state as saturated vapor at 0.12 MPa and exits at 1.2 MPa and \(70^{\circ} \mathrm{C}\) at a mass flow rate of 0.108 kg/s. As the refrigerant passes through the compressor, heat transfer to the surroundings occurs at a rate of 0.32 kJ/s. Determine at steady state the power input to the compressor, in kW.

Carbon dioxide gas is compressed at steady state from a pressure of \(20 \mathrm{lbf} / \mathrm{in}^{2}\) and a temperature of \(32^{\circ} \mathrm{F}\) to a pressure of \(50 \mathrm{lbf} / \mathrm{in} .^{2}\) and a temperature of \(120^{\circ} \mathrm{F}\). The gas enters the compressor with a velocity of 30 ft/s and exits with a velocity of 80 ft/s. The mass flow rate is 0.98 lb/s. The magnitude of the heat transfer rate from the compressor to its surroundings is 5% of the compressor power input. Using the ideal gas model with \(c_{p}=0.21 \mathrm{Btu} / \mathrm{lb} \cdot{ }^{\circ} \mathrm{R}\) and neglecting potential energy effects, determine the compressor power input, in horsepower.

At steady state, a well-insulated compressor takes in nitrogen at \(60^{\circ} \mathrm{F}, 14.2 \mathrm{lbf} / \mathrm{in}^{2}\), with a volumetric flow rate of \(1200 \mathrm{ft}^{3} / \mathrm{min}\). Compressed nitrogen exits at \(500^{\circ} \mathrm{F}, 120 \mathrm{lbf} / \mathrm{in} .^{2}\) Kinetic and potential energy changes from inlet to exit can be neglected. Determine the compressor power, in hp, and the volumetric flow rate at the exit, in \(\mathrm{ft}^{3} / \mathrm{min}\).

Air enters a compressor operating at steady state with a pressure of \(14.7 \mathrm{lbf} / \mathrm{in.}^{2}\), a temperature of 808F, and a volumetric flow rate of \(18 \mathrm{ft}^{3} / \mathrm{s}\). The air exits the compressor at a pressure of \(90 \mathrm{lbf} / \mathrm{in.}^{2}\) Heat transfer from the compressor to its surroundings occurs at a rate of 9.7 Btu per lb of air flowing. The compressor power input is 90 hp. Neglecting kinetic and potential energy effects and modeling air as an ideal gas, determine the exit temperature, in \({ }^{\circ} \mathrm{F}\).

Refrigerant 134a enters an air conditioner compressor at 4 bar, \(20^{\circ} \mathrm{C}\), and is compressed at steady state to 12 bar, \(80^{\circ} \mathrm{C}\). The volumetric flow rate of the refrigerant entering is \(4 \mathrm{~m}^{3} / \mathrm{min}\). The work input to the compressor is 60 kJ per kg of refrigerant flowing. Neglecting kinetic and potential energy effects, determine the heat transfer rate, in kW.

Refrigerant 134a enters an insulated compressor operating at steady state as saturated vapor at \(-20^{\circ} \mathrm{C}\) with a mass flow rate of 1.2 kg/s. Refrigerant exits at 7 bar, \(70^{\circ} \mathrm{C}\). Changes in kinetic and potential energy from inlet to exit can be ignored. Determine (a) the volumetric flow rates at the inlet and exit, each in \(\mathrm{m}^{3} / \mathrm{s}\), and (b) the power input to the compressor, in kW.

Refrigerant 134a enters a water-jacketed compressor operating at steady state at \(210^{\circ} \mathrm{C}\), 1.4 bar, with a mass flow rate of 4.2 kg/s, and exits at \(50^{\circ} \mathrm{C}\), 12 bar. The compressor power required is 150 kW. Neglecting kinetic and potential energy effects, determine the rate of heat transfer to the cooling water circulating through the water jacket.

Air, modeled as an ideal gas, is compressed at steady state from 1 bar, 300 K, to 5 bar, 500 K, with 150 kW of power input. Heat transfer occurs at a rate of 20 kW from the air to cooling water circulating in a water jacket enclosing the compressor. Neglecting kinetic and potential energy effects, determine the mass flow rate of the air, in kg/s.

Air enters a compressor operating at steady state with a pressure of \(14.7 \mathrm{lbf} / \mathrm{in}^{2}\) and a temperature of \(70^{\circ} \mathrm{F}\). The volumetric flow rate at the inlet is \(16.6 \mathrm{ft}^{3} / \mathrm{s}\), and the flow area is \(0.26 \mathrm{ft}^{2}\). At the exit, the pressure is \(35 \text { lbf/in. }{ }^{2}\), the temperature is \(280^{\circ} \mathrm{F}\), and the velocity is 50 ft/s. Heat transfer from the compressor to its surroundings is 1.0 Btu per lb of air flowing. Potential energy effects are negligible, and the ideal gas model can be assumed for the air. Determine (a) the velocity of the air at the inlet, in ft/s, (b) the mass flow rate, in lb/s, and (c) the compressor power, in Btu/s and hp.

Air enters a compressor operating at steady state at \(14.7 \mathrm{lbf} / \mathrm{in}^{2}\) and \(60^{\circ} \mathrm{F}\) and is compressed to a pressure of \(150 \mathrm{lbf} / \mathrm{in}^{2}\) As the air passes through the compressor, it is cooled at a rate of 10 Btu per lb of air flowing by water circulated through the compressor casing. The volumetric flow rate of the air at the inlet is \(5000 \mathrm{ft}^{3} / \mathrm{min}\), and the power input to the compressor is 700 hp. The air behaves as an ideal gas, there is no stray heat transfer, and kinetic and potential effects are negligible. Determine (a) the mass flow rate of the air, lb/s, and (b) the temperature of the air at the compressor exit, in \({ }^{\circ} \mathrm{F}\).

As shown in Fig. P4.65, a pump operating at steady state draws water from a pond and delivers it though a pipe whose exit is 90 ft above the inlet. At the exit, the mass flow rate is 10 lb/s. There is no significant change in water temperature, pressure, or kinetic energy from inlet to exit. If the power required by the pump is 1.68 hp, determine the rate of heat transfer between the pump and its surroundings, in hp and Btu/min. Let \(g=32.0 \mathrm{ft} / \mathrm{s}^{2}\).

Figure P4.66 provides steady-state operating data for a pump drawing water from a reservoir and delivering it at a pressure of 3 bar to a storage tank perched above the reservoir. The mass flow rate of the water is 1.5 kg/s. The water temperature remains nearly constant at \(15^{\circ} \mathrm{C}\), there is no significant change in kinetic energy from inlet to exit, and heat transfer between the pump and its surroundings is negligible. Determine the power required by the pump, in kW. Let \(g=9.81 \mathrm{m} / \mathrm{s}^{2}\).

Figure P4.67 provides steady-state operating data for a submerged pump and an attached delivery pipe. At the inlet, the volumetric flow rate is \(0.75 \mathrm{~m}^{3} / \mathrm{min}\) and the temperature is \(15^{\circ} \mathrm{C}\). At the exit, the pressure is 1 atm. There is no significant change in water temperature or kinetic energy from inlet to exit. Heat transfer between the pump and its surroundings is negligible. Determine the power required by the pump, in kW. Let \(g=9.81 \mathrm{m} / \mathrm{s}^{2}\).

As shown in Fig. P4.68, a power washer used to clean the siding of a house has water entering through a hose at (20 ^{\circ} \mathrm{C}\), 1 atm and a velocity of 0.2 m/s. A jet of water exits with a velocity of 20 m/s at an average elevation of 5 m with no significant change in temperature or pressure. At steady state, the magnitude of the heat transfer rate from the power washer to the surroundings is 10% of the electrical power input. Evaluating electricity at 8 cents per \(\mathrm{kW} \cdot \mathrm{h}\), determine the cost of the power required, in cents per liter of water delivered. Compare with the cost of water, assuming 0.05 cent per liter, and comment.

During cardiac surgery, a heart-lung machine achieves extracorporeal circulation of the patient’s blood using a pump operating at steady state. Blood enters the well-insulated pump at a rate of 5 liters/min. The temperature change of the blood is negligible as it flows through the pump. The pump requires 20 W of power input. Modeling the blood as an incompressible substance with negligible kinetic and potential energy effects, determine the pressure change, in kPa, of the blood as it flows through the pump.

A pump is used to circulate hot water in a home heating system. Water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. The inlet pressure and temperature are \(14.7 \mathrm{lbf} / \mathrm{in}{ }^{2} \text {, and } 180^{\circ} \mathrm{F}\), respectively; at the exit the pressure is \(120 \mathrm{lbf} / \mathrm{in} .^{2}\) The pump requires 1/35 hp of power input. Water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of \(1 \mathrm{Btu} / \mathrm{lb} \cdot{ }^{\circ} \mathrm{R}\). Neglecting kinetic and potential energy effects, determine the temperature change, in \({ }^{\circ} R\), as the water flows through the pump. Comment on this change.

Refrigerant 134a at a flow rate of 0.5 lb/s enters a heat exchanger in a refrigeration system operating at steady state as saturated liquid at \(0^{\circ} \mathrm{F}\) and exits at \(20^{\circ} \mathrm{F}\) at a pressure of \(20 \mathrm{lbf} / \mathrm{in}^{2}\) A separate air stream passes in counterflow to the Refrigerant 134a stream, entering at \(120^{\circ} \mathrm{F}\) and exiting at \(77^{\circ} \mathrm{F}\). The outside of the heat exchanger is well insulated. Neglecting kinetic and potential energy effects and modeling the air as an ideal gas, determine the mass flow rate of air, in lb/s.

Oil enters a counterflow heat exchanger at 450 K with a mass flow rate of 10 kg/s and exits at 350 K. A separate stream of liquid water enters at \(20^{\circ} \mathrm{C}\), 5 bar. Each stream experiences no significant change in pressure. Stray heat transfer with the surroundings of the heat exchanger and kinetic and potential energy effects can be ignored. The specific heat of the oil is constant, \(c=2 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\). If the designer wants to ensure no water vapor is present in the exiting water stream, what is the allowed range of mass flow rates for the water, in kg/s?

As shown in Fig. P4.73, Refrigerant 134a enters a condenser operating at steady state at \970 \mathrm{lbf} / \mathrm{in.}^{2}, 160^{\circ} \mathrm{F}\) and is condensed to saturated liquid at \(60 \mathrm{lbf} / \mathrm{in}^{2}\) on the outside of tubes through which cooling water flows. In passing through the tubes, the cooling water increases in temperature by \(20^{\circ} \mathrm{F}\) and experiences no significant pressure drop. Cooling water can be modeled as incompressible with \(v=0.0161 \mathrm{ft}^{3} / \mathrm{lb} \text { and } c=1 \mathrm{Btu} / \mathrm{lb} \cdot{ }^{\circ} \mathrm{R}\). The mass flow rate of the refrigerant is 3100 lb/h. Neglecting kinetic and potential energy effects and ignoring heat transfer from the outside of the condenser, determine (a) the volumetric flow rate of the entering cooling water, in gal/min. (b) the rate of heat transfer, in Btu/h, to the cooling water from the condensing refrigerant.

Steam at a pressure of 0.08 bar and a quality of 93.2% enters a shell-and-tube heat exchanger where it condenses on the outside of tubes through which cooling water flows, exiting as saturated liquid at 0.08 bar. The mass flow rate of the condensing steam is \(3.4 \times 10^{5} \mathrm{~kg} / \mathrm{h}\). Cooling water enters the tubes at \(15^{\circ} \mathrm{C}\) and exits at \(35^{\circ} \mathrm{C}\) with negligible change in pressure. Neglecting stray heat transfer and ignoring kinetic and potential energy effects, determine the mass flow rate of the cooling water, in kg/h, for steady-state operation.

An air-conditioning system is shown in Fig. P4.75 in which air flows over tubes carrying Refrigerant 134a. Air enters with a volumetric flow rate of \(50 \mathrm{~m}^{3} / \mathrm{min} \text { at } 32^{\circ} \mathrm{C}\), 1 bar, and exits at \(22^{\circ} \mathrm{C}\), 0.95 bar. Refrigerant enters the tubes at 5 bar with a quality of 20% and exits at 5 bar, \(20^{\circ} \mathrm{C}\). Ignoring heat transfer at the outer surface of the air conditioner, and neglecting kinetic and potential energy effects, determine at steady state (a) the mass flow rate of the refrigerant, in kg/min. (b) the rate of heat transfer, in kJ/min, between the air and refrigerant.

Steam enters a heat exchanger operating at steady state at 250 kPa and a quality of 90% and exits as saturated liquid at the same pressure. A separate stream of oil with a mass flow rate of 29 kg/s enters at \(20^{\circ} \mathrm{C}\) and exits at \(100^{\circ} \mathrm{C}\) with no significant change in pressure. The specific heat of the oil is \(c=2.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\). Kinetic and potential energy effects are negligible. If heat transfer from the heat exchanger to its surroundings is 10% of the energy required to increase the temperature of the oil, determine the steam mass flow rate, in kg/s.

Refrigerant 134a enters a heat exchanger at \(-12^{\circ} \mathrm{C}\) and a quality of 42% and exits as saturated vapor at the same temperature with a volumetric flow rate of \(0.85 \mathrm{~m}^{3} / \mathrm{min}\). A separate stream of air enters at \(22^{\circ} \mathrm{C}\) with a mass flow rate of 188 kg/min and exits at \(17^{\circ} \mathrm{C}\). Assuming the ideal gas model for air and ignoring kinetic and potential energy effects, determine (a) the mass flow rate of the Refrigerant 134a, in kg/min, and (b) the heat transfer between the heat exchanger and its surroundings, in kJ/min.

As sketched in Fig. P4.78, a condenser using river water to condense steam with a mass flow rate of \(2 \times 10^{5} \mathrm{~kg} / \mathrm{h}\) from saturated vapor to saturated liquid at a pressure of 0.1 bar is proposed for an industrial plant. Measurements indicate that several hundred meters upstream of the plant, the river has a volumetric flow rate of \(2 \times 10^{5} \mathrm{~m}^{3} / \mathrm{h}\) and a temperature of \(15^{\circ} \mathrm{C}\). For operation at steady state and ignoring changes in kinetic and potential energy, determine the river-water temperature rise, in \({ }^{\circ} \mathrm{C}\), downstream of the plant traceable to use of such a condenser, and comment.

Figure P4.79 shows a solar collector panel embedded in a roof. The panel, which has a surface area of \(24 \mathrm{ft}^{2}\), receives energy from the sun at a rate of \(200 \mathrm{Btu} / \mathrm{h} \text { per } \mathrm{ft}^{2}\) of collector surface. Twenty-five percent of the incoming energy is lost to the surroundings. The remaining energy is used to heat domestic hot water from 90 to \(120^{\circ} \mathrm{F}\). The water passes through the solar collector with a negligible pressure drop. Neglecting kinetic and potential effects, determine at steady state how many gallons of water at \(120^{\circ} \mathrm{F}\) the collector generates per hour.

Steam enters a counterflow heat exchanger operating at steady state at 0.07 MPa with a specific enthalpy of 2431.6 kJ/kg and exits at the same pressure as saturated liquid. The steam mass flow rate is 1.5 kg/min. A separate stream of air with a mass flow rate of 100 kg/min enters at \(30^{\circ} \mathrm{C}\) and exits at \(60^{\circ} \mathrm{C}\). The ideal gas model with \(c_{p}=1.005 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\) can be assumed for air. Kinetic and potential energy effects are negligible. Determine (a) the quality of the entering steam and (b) the rate of heat transfer between the heat exchanger and its surroundings, in kW.

Figure P4.81 provides steady-state operating data for a parallel flow heat exchanger in which there are separate streams of air and water. Each stream experiences no significant change in pressure. Stray heat transfer with the surroundings of the heat exchanger and kinetic and potential energy effects can be ignored. The ideal gas model applies to the air. If each stream exits at the same temperature, determine the value of that temperature, in K.

Figure P4.82 provides steady-state operating data for a parallel flow heat exchanger in which there are separate streams of air and carbon dioxide (\(CO_{2}\)). Stray heat transfer with the surroundings of the heat exchanger and kinetic and potential energy effects can be ignored. The ideal gas model applies to each gas. A constraint on heat exchanger size requires the temperature of the exiting air to be 20 degrees greater than the temperature of the exiting \(CO_{2}\). Determine the exit temperature of each stream, in \({ }^{\circ} \mathrm{R}\).

An open feedwater heater operates at steady state with liquid water entering inlet 1 at 10 bar, \(50^{\circ} \mathrm{C}\), and a mass flow rate of 60 kg/s. A separate stream of steam enters inlet 2 at 10 bar and \(200^{\circ} \mathrm{C}\). Saturated liquid at 10 bar exits the feedwater heater at exit 3. Ignoring heat transfer with the surroundings and neglecting kinetic and potential energy effects, determine the mass flow rate, in kg/s, of the steam at inlet 2.

Figure P4.84 provides steady-state data for the ducting ahead of the chiller coils in an air-conditioning system. Outside air at \(90^{\circ} \mathrm{F}\) is mixed with return air at \(75^{\circ} \mathrm{F}\). Stray heat transfer is negligible, kinetic and potential energy effects can be ignored, and the pressure throughout is 1 atm. Modeling the air as an ideal gas with \(c_{p}=0.24 \mathrm{Btu} / \mathrm{lb} \cdot{ }^{\circ} \mathrm{R}\), determine (a) the mixed-air temperature, in 8F, and (b) the diameter of the mixed-air duct, in ft.

For the desuperheater shown in Fig. P4.85, liquid water at state 1 is injected into a stream of superheated vapor entering at state 2. As a result, saturated vapor exits at state 3. Data for steady state operation are shown on the figure. Ignoring stray heat transfer and kinetic and potential energy effects, determine the mass flow rate of the incoming superheated vapor, in kg/min.

Three return steam lines in a chemical processing plant enter a collection tank operating at steady state at 1 bar. Steam enters inlet 1 with flow rate of 0.8 kg/s and quality of 0.9. Steam enters inlet 2 with flow rate of 2 kg/s at \(200^{\circ} \mathrm{C}\). Steam enters inlet 3 with flow rate of 1.2 kg/s at \(95^{\circ} \mathrm{C}\). Steam exits the tank at 1 bar. The rate of heat transfer from the collection tank is 40 kW. Neglecting kinetic and potential energy effects, determine for the steam exiting the tank (a) the mass flow rate, in kg/s. (b) the temperature, in \({ }^{\circ} \mathrm{C}\).

A well-insulated tank in a vapor power plant operates at steady state. Water enters at inlet 1 at a rate of 125 lb/s at \(14.7 \mathrm{lbf} / \mathrm{in}^{2}\) Make-up water to replenish steam losses from the plant enters at inlet 2 at a rate of 10 lb/s at \(14.7 \mathrm{lbf} / \mathrm{in} .^{2} \text { and } 60^{\circ} \mathrm{F}\). Water exits the tank at 14.7 lbf/in.2 Neglecting kinetic and potential energy effects, determine for the water exiting the tank (a) the mass flow rate, in lb/s. (b) the specific enthalpy, in Btu/lb. (c) the temperature, in \({ }^{\circ} \mathrm{F}\).

Steam with a quality of 0.7, pressure of 1.5 bar, and flow rate of 10 kg/s enters a steam separator operating at steady state. Saturated vapor at 1.5 bar exits the separator at state 2 at a rate of 6.9 kg/s while saturated liquid at 1.5 bar exits the separator at state 3. Neglecting kinetic and potential energy effects, determine the rate of heat transfer, in kW, and its associated direction.

Ammonia enters the expansion valve of a refrigeration system at a pressure of 10 bar and a temperature of \(24^{\circ} \mathrm{C}\) and exits at 1 bar. If the refrigerant undergoes a throttling process, what is the quality of the refrigerant exiting the expansion valve?

Propane vapor enters a valve at 1.0 MPa, \(60^{\circ} \mathrm{C}\), and leaves at 0.3 MPa. If the propane undergoes a throttling process, what is the temperature of the propane leaving the valve, in \({ }^{\circ} \mathrm{C}\)?

Steam enters a partially open valve operating at steady state as saturated liquid at \(3000^{\circ} \mathrm{F}\) and exits at \(60 \mathrm{lbf} / \mathrm{in}^{2}\) Neglecting kinetic and potential energy effects and any stray heat transfer with the surroundings, determine the temperature, in \({ }^{\circ} \mathrm{F}\), and the quality of the steam exiting the valve.

At steady state, a valve and steam turbine operate in series. The steam flowing through the valve undergoes a throttling process. At the valve inlet, the conditions are \(600 \mathrm{lbf} / \mathrm{in.}^{2}\), \(800^{\circ} \mathrm{F}\). At the valve exit, corresponding to the turbine inlet, the pressure is \(300 \mathrm{lbf} / \mathrm{in.}^{2}\) At the turbine exit, the pressure is \(5 \mathrm{lbf} / \mathrm{in}^{2}\) The work developed by the turbine is 350 Btu per lb of steam flowing. Stray heat transfer and kinetic and potential energy effects can be ignored. Fix the state at the turbine exit: If the state is superheated vapor, determine the temperature, in \({ }^{\circ} \mathrm{F}\). If the state is a two-phase liquid–vapor mixture, determine the quality.

A horizontal constant-diameter pipe with a build-up of debris is shown in Fig. P4.93. Air modeled as an ideal gas enters at 320 K, 900 kPa, with a velocity of 30 m/s and exits at 305 K. Assuming steady state and neglecting stray heat transfer, determine for the air exiting the pipe (a) the velocity, in m/s. (b) the pressure, in kPa.

Liquid water enters a valve at 300 kPa and exits at 275 kPa. As water flows through the valve, the change in its temperature, stray heat transfer with the surroundings, and potential energy effects are negligible. Operation is at steady state. Modeling the water as incompressible with constant \(\rho=1000 \mathrm{~kg} / \mathrm{m}^{3}\), determine the change in kinetic energy per unit mass of water flowing through the valve, in kJ/kg.

Figure P4.95 shows a turbine operating at a steady state that provides power to an air compressor and an electric generator. Air enters the turbine with a mass flow rate of 5.4 kg/s at \(527^{\circ} \mathrm{C}\) and exits the turbine at \(107^{\circ} \mathrm{C}\), 1 bar. The turbine provides power at a rate of 900 kW to the compressor and at a rate of 1400 kW to the generator. Air can be modeled as an ideal gas, and kinetic and potential energy changes are negligible. Determine (a) the volumetric flow rate of the air at the turbine exit, in \(\mathrm{m}^{3} / \mathrm{s}\), and (b) the rate of heat transfer between the turbine and its surroundings, in kW.

Figure P4.96 provides steady-state data for a throttling valve in series with a heat exchanger. Saturated liquid Refrigerant 134a enters the valve at a pressure of 9 bar and is throttled to a pressure of 2 bar. The refrigerant then enters the heat exchanger, exiting at a temperature of \(10^{\circ} \mathrm{C}\) with no significant decrease in pressure. In a separate stream, liquid water at 1 bar enters the heat exchanger at a temperature of \(25^{\circ} \mathrm{C}\) with a mass flow rate of 2 kg/s and exits at 1 bar as liquid at a temperature of \(15^{\circ} \mathrm{C}\). Stray heat transfer and kinetic and potential energy effects can be ignored. Determine (a) the temperature, in \({ }^{\circ} \mathrm{C}\), of the refrigerant at the exit of the valve. (b) the mass flow rate of the refrigerant, in kg/s.

As shown in Fig. P4.97, Refrigerant 22 enters the compressor of an air-conditioning unit operating at steady state at \(40^{\circ} \mathrm{F}, 80 \mathrm{lbf} / \text { in. }^{2}\) and is compressed to \(140^{\circ} \mathrm{F}, 200 \mathrm{lbf} / \mathrm{in} .^{2}\) The refrigerant exiting the compressor enters a condenser where energy transfer to air as a separate stream occurs and the refrigerant exits as a liquid at \(200 \mathrm{lbf} / \mathrm{in} .^{2}, 90^{\circ} \mathrm{F}\). Air enters the condenser at \(80^{\circ} \mathrm{F}, 14.7 \mathrm{lbf} / \mathrm{in} .^{2}\) with a volumetric flow rate of \(750 \mathrm{ft}^{3} / \mathrm{min}\) and exits at 1108F. Neglecting stray heat transfer and kinetic and potential energy effects, and assuming ideal gas behavior for the air, determine (a) the mass flow rate of refrigerant, in lb/min, and (b) the compressor power, in horsepower.

Figure P4.98 shows three components of an air-conditioning system. Refrigerant 134a flows through a throttling valve and a heat exchanger while air flows through a fan and the same heat exchanger. Data for steady-state operation are given on the figure. There is no significant heat transfer between any of the components and the surroundings. Kinetic and potential energy effects are negligible. Modeling air as an ideal gas with constant \(c_{p}=0.240 \mathrm{Btu} / \mathrm{lb} \cdot{ }^{\circ} \mathrm{R}\), determine the mass flow rate of the air, in lb/s.

Figure P4.99 shows a turbine-driven pump that provides water to a mixing chamber located 25 m higher than the pump. Steady-state operating data for the turbine and pump are labeled on the figure. Heat transfer from the water to its surroundings occurs at a rate of 2 kW. For the turbine, heat transfer with the surroundings and potential energy effects are negligible. Kinetic energy effects at all numbered states can be ignored. Determine (a) the power required by the pump, in kW, to supply water to the inlet of the mixing chamber. (b) the mass flow rate of steam, in kg/s, that flows through the turbine.

Separate streams of air and water flow through the compressor and heat exchanger arrangement shown in Fig. P4.100. Steady-state operating data are provided on the figure. Heat transfer with the surroundings can be neglected, as can all kinetic and potential energy effects. The air is modeled as an ideal gas. Determine (a) the total power required by both compressors, in kW. (b) the mass flow rate of the water, in kg/s.

Figure P4.101 shows a pumped-hydro energy storage system delivering water at steady state from a lower reservoir to an upper reservoir using off-peak electricity (see Sec. 4.8.3). Water is delivered to the upper reservoir at a volumetric flow rate of \(150 \mathrm{~m}^{3} / \mathrm{s}\) with an increase in elevation of 20 m. There is no significant change in temperature, pressure, or kinetic energy from inlet to exit. Heat transfer from the pump to its surroundings occurs at a rate of 0.6 MW and \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\). Determine the pump power required, in MW. Assuming the same volumetric flow rate when the system generates on-peak electricity using this water, will the power be greater, less, or the same as the pump power? Explain.

Steady-state operating data for a simple steam power plant are provided in Fig. P4.102. Stray heat transfer and kinetic and potential energy effects can be ignored. Determine the (a) thermal efficiency and (b) the mass flow rate of the cooling water, in kg per kg of steam flowing.

Steady-state operating data are provided for a compressor and heat exchanger in Fig. P4.103. The power input to the compressor is 50 kW. As shown in the figure, nitrogen (\(N_{2}\)) flows through the compressor and heat exchanger with a mass flow rate of 0.25 kg/s. The nitrogen is modeled as an ideal gas. A separate cooling stream of helium, modeled as an ideal gas with k = 1.67, also flows through the heat exchanger. Stray heat transfer and kinetic and potential energy effects are negligible. Determine the mass flow rate of the helium, in kg/s.

Figure P4.104 provides steady-state operating data for a cogeneration system with water vapor at 20 bar, \(360^{\circ} \mathrm{C}\) entering at location 1. Power is developed by the system at a rate of 2.2 MW. Process steam leaves at location 2, and hot water for other process uses leaves at location 3. Evaluate the rate of heat transfer, in MW, between the system and its surroundings. Let \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\).

As shown in Fig. P4.105, hot industrial waste water at 15 bar, \(180^{\circ} \mathrm{C}\) with a mass flow rate of 5 kg/s enters a flash chamber via a valve. Saturated vapor and saturated liquid streams, each at 4 bar, exit the flash chamber. The saturated vapor enters the turbine and expands to 0.08 bar, x = 90%. Stray heat transfer and kinetic and potential energy effects are negligible. For operation at steady state, determine the power, in hp, developed by the turbine.

A simple gas turbine power cycle operating at steady state with air as the working substance is shown in Fig. P4.106. The cycle components include an air compressor mounted on the same shaft as the turbine. The air is heated in the high-pressure heat exchanger before entering the turbine. The air exiting the turbine is cooled in the low-pressure heat exchanger before returning to the compressor. Kinetic and potential effects are negligible. The compressor and turbine are adiabatic. Using the ideal gas model for air, determine the (a) power required for the compressor, in hp, (b) power output of the turbine, in hp, and (c) thermal efficiency of the cycle.

A residential air-conditioning system operates at steady state, as shown in Fig. P4.107. Refrigerant 22 circulates through the components of the system. Property data at key locations are given on the figure. If the evaporator removes energy by heat transfer from the room air at a rate of 600 Btu/min, determine (a) the rate of heat transfer between the compressor and the surroundings, in Btu/min, and (b) the coefficient of performance.

Separate streams of steam and air flow through the turbine and heat exchanger arrangement shown in Fig. P4.108. Steady-state operating data are provided on the figure. Heat transfer with the surroundings can be neglected, as can all kinetic and potential energy effects. Determine (a) \(T_{3}\), in K, and (b) the power output of the second turbine, in kW.

A rigid tank whose volume is 10 L is initially evacuated. A pinhole develops in the wall, and air from the surroundings at 1 bar, \(25^{\circ} \mathrm{C}\) enters until the pressure in the tank becomes 1 bar. No significant heat transfer between the contents of the tank and the surroundings occurs. Assuming the ideal gas model with k = 1.4 for the air, determine (a) the final temperature in the tank, in \({ }^{\circ} \mathrm{C}\), and (b) the amount of air that leaks into the tank, in g.

A tank whose volume is \(0.01 \mathrm{~m}^{3}\) is initially evacuated. A pinhole develops in the wall, and air from the surroundings at \(21^{\circ} \mathrm{C}\), 1 bar enters until the pressure in the tank is 1 bar. If the final temperature of the air in the tank is \(21^{\circ} \mathrm{C}\), determine (a) the final mass in the tank, in g, and (b) the heat transfer between the tank contents and the surroundings, in kJ.

A rigid tank whose volume is \(2 \mathrm{m}^{3}\), initially containing air at 1 bar, 295 K, is connected by a valve to a large vessel holding air at 6 bar, 295 K. The valve is opened only as long as required to fill the tank with air to a pressure of 6 bar and a temperature of 350 K. Assuming the ideal gas model for the air, determine the heat transfer between the tank contents and the surroundings, in kJ.

An insulated, rigid tank whose volume is \(0.5 \mathrm{m}^{3}\) is connected by a valve to a large vessel holding steam at 40 bar, \(500^{\circ} \mathrm{C}\). The tank is initially evacuated. The valve is opened only as long as required to fill the tank with steam to a pressure of 20 bar. Determine the final temperature of the steam in the tank, in \({ }^{\circ} \mathrm{C}\), and the final mass of the steam in the tank, in kg.

An insulated, rigid tank whose volume is 10 ft3 is connected by a valve to a large steam line through which steam flows at \(500 \mathrm{lbf} / \mathrm{in} .^{2}, 800^{\circ} \mathrm{F}\). The tank is initially evacuated. The valve is opened only as long as required to fill the tank with steam to a pressure of \(500 \mathrm{lbf} / \mathrm{in} .^{2}\) Determine the final temperature of the steam in the tank, in \({ }^{\circ} \mathrm{F}\), and the final mass of steam in the tank, in lb.

Figure P4.114 provides operating data for a compressed-air energy storage system using off-peak electricity to power a compressor that fills a cavern with pressurized air (see Sec. 4.8.3). The cavern shown in the figure has a volume of \(10^{5} \mathrm{~m}^{3}\) and initially holds air at 290 K, 1 bar, which corresponds to ambient air. After filling, the air in the cavern is at 790 K, 21 bar. Assuming ideal gas behavior for the air, determine (a) the initial and final mass of air in the cavern, each in kg, and (b) the work required by the compressor, in GJ. Ignore heat transfer and kinetic and potential energy effects.

A rigid tank whose volume is \(0.5 \mathrm{m}^{3}\), initially containing ammonia at \(20^{\circ} \mathrm{C}\), 1.5 bar, is connected by a valve to a large supply line carrying ammonia at 12 bar, \(60^{\circ} \mathrm{C}\). The valve is opened only as long as required to fill the tank with additional ammonia, bringing the total mass of ammonia in the tank to 143.36 kg. Finally, the tank holds a two-phase liquid–vapor mixture at \(20^{\circ} \mathrm{C}\). Determine the heat transfer between the tank contents and the surroundings, in kJ, ignoring kinetic and potential energy effects.

As shown in Fig. P4.116, a \(247.5-\mathrm{ft}^{3}\) tank contains saturated vapor water initially at \(30 \mathrm{lbf} / \mathrm{in} .^{2}\) The tank is connected to a large line carrying steam at \(180 \mathrm{lbf} / \mathrm{in}^{2}, 450^{\circ} \mathrm{F}\). Steam flows into the tank through a valve until 2.9 lb of steam have been added to the tank. The valve is then closed and the pressure in the tank is \(40 \mathrm{lbf} / \mathrm{in} .^{2}\) Determine the specific volume, in \(\mathrm{ft}^{3} / \mathrm{lb}^{2}\), at the final state of the control volume and the magnitude and direction of the heat transfer between the tank and its surroundings, in Btu.

A rigid copper tank, initially containing \(1 \mathrm{~m}^{3}\) of air at 295 K, 5 bar, is connected by a valve to a large supply line carrying air at 295 K, 15 bar. The valve is opened only as long as required to fill the tank with air to a pressure of 15 bar. Finally, the air in the tank is at 310 K. The copper tank, which has a mass of 20 kg, is at the same temperature as the air in the tank, initially and finally. The specific heat of the copper is \(c=0.385 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\). Assuming ideal gas behavior for the air, determine (a) the initial and final mass of air within the tank, each in kg, and (b) the heat transfer to the surroundings from the tank and its contents, in kJ, ignoring kinetic and potential energy effects.

A rigid, insulated tank, initially containing \(0.4 \mathrm{~m}^{3}\) of saturated water vapor at 3.5 bar, is connected by a valve to a large vessel holding steam at 15 bar, \(320^{\circ} \mathrm{C}\). The valve is opened only as long as required to bring the tank pressure to 15 bar. For the tank contents, determine the final temperature, in \({ }^{\circ} \mathrm{C}\), and final mass, in kg.

A rigid, well-insulated tank of volume \(0.9 \mathrm{~m}^{3}\) is initially evacuated. At time t = 0, air from the surroundings at 1 bar, \(27^{\circ} \mathrm{C}\) begins to flow into the tank. An electric resistor transfers energy to the air in the tank at a constant rate for 5 minutes, after which time the pressure in the tank is 1 bar and the temperature is \(457^{\circ} \mathrm{C}\). Modeling air as an ideal gas, determine the power input to the tank, in kW.

A well-insulated rigid tank of volume \(15 \mathrm{m}^{3}\) is connected to a large steam line through which steam flows at 1 MPa and \(320^{\circ} \mathrm{C}\). The tank is initially evacuated. Steam is allowed to flow into the tank until the pressure inside is p. (a) Determine the amount of mass in the tank, in kg, and the temperature in the tank, in \({ }^{\circ} \mathrm{C}\), when p = 500 kPa. (b) Plot the quantities of part (a) versus p ranging from 0 kPa to 500 kPa.

A 50-gallon-capacity hot-water heater is shown in Fig. P4.121. Water in the tank of the heater initially has a temperature of \(120^{\circ} \mathrm{F}\). When someone turns on the shower faucet, water flows from the tank at a rate of 0.47 lb/s, and replenishment water at \(40^{\circ} \mathrm{F}\) flows into the tank from the municipal water distribution system. Water in the tank receives an energy input at a rate of 40,000 Btu/h from electrical resistors. If the water within the tank is well mixed, the temperature at any time can be taken as uniform throughout. The tank is well insulated so stray heat transfer with the surroundings is negligible. Neglecting kinetic and potential energy effects, assuming negligible change in pressure from inlet to exit of the tank, and modeling water as an incompressible substance with density of \(62.28 \mathrm{lb} / \mathrm{ft}^{3}\) and specific heat of \(1.0 \mathrm{Btu} / \mathrm{lb} \cdot{ }^{\circ} \mathrm{R}\), plot the temperature, in \({ }^{\circ} \mathrm{F}\), of the water in the tank versus time from t = 0 to 20 min.

A rigid tank having a volume of \(0.1 \mathrm{m}^{3}\) initially contains water as a two-phase liquid–vapor mixture at 1 bar and a quality of 1%. The water is heated in two stages: Stage 1: Constant-volume heating until the pressure is 20 bar. Stage 2: Continued heating while saturated water vapor is slowly withdrawn from the tank at a constant pressure of 20 bar. Heating ceases when all the water remaining in the tank is saturated vapor at 20 bar. For the water, evaluate the heat transfer, in kJ, for each stage of heating. Ignore kinetic and potential energy effects.

A rigid, insulated tank having a volume of \(50 \mathrm{ft}^{3}\) initially contains a two-phase liquid–vapor mixture of ammonia at \(100^{\circ} \mathrm{F}\) and a quality of 1.9%. Saturated vapor is slowly withdrawn from the tank until a two-phase liquid–vapor mixture at \(80^{\circ} \mathrm{F}\) remains. Determine the mass of ammonia in the tank initially and finally, each in lb.

A pressure cooker has a volume of \(0.011 \mathrm{m}^{3}\) and initially contains a two-phase liquid–vapor mixture of \(\mathrm{H}_{2} \mathrm{O}\) at a temperature of \(100^{\circ} \mathrm{C}\) and a quality of 10%. As the water is heated at constant volume, the pressure rises to 2 bar and the quality becomes 18.9%. With further heating a pressure-regulating valve keeps the pressure constant in the cooker at 2 bar by allowing saturated vapor at 2 bar to escape. Neglecting kinetic and potential energy effects, (a) determine the quality of the \(\mathrm{H}_{2} \mathrm{O}\) at the initial onset of vapor escape (state 2) and the amount of heat transfer, in kJ, to reach this state. (b) determine the final mass in the cooker, in kg, and the additional amount of heat transfer, in kJ, if heating continues from state 2 until the final quality is 1.0. (c) plot the quantities of part (b) versus quality increasing from the value at state 2 to 100%.

A well-insulated rigid tank of volume \(8 \mathrm{ft}^{3}\) initially contains carbon dioxide at \(180^{\circ} \mathrm{F} \text { and } 40 \mathrm{lbf} / \mathrm{in} .^{2}\) A valve connected to the tank is opened, and carbon dioxide is withdrawn slowly until the pressure within the tank drops to p. An electrical resistor inside the tank maintains the temperature at \(180^{\circ} \mathrm{F}\). Modeling carbon dioxide as an ideal gas and neglecting kinetic and potential energy effects, (a) determine the mass of carbon dioxide withdrawn, in lb, and the energy input to the resistor, in Btu, when \(p=22 \mathrm{lbf} / \mathrm{in} .^{2}\) (b) plot the quantities of part (a) versus p ranging from 15 to \(40 \mathrm{lbf} / \mathrm{in}^{2}\)

A tank of volume \(1.2 \mathrm{m}^{3}\) initially contains steam at 8 MPa and \(400^{\circ} \mathrm{C}\). Steam is withdrawn slowly from the tank until the pressure drops to p. Heat transfer to the tank contents maintains the temperature constant at \(400^{\circ} \mathrm{C}\). Neglecting all kinetic and potential energy effects and assuming specific enthalpy of the exiting steam is linear with the mass in the tank, (a) determine the heat transfer, in kJ, if p = 2 MPa. (b) plot the heat transfer, in kJ, versus p ranging from 0.5 to 8 MPa.

An open cooking pot containing 0.5 liter of water at \(20^{\circ} \mathrm{C}\), 1 bar sits on a stove burner. Once the burner is turned on, the water is gradually heated at a rate of 0.85 kW while pressure remains constant. After a period of time, the water starts boiling and continues to do so until all of the water has evaporated. Determine (a) the time required for the onset of evaporation, in s. (b) the time required for all of the water to evaporate, in s, once evaporation starts.

Nitrogen gas is contained in a rigid 1-m tank, initially at 10 bar, 300 K. Heat transfer to the contents of the tank occurs until the temperature has increased to 400 K. During the process, a pressure-relief valve allows nitrogen to escape, maintaining constant pressure in the tank. Neglecting kinetic and potential energy effects, and using the ideal gas model with constant specific heats evaluated at 350 K, determine the mass of nitrogen that escapes, in kg, and the amount of energy transfer by heat, in kJ.

The air supply to a \(2000-\mathrm{ft}^{3}\) office has been shut off overnight to conserve utilities, and the room temperature has dropped to \(40^{\circ} \mathrm{F}\). In the morning, a worker resets the thermostat to \(70^{\circ} \mathrm{F}\), and \(200 \mathrm{ft}^{3} / \mathrm{min}\) of air at \(120^{\circ} \mathrm{F}\) begins to flow in through a supply duct. The air is well mixed within the room, and an equal mass flow of air at room temperature is withdrawn through a return duct. The air pressure is nearly 1 atm everywhere. Ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach \(70^{\circ} \mathrm{F}\). Plot the room temperature as a function of time.

The procedure to inflate a hot-air balloon requires a fan to move an initial amount of air into the balloon envelope followed by heat transfer from a propane burner to complete the inflation process. After a fan operates for 10 minutes with negligible heat transfer with the surroundings, the air in an initially deflated balloon achieves a temperature of \(80^{\circ} \mathrm{F}\) and a volume of \(49,100 \mathrm{ft}^{3}\). Next the propane burner provides heat transfer as air continues to flow into the balloon without use of the fan until the air in the balloon reaches a volume of \(65,425 \mathrm{ft}^{3}\) and a temperature of \(210^{\circ} \mathrm{F} \text {. Air at } 77^{\circ} \mathrm{F} \text { and } 14.7 \mathrm{lbf} / \mathrm{in} .^{2}\) surrounds the balloon. The net rate of heat transfer is \(7 \times 10^{6} \mathrm{Btu} / \mathrm{h}\). Ignoring effects due to kinetic and potential energy, modeling the air as an ideal gas, and assuming the pressure of the air inside the balloon remains the same as that of the surrounding air, determine (a) the power required by the fan, in hp. (b) the time required for full inflation of the balloon, in min.

Using the Internet, identify at least five medical applications of MEMS technology. In each case, explain the scientific and technological basis for the application, discuss the state of current research, and determine how close the technology is in terms of commercialization. Write a report of your findings, including at least three references.

A group of cells called the sinus node is the natural pacemaker of the heart and controls the heartbeat. Sinus node dysfunction is one source of the medical condition known as heart arrhythmia: irregular heartbeat. Significant arrhythmias are treated in several ways, including the use of an artificial pacemaker, which is an electrical device that sends the signals needed to make the heart beat properly. Research how both natural and artificial pacemakers operate to achieve their goal of maintaining a regular heartbeat. Place your findings in a memorandum that includes annotated sketches of each type of pacemaker.

Conduct a term-length project centered on using a low-wind turbine to meet the electricity needs of a small business, farm, or neighborhood selected by, or assigned to, your project group. Take several days to research the project and then prepare a brief written plan having a statement of purpose, a list of objectives, and several references. As part of your plan, schedule on-site wind-speed measurements for at least three different days to achieve a good match between the requirements of candidate low-wind turbines and local conditions. Your plan also should recognize the need for compliance with applicable zoning codes. During the project, observe good practices such as discussed in Sec. 1.3 of Thermal Design and Optimization, John Wiley & Sons Inc., New York, 1996, by A. Bejan, G. Tsatsaronis, and M.J. Moran. Provide a well-documented report, including an assessment of the economic viability of the selected turbine for the application considered.

Generation of electricity by harnessing currents, waves, and tides is being studied across the globe. Electricity can be generated from currents using underwater turbines, as illustrated in Fig. P4.4D. Electricity also can be generated from the undulating motion of waves using tethered buoys. Like means can be used to generate power from tidal movements. Although currents and waves have long been used to meet relatively modest power needs, many observers today are thinking of large-scale power generation systems. Some see the oceans as providing a nearly unlimited renewable source of power. For a site in U.S. coastal waters, estuaries, or rivers, critically evaluate the viability of currents and/or waves for large-scale power generation by 2025. Consider technical and economic factors and effects on the ecosystem. Write a report including at least three references.

Owing to their relatively compact size, simple construction, and modest power requirement, centrifugal-type blood pumps are under consideration for several medical applications. Still, centrifugal pumps have met with limited success thus far for blood flow because they can cause damage to blood cells and are subject to mechanical failure. The goal of current development efforts is a device having sufficient long-term biocompatibility, performance, and reliability for widespread deployment. Investigate the status of centrifugal blood pump development, including identifying key technical challenges and prospects for overcoming them. Summarize your findings in a report, including at least three references.

Design an experiment to determine the energy, in kW-h, required to completely evaporate a fixed quantity of water. For the experiment develop written procedures that include identification of all equipment needed and specification of all required calculations. Conduct the experiment, and communicate your results in an executive summary.

Investigate the water system for your local municipality. Prepare a diagram that traces the water from its original source through municipal treatment, storage, and distribution systems to wastewater collection, treatment, and disposal systems. Identify steady-flow and transient-flow devices incorporated in these systems to achieve the necessary flow, storage, and treatment. Summarize your findings in a PowerPoint presentation.

The technical literature contains discussions of ways for using tethered kite-mounted wind turbine systems to harvest power from high-altitude winds, including jet streams at elevations from 6 to 15 kilometers (4 to 9 miles). Analysts estimate that if such systems were deployed in sufficient numbers, they could meet a significant share of total U.S. demand for electricity. Critically evaluate the feasibility of such a kite system, selected from the existing literature, to be fully operational by 2025. Consider means for deploying the system to the proper altitude, how the power developed is transferred to earth, infrastructure requirements, environmental impact, cost, and other pertinent issues. Write a report including at least three references.

Reverse engineer a handheld hair dryer by disassembling the dryer into its individual parts. Mount each part onto a presentation board to illustrate how the parts are connected when assembled. Label each part with its name. Next to each part identify its purpose and describe its fundamental operating principle (if applicable). Include a visual trace of the mass and energy flows through the hair dryer during operation. Display the presentation board where others can learn from it.

Residential integrated systems capable of generating electricity and providing space heating and water heating will reduce reliance on electricity supplied from central power plants. For a \(2500-\mathrm{ft}^{2}\) dwelling in your locale, evaluate two alternative technologies for combined power and heating: a solar energy-based system and a natural gas fuel cell system. For each alternative, specify equipment and evaluate costs, including the initial system cost, installation cost, and operating cost. Compare total cost with that for conventional means for powering and heating the dwelling. Write a report summarizing your analysis and recommending either or both of the options if they are preferable to conventional means.

Figure P4.11D provides the schematic of a device for producing a combustible fuel gas for transportation from biomass. While several types of solid biomass can be employed in current gasifier designs, wood chips are commonly used. Wood chips are introduced at the top of the gasifier unit. Just below this level, the chips react with oxygen in the combustion air to produce charcoal. At the next depth, the charcoal reacts with hot combustion gases from the charcoal-formation stage to produce a fuel gas consisting mainly of hydrogen, carbon monoxide, and nitrogen from the combustion air. The fuel gas is then cooled, filtered, and ducted to the internal combustion engine served by the gasifier. Critically evaluate the suitability of this technology for transportation use today in the event of a prolonged petroleum shortage in your locale. Document your conclusions in a memorandum.