In cold climates, water pipes may freeze and burst if

Problem 7P 1-m3 rigid tank initially contains air whose density is 1.18 kg/m3. The tank is connected to a high-pressure supply line through a valve. The valve is opened, and air is allowed to enter the tank until the density in the tank rises to 7.20 kg/m3. Determine the mass of air that has entered the tank. Answer:6.02kg

Problem 8P The ventilating fan of the bathroom of a building (Fig. P5-10) has a volume flow rate of 50 L/s and runs continuously. If the density of air inside is 1.20 kg/m3, determine the mass of air vented out in one day. 50 L/s

Problem 9P A desktop computer is to be cooled by a fan whose flow rate is 0.40 m3/min. Determine the mass flow rate of air through the fan at an elevation of 3400 m where the air density is 0.7 kg/m3. Also, if the average velocity of air is not to exceed 110 m/min, determine the minimum diameter of the casing of the fan.

Problem 12P Air enters a nozzle steadily at 2.21 kg/m3 and 45 m/s; and leaves at 0.762 kg/m3 and 150 m/s. If the inlet area of the nozzle is 80 cm2, determine(a)the mass flow rate through the nozzle, and (b) the exit area of the nozzle.

Problem 11P The minimum fresh air requirement of a residential building is specified to be 0.35 air changes per hour IASHRAE, Standard 62, 1989). That is, 35 percent of the entire air contained in a residence should be replaced by 'fresh outdoor air every hour. If the ventilation requirement of a 2.7-m-high, 200-m2 residence is to be met entirely by a fan, determine the flow capacity in L/min of the fan that needs to be installed. Also determine the minimum diameter of the duct if the average air velocity is not to exceed 5 m/s.

Problem 10P A smoking lounge is to accommodate 15 heavy smokers. The minimum fresh air requirement for smoking lounges is specified to be 30 L/s per person (ASHRAE, Standard 62, 1989). Determine the minimum required flow rate of fresh air that needs to be supplied to the lounge, and the minimum diameter of the duct if the air velocity is not to exceed 8m/s.

Problem 13P A hair dryer is basically a duct of constant diameter in which a few layers of electric resistors are placed. A small fan pulls the air in and forces it through -the resistors where it is heated. If the density of air is 1.20 kg/m3 at the inlet and 1.05 kg/m3 at the exit, determine the percent increase in the velocity of air as it flows through the dryer.

Problem 14P What is mechanical energy?. How does it differ from thermal energy? What are the forms of mechanical energy of a fluid stream?

Problem 15P What is mechanical efficiency? What does a mechanical efficiency of 100 percent mean for a hydraulic turbine?

Problem 17P Define turbine efficiency, generator efficiency, and combined turbine-generator efficiency.

Problem 16P How is the combined pump-motor efficiency of a pump and motor system defined? Can the combined pumpmotor efficiency be greater than either the pump or the motor efficiency?

Problem 18P At a certain location, wind is blowing steadily at 8 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 50-m-diameter blades at that location. Also determine the actual electric power generation assuming an overall efficiency of 30 percent. Take the air density to be 1.25 kg/m3.

Problem 22P Electric power is to be generated by installing a hydraulic turbine - generator at a site 70 m below the free surface of a large water reservoir that can supply water at a rate of 1500 kg/s steadily. If the mechanical power output of the turbine is 800 kW and the electric power generation is 750 kW, determine the turbine efficiency and the combined turbine-generator efficiency of this plant. Neglect losses in the pipes.

Problem 23P What is streamwise acceleration? How does it differ from normal acceleration? Can a fluid particle accelerate in steady flow?

Problem 24P Express the Bernoulli equation in three different ways using (a)energies, (b)pressures, and (c) heads.

Problem 25P What are the three major assumptions used in the derivation of the Bernoulli equation?

Problem 26P Define static, dynamic, and hydrostatic pressure. Under what conditions is their sum constant for a flow stream?

Problem 27P What is stagnation pressure? Explain how it can be measured.

Problem 45P An airplane is flying at an altitude of 12.000 m. Determine the gage pressure at the stagnation point on the nose of the plane if the speed of the plane is 300 km/h. How would you solve this problem if the speed were 1050 km/h? Explain.

Problem 46P The air velocity in the duct of a heating system is to be measured by a Pitot-static probe inserted into the duct parallel to flow. If the differential height between the water columns connected to the two outlets of the probe is 2.4 cm, determine (a)the flow velocity and (b)the pressure rise at the tip of the probe. The air temperature and pressure in the duct are 45°C and 98 kPa, respectively.

Problem 48P Reconsider Prob. 5-51. Determine how long it will take to empty the swimming pool completely. PROBLEM: The water in a 8-m-diameter, 3-m-high above ground swimming pool is to be emptied by unplugging a 3-cm- diameter, 25-m-long horizontal pipe attached to the bottom of the pool. Determine the maximum discharge rate of water through the pipe. Also, explain why the actual flow rate will be less.

Problem 47P The water in a 8-m-diameter, 3-m-high aboveground swimming pool is to be emptied by unplugging a 3-cm- diameter, 25-m-long horizontal pipe attached to the bottom of the pool. Determine the maximum discharge rate of water through the pipe. Also, explain why the actual flow rate will be less.

Problem 50P Air at 110 kPa and 50°C flows upward through a 6-cm-diameter inclined duct at a rate of 45 L/s. The duct diameter is then reduced to 4 cm through a reducer. The pressure change across the reducer is measured by a water manometer. The elevation difference between the two points on the pipe where the two arms of the manometer are attached is 0.20 m. Determine the differential height between the fluid levels of the two arms of the manometer. FIGURE P12-41

Problem 49P Reconsider Prob. 5-52. Using EES (or other) software, investigate the effect of the discharge pipe diameter on the time required to empty the pool completely. Let the diameter vary from 1 to 10 cm in increments of 1 cm. Tabulate and plot the results.

Problem 53P A pressurized tank of water has a 10-cm-diameter orifice at the bottom, where water discharges to the atmosphere. The water level is 2.5 m above the outlet. The tank air pressure above the water level is 250 kPa (absolute) while the atmospheric pressure is 100 kPa. Neglecting frictional effects, determine the initial discharge rate of water from the tank.

Problem 52P The water pressure in the mains of a city at a particular location is 350 kPa gage. Determine if this main can serve water to neighborhoods that are 50 m above this location.

Problem 54P Reconsider Prob. 5-57. Using EES (or other) software, investigate the effect of water height in the tank on the discharge velocity. Let the water height vary from 0 to 5 m in increments of 0.5 m. Tabulate and plot the results.

Problem 55P A handheld bicycle pump can be used as an atomizer to generate a fine mist of paint or pesticide by forcing air at a high velocity through a small hole and placing a short tube between the liquid reservoir and the high-speed air jet. The pressure across a subsonic jet exposed to the atmosphere is nearly atmospheric, and the surface of the liquid in the reservoir is also open to atmospheric pressure. In light of this, explain how the liquid is sucked up the tube.Hint: Read Sec. 5-4 carefully.

Problem 56P The water level in a tank is 15 m above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The tank cover is airtight, and the air pressure above the water surface is 3 atm, gage. The system is at sea level. Determine the maximum height to which the water stream could rise.

Problem 65P Consider the steady adiabatic flow of an incompressible fluid. Can the temperature of the fluid decrease during flow? Explain.

Problem 66P What is irreversible head loss? How is it related to the mechanical energy loss?

Problem 57P A Pitot-static probe connected to a water manometer is used to measure the velocity of air. If the deflection (the vertical distance between the fluid levels in the two arms) is 7.3 cm, determine the air velocity. Take the density of air to be 1.25 kg/m3.

Problem 67P What is useful pump head? How is it related to the power input to the pump?

Problem 68P What is the kinetic energy correction factor? Is it significant?

Problem 69P The water level in a tank is 20 m above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The water stream from the nozzle is observed to rise 25 m above the ground. Explain what may cause the water from the hose to rise above the tank level.

Problem 70P \ A person is filling a knee-high bucket with water using a garden hose and holding it such that water discharges from the hose at the level of his waist. Someone suggests that the bucket will fill faster if the hose is lowered such that water discharges from the hose at the knee level. Do you agree with this suggestion? Explain. Disregard any frictional effects.

Problem 73P Water is being pumped from a large lake to a reservoir 25 m above at a rate of 25 L/s by a 10-kW (shaft) pump. If the irreversible head loss of the piping system is 5 m, determine the mechanical efficiency of the pump.

Problem 72P A fan is to be selected to ventilate a bathroom whose dimensions are 2 m × 3 m × 3 m. The air velocity is not to exceed 8 m/s to minimize vibration noise. The combined efficiency of the fan-motor unit to be used can be taken to be 50 percent. If the fan is to replace the entire volume of air in 10 min, determine (a) the wattage the fan-motor unit to be purchased, (b) the diameter of the FIGURE P12-56 fan casing, and (c) the pressure difference across the fan. Take the air density to be 1.25 kg/m3 and disregard the effect of the kinetic energy correction factors.

Problem 87P The demand for electric power is usually much higher during the day than it is at night, and utility companies often sell power at night at much lower prices to encourage consumers to use the available power generation capacity and to avoid building new expensive power plants that will be used only a short time during peak periods. Utilities are also willing to purchase power produced during the day from private parties at a high price. Suppose a utility company is selling electric power for $0.03/kWh at night and is willing to pay $0.08/kWh for power produced during the day. To take advantage of this opportunity, an entrepreneur is considering building a large reservoir 50 m above the lake level, pumping water from the lake to the reservoir at night using cheap power, and letting the water flow from the reservoir back to the lake during the day. producing power as the pump-motor operates as a turbine-generator during reverse flow. Preliminary analysis shows that a water flow rate of 2 m3/s can be used in either direction, and the irreversible head loss of the piping system is 4 m. The combined pump-motor and turbine-generator efficiencies are expected to be 75 percent each. Assuming the system operates for 10 h each in the pump and turbine modes during a typical day, determine the potential revenue this pump-turbine system can generate per year.

Problem 90P Reconsider Prob. 5-95. Determine the flow rate of water and the pressure difference across the pump if the irreversible head loss of the piping system is 4 m.

Problem 91P A fireboat is to fight fires at coastal areas by drawing seawater with a density of 1030 kg/m3 through a 20-cm-diameter pipe at a rate of 0.1 m3/s and discharging it through a hose nozzle with an exit diameter of 5 cm. The total irreversible head loss of the system is 3 m, and the position of the nozzle is 3 m above sea level. For a pump efficiency of 70 percent, determine the required shaft power input to the pump and the water discharge velocity.

Problem 89P Underground water is to be pumped by a 78 percent efficient 5-kW submerged pump to a pool whose free surface is 30 m above the underground water level. The diameter of the pipe is 7 cm on the intake side and 5 cm on the discharge side. Determine(a) the maximum flow rate of water and (b) the pressure difference across the pump. Assume the elevation difference between the pump inlet and the outlet and the effect of the kinetic energy correction factors to be negligible.

Problem 93P Underground water is being pumped into a pool whose cross section is 3 m × 4 m while water is discharged through a 5-cm-diameter orifice at a constant average velocity of 5 m/s. If the water level in the pool rises at a rate of 1.5 cm/min, determine the rate at which water is supplied to the pool, in m3/s.

Problem 94P The velocity of a liquid flowing in a circular pipe of radiusR varies from zero at the wall to a maximum at the pipe center. The velocity distribution in the pipe can be represented asV(r), wherer is the radial distance from the pipe center. Based on the definition of mass flow rate m, obtain a relation for the average velocity in terms ofV(r), R, and r.

Problem 92P The air in a 6-m × 5-m × 4-m hospital room is to be completely replaced by conditioned air every 20 min. If the average air velocity in the circular air duct leading to the room is not to exceed 5 m/s, determine the minimum diameter of the duct.

Problem 95P Air at 3.80 kg/m3 enters a nozzle that has an inlet-to- exit area ratio of 2:1 with a velocity of 120 m/s and leaves with a velocity of 380 m/s. Determine the density of air at the exit.

Problem 96P A D0 = 8-m-diameter tank is initially filled with water 2 m above the center of aD = 10-cm-diameter valve near the bottom. The tank surface is open to the atmosphere, and the tank drains through aL = 80-m-long pipe connected to the valve. The friction factor of the pipe is given to be f= 0.015, and the discharge velocity is expressed as where z is the water height above the center of the valve. Determine (a) the initial discharge velocity from the tank and (b) the time required to empty the tank. The tank can be considered to be empty when the water level drops to the center of the valve.

Problem 98P Air flows through a pipe at a rate of 170 L/s. The pipe consists of two sections of diameters 18 cm and 10 cm with a smooth reducing section that connects them. The pressure difference between the two pipe sections is measured by a water manometer. Neglecting frictional effects, determine the differential height of water between the two pipe sections. Take the air density to be 1.20 kg/m3.

Problem 103P A 3-m-high large tank is initially filled with water. The tank water surface is open to the atmosphere, and a sharp-edged 10-cm-diameter orifice at the bottom drains to the atmosphere through a horizontal 80-m-long pipe. If the total irreversible head loss of the system is determined to be 1.5 m, determine the initial velocity of the water from the tank. Disregard the effect of the kinetic energy correction factors.

Problem 97P A pressurized 2-m-diameter tank of water has a 10-cm-diameter orifice at the bottom, where water discharges to the atmosphere. The water level initially is 3 m above the outlet. The tank air pressure above the water level is maintained at 450 kPa absolute and the atmospheric pressure is 100 kPa. Neglecting frictional effects, determine (a)how long it will take for half of the water in the tank to be discharged and (b)the water level in the tank after 10 s.

Problem 104P Reconsider Prob. 5-109. Using EES (or other) software, investigate the effect of the tank height on the initial discharge velocity of water from the completely filled tank. Let the tank height vary from 2 to 15 m in increments of 1 m, and assume the irreversible head loss to remain constant. Tabulate and plot the results.

Problem 106P A wind tunnel draws atmospheric air at 20°C and 101.3 kPa by a large fan located near the exit of the tunnel. If air velocity in the tunnel is 80 m/s, determine the pressure in the tunnel. FIGURE P12-72

Problem 99P Air at 100 kPa and 25°C flows in a horizontal duct of variable cross section. The water column in the manometer that measures the difference between two sections has a vertical displacement of 8 cm. If the velocity in the first section is low and the friction is negligible, determine the velocity at the second section. Also, if the manometer reading has a possible error of ±2 mm, conduct an error analysis to estimate the range of validity for the velocity found.

Problem 19P Reconsider Prob. 5-20. Using EES (or other) software, investigate the effect of wind velocity and the blade span diameter on wind power generation. Let the velocity vary from5 to20 m/s in increments of5 m/s, and the diameter to vary from 20 to 80 m in increments of 20 m. Tabulate the results, and discuss their significance.

Problem 20P Water is pumped from a lake to a storage tank 18 m above at a rate of 70 L/s while consuming20.4 kW of electric power. Disregarding any frictional losses in the pipes and any changes in kinetic energy, determine (a) the overall efficiency of the pump-motor unit and(b) the pressure difference between the inlet and the exit of the pump.

Problem 59P In cold climates, water pipes may freeze and burst if proper precautions are not taken. In such an occurrence, the exposed part of a pipe on the ground ruptures, and water shoots up to 42 m. Estimate the gage pressure of water in the pipe. State your assumptions and discuss if the actual pressure is more or less than the value you predicted.

Problem 21P Consider a river flowing toward a lake at an average speed of4 m/s at a rate of 500 m3/s at a location70 m above the lake surface. Determine the total mechanical energy of the river water per unit mass and the power generation potential of the entire river at that location.

Problem 62P A fluid of density ? and viscosity ? flows through a section of horizontal converging-diverging duct. The duct cross-sectional areas Ainlet, Athroat, and Aoutlet are known at the inlet, throat (minimum area), and outlet, respectively. Average pressure Poutlet is measured at the outlet, and average velocity Vinlet is measured at the inlet. (a) Neglecting any irreversibilities such as friction, generate expressions for the average velocity and average pressure at the inlet and the throat in terms of the given variables, (b) In a real flow (with irreversibilities), do you expect the actual pressure at the inlet to be higher or lower than the prediction? Explain.

Problem 64P Consider the steady adiabatic flow of an incompressible fluid. If the temperature of the fluid remains constant during flow, is it accurate to say that the frictional effects are negligible?

Problem 100P A very large tank contains air at 102 kPa at a location where the atmospheric air is at 100 kPa and 20°C. Now a 2-cm-diameter tap is opened. Determine the maximum flow rate of air through the hole. What would your response be if air is discharged through a 2-m-long, 4-cm-diameter tube with a 2-cm-diameter nozzle? Would you solve the problem the same way if the pressure in the storage tank were 300 kPa?

Problem 101P Water is flowing through a Venturi meter whose diameter is 7 cm at the entrance part and 4 cm at the throat. The pressure is measured to be 380 kPa at the entrance and 150 kPa at the throat. Neglecting frictional effects, determine the flow rate of water.

Problem 102P Water flows at a rate of 0.025 m3/s in a horizontal pipe whose diameter increases from 6 to 11 cm by an enlargement section. If the head loss across the enlargement section is 0.45 m and the kinetic energy collection factor at both the inlet and the outlet is 1.05, determine the pressure change.

Problem 105P Reconsider Prob. 5-109. In order to drain the tank faster, a pump is installed near the tank exit. Determine the pump head input necessary to establish an average water velocity of 5m/s when the tank is full. PROB. 5-109: A 3-m-high large tank is initially filled with water. The tank water surface is open to the atmosphere, and a sharp-edged 10-cm-diameter orifice at the bottom drains to the atmosphere through a horizontal 80-m-long pipe. If the total irreversible head loss of the system is determined to be 1.5 m, determine the initial velocity of the water from the tank. Disregard the effect of the kinetic energy correction factors.

Problem 28P Define pressure head, velocity head, and elevation head for a fluid stream and express them for a fluid stream whose pressure is P,velocity is V, and elevation is z.

Problem 29P What is the hydraulic grade line? How does it differ from the energy grade line? Under what conditions do both lines coincide with the free surface of a liquid?

Problem 30P How is the location of the hydraulic grade line determined for open-channel flow? How is it determined at the outlet of a pipe discharging to the atmosphere?

Problem 71P A 3-m-high tank filled with water has a discharge valve near the bottom and another near the top. (a) If these two valves are opened, will there be any difference between the discharge velocities of the two water streams? (b) If a hose whose discharge end is left open on the ground is first connected to the lower valve and then to the higher valve, will there be any difference between the discharge rates of water for the two cases? Disregard any frictional effects.

Problem 31P In a certain application, a siphon must go over a high wall. Can water or oil with a specific gravity of 0.8 go over a higher wall? Why?

Problem 32P Explain how and why a siphon works. Someone proposes siphoning cold water over a 7-m-high wall. Is this feasible? Explain.

Problem 33P A glass manometer with oil as the working fluid is connected to an air duct as shown in Fig. P12-23C Will the oil levels in the manometer be as in Fig. P12-23Ca or b?Explain. What would your response be if the flow direction is reversed? FIGURE P12-23C

Problem 74P Reconsider Prob. 5-79. Using EES (or other) software, investigate the effect of irreversible head loss on the mechanical efficiency of the pump. Let the head loss vary from 0 to 15 m in increments of 1 m. Plot the results, and discuss them.

Problem 75P A 7-hp (shaft) pump is used to raise water to a 15-m higher elevation. I f the mechanical efficiency of the pump is 82 percent, determine the maximum volume flow rate of water.

Problem 76P Water flows at a rate of 0.035 m3/s in a horizontal pipe whose diameter is reduced from 15 cm to 8 cm by a reducer. If the pressure at the centerline is measured to be 480 kPa and 445 kPa before and after the reducer, respectively, determine the irreversible head loss in the reducer. Take the kinetic energy correction factors to be 1.05.

Problem 34P The velocity of a fluid flowing in a pipe is to be measured by two different Pitot-type mercury manometers shown in Fig. P12-24C. Would you expect both manometers to predict the same velocity for flowing water? If not, which would be more accurate? Explain. What would your response be if air were flowing in the pipe instead of water? FIGURE P12-24C

Problem 35P The water level of a tank on a building roof is 20 m above the ground. A hose leads from the tank bottom to the ground. The end of the hose has a nozzle, which is pointed straight up . What is the maximum height to which the water could rise? What factors would reduce this height?

Problem 36P A student siphons water over a 8.5-m-high wall at sea level. She then climbs to the summit of Mount Shasta (elevation 4390 m, Patm = 58.5 kPa) and attempts the same experiment. Comment on her prospects for success.

Problem 77P The water level in a tank is 20 m above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The tank is at sea level, and the water surface is open to the atmosphere. In the line leading from the tank to the nozzle is a pump, which increases the pressure of water. If the water jet rises to a height of 27 m from the ground, determine the minimum pressure rise supplied by the pump to the water line.

Problem 78P A hydraulic turbine has 85 m of head available at a flow rate of 0.25 m3/s, and its overall turbine-generator efficiency is 78 percent. Determine the electric power output of this turbine.

Problem 79P An oil pump is drawing 25 kW of electric power while pumping oil with? = 860 kg/m3 at a rate of 0.1 m3/s. The inlet and outlet diameters of the pipe are 8 cm and 12 cm, respectively. If the pressure rise of oil in the pump is measured to be 250 kPa and the motor efficiency is 90 percent, determine the mechanical efficiency of the pump. Take the kinetic energy correction factor to be 1.05.

Problem 1P Define mass and volume flow rates. How are they related to each other?

Problem 2P Does the amount of mass entering a control volume have to be equal to the amount of mass leaving during an unsteady-flow process?

Problem 37P In a hydroelectric power plant, water enters the turbine nozzles at 800 kPa absolute with a low velocity. If the nozzle outlets are exposed to atmospheric pressure of 100 kPa, determine the maximum velocity to which water can be accelerated by the nozzles before striking the turbine blades.

Problem 38P A Pitot-static probe is used to measure the velocity of an aircraft flying at 3000 m. If the differential pressure reading is 3 kPa, determine the velocity of the aircraft.

Problem 39P While traveling on a dirt road, the bottom of a car hits a sharp rock and a small hole develops at the bottom of its gas tank. If the height of the gasoline in the tank is 40 cm, determine the initial velocity of the gasoline at the hole. Discuss how the velocity will change with time and how the flow will be affected if the lid of the tank is closed tightly.

Problem 80P Water flows at a rate of 20 L/s through a horizontal pipe whose diameter is constant at 3 cm as shown in Fig. P12-64. The pressure drop across a valve in the pipe is measured to be 2 kPa. Determine the irreversible head loss of the valve, and the useful pumping power needed to overcome the resulting pressure drop.

Problem 82P A large tank is initially filled with water 5 m above the center of a sharp-edged 10-cm-diameter orifice. The tank water surface is open to the atmosphere, and the orifice drains to the atmosphere. If the total irreversible head loss in the system is 0.3 m, determine the initial discharge velocity of water from the tank. Take the kinetic energy correction factor at the orifice to be 1.2.

Problem 83P Water enters a hydraulic turbine through a 30-cmdiameter pipe at a rate of 0.6 m3/s and exits through a 25-cmdiameter pipe. The pressure drop in the turbine is measured by a mercury manometer to be 1.2 m. For a combined turbine-generator efficiency of 83 percent, determine the net electric power output. Disregard the effect of the kinetic energy correction factors. FIGURE P12-65

Problem 4P Name four physical quantities that are conserved and two quantities that are not conserved during a process.

Problem 3P When is the flow through a control volume steady?

Problem 5P In climates with low night-time temperatures, an energy-efficient way of cooling a house is to install a fan in the ceiling that draws air from the interior of the house and discharges it to a ventilated attic space. Consider a house whose interior air volume is 450 m3. If air in the house is to be exchanged once every 5 minutes, determine (a) the required flow rate of the fan and (b) the average discharge speed of air if the fan diameter is 1.20 m.

Problem 41P A piezometer and a Pitot tube are tapped into a 4-cm diameter horizontal water pipe, and the height of the water columns are measured to be 26 cm in the piezometer and 35 cm in the Pitot tube (both measured from the top surface of the pipe). Determine the velocity at the center of the pipe.

Problem 42P The diameter of a cylindrical water tank isD0 and its height isH. The tank is filled with water, which is open to the atmosphere. An orifice of diameterD with a smooth entrance (i.e., negligible losses) is open at the bottom. Develop a relation for the time required for the tank (a)to empty halfway and (b) to empty completely.

Problem 44P Water enters a tank of diameter DT steadily at a mass flow rate of An orifice at the bottom with diameter D0 FIGURE P12-34 allows water to escape. The orifice has a rounded entrance, so the frictional losses are negligible. If the tank is initially empty, (a) determine the maximum height that the water will reach in the tank and (b) obtain a relation for water height zas a function of time.

Problem 84P The velocity profile for turbulent flow in a circular pipe is usually approximated as u(r)= umax ( l – r/R)1/n,where n =7. Determine the kinetic energy correction factor for this flow.

Problem 85P Water is pumped from a lower reservoir to a higher reservoir by a pump that provides 20 kW of useful mechanical power to the water. The free surface of the upper reservoir is 45 m higher than the surface of the lower reservoir. If the flow rate of water is measured to be 0.03 m3/s. determine the irreversible head loss of the system and the lost mechanical power during this process.

Problem 86P Water in a partially filled large tank is to be supplied to the roof top, which is 8 m above the water level in the tank, through a 2.5-cm-internal-diameter pipe by maintaining a constant air pressure of 300 kPa (gage) in the tank. If the head loss in the piping is 2 m of water, determine the discharge rate of the supply of water to the roof top.