The density of a fluid decreases by 5 percent at constantpressure when its temperature

For a substance, what is the difference between mass and molar mass? How are these two related?

What is the difference between intensive and extensive properties?

What is specific gravity? How is it related to density?

The specific weight of a system is defined as the weight per unit volume (note that this definition violates the normal specific property-naming convention). Is the specific weight an extensive or intensive property?

What is the state postulate?

Under what conditions is the ideal-gas assumption suitable for real gases?

What is the difference between R and Ru? How are these two related?

A fluid that occupies a volume of 24 L weighs 225 N at a location where the gravitational acceleration is 9.80 m/s2. Determine the mass of this fluid and its density.

A 100-L container is filled with 1 kg of air at a temperature of 27C. What is the pressure in the container?

A mass of 1-lbm of argon is maintained at 200 psia and 100F in a tank. What is the volume of the tank?

What is the specific volume of oxygen at 40 psia and 80F?

The air in an automobile tire with a volume of 2.60 ft3 is at 90F and 20 psig. Determine the amount of air that must be added to raise the pressure to the recommended value of 30 psig. Assume the atmospheric pressure to be 14.6 psia and the temperature and the volume to remain constant. Answer: 0.128 lbm

The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25C, the pressure gage reads 210 kPa. If the volume of the tire is 0.025 m3, determine the pressure rise in the tire when the air temperature in the tire rises to 50C. Also, determine the amount of air that must be bled off to restore pressure to its original value at this temperature. Assume the atmospheric pressure to be 100 kPa.

A spherical balloon with a diameter of 9 m is filled with helium at 20C and 200 kPa. Determine the mole number and the mass of the helium in the balloon. Answers: 31.3 kmol, 125 kg

Reconsider Prob. 214. Using EES (or other) software, investigate the effect of the balloon diameter on the mass of helium contained in the balloon for the pressures of (a) 100 kPa and (b) 200 kPa. Let the diameter vary from 5 m to 15 m. Plot the mass of helium against the diameter for both cases.

A cylindrical tank of methanol has a mass of 40 kg and a volume of 51 L. Determine the methanols weight, density, and specific gravity. Take the gravitational acceleration to be 9.81 m/s2. Also, estimate how much force is needed to accelerate this tank linearly at 0.25 m/s2.

The density of saturated liquid refrigerant134a for 220C # T # 100C is given in Table A 4. Using this value develop an expression in the form r 5 aT 2 1 bT 1 c for the density of refrigerant134a as a function of absolute temperature, and determine relative error for each data set.

A rigid tank contains 40 lbm of air at 20 psia and 70F. More air is added to the tank until the pressure and temperature rise to 35 psia and 90F, respectively. Determine the amount of air added to the tank. Answer: 27.4 lbm

The density of atmospheric air varies with elevation, decreasing with increasing altitude. (a) Using the data given in the table, obtain a relation for the variation of density with elevation, and calculate the density at an elevation of 7000 m. (b) Calculate the mass of the atmosphere using the correlation you obtained. Assume the earth to be a perfect sphere with a radius of 6377 km, and take the thickness of the atmosphere to be 25 km. r, km r,kg/m3 6377 1.225 6378 1.112 6379 1.007 6380 0.9093 6381 0.8194 6382 0.7364 6383 0.6601 6385 0.5258 6387 0.4135 6392 0.1948 6397 0.08891 6402 0.04008

What is cavitation? What causes it?

Does water boil at higher temperatures at higher pressures? Explain.

If the pressure of a substance is increased during a boiling process, will the temperature also increase or will it remain constant? Why?

What is vapor pressure? How is it related to saturation pressure?

The analysis of a propeller that operates in water at 70F shows that the pressure at the tips of the propeller drops to 0.1 psia at high speeds. Determine if there is a danger of cavitation for this propeller.

A pump is used to transport water to a higher reservoir. If the water temperature is 20C, determine the lowest pressure that can exist in the pump without cavitation.

In a piping system, the water temperature remains under 30C. Determine the minimum pressure allowed in the system to avoid cavitation.

The analysis of a propeller that operates in water at 20C shows that the pressure at the tips of the propeller drops to 2 kPa at high speeds. Determine if there is a danger of cavitation for this propeller.

What is flow energy? Do fluids at rest possess any flow energy?

How do the energies of a flowing fluid and a fluid at rest compare? Name the specific forms of energy associated with each case.

What is the difference between the macroscopic and microscopic forms of energy?

What is total energy? Identify the different forms of energy that constitute the total energy.

List the forms of energy that contribute to the internal energy of a system.

How are heat, internal energy, and thermal energy related to each other?

Using average specific heats, explain how internal energy changes of ideal gases and incompressible substances can be determined.

Using average specific heats, explain how enthalpy changes of ideal gases and incompressible substances can be determined.

Saturated water vapor at 150C (enthalpy h 5 2745.9 kJ/kg) flows in a pipe at 50 m/s at an elevation of z 5 10 m. Determine the total energy of vapor in J/kg relative to the ground level.

What does the coefficient of compressibility of a fluid represent? How does it differ from isothermal compressibility?

What does the coefficient of volume expansion of a fluid represent? How does it differ from the coefficient of compressibility?

Can the coefficient of compressibility of a fluid be negative? How about the coefficient of volume expansion?

Water at 15C and 1 atm pressure is heated to 100C at constant pressure. Using coefficient of volume expansion data, determine the change in the density of water. Answer: 238.7 kg/m3

It is observed that the density of an ideal gas increases by 10 percent when compressed isothermally from 10 atm to 11 atm. Determine the percent increase in density of the gas if it is compressed isothermally from 1000 atm to 1001 atm.

Using the definition of the coefficient of volume expansion and the expression bideal gas 5 1/T, show that the percent increase in the specific volume of an ideal gas during isobaric expansion is equal to the percent increase in absolute temperature.

Water at 1 atm pressure is compressed to 400 atm pressure isothermally. Determine the increase in the density of water. Take the isothermal compressibility of water to be 4.80 3 1025 atm21.

The volume of an ideal gas is to be reduced by half by compressing it isothermally. Determine the required change in pressure.

Saturated refrigerant-134a liquid at 10C is cooled to 0C at constant pressure. Using coefficient of volume expansion data, determine the change in the density of the refrigerant.

A water tank is completely filled with liquid water at 20C. The tank material is such that it can withstand tension caused by a volume expansion of 0.8 percent. Determine the maximum temperature rise allowed without jeopardizing safety. For simplicity, assume b 5 constant 5 b at 40C.

Repeat Prob. 246 for a volume expansion of 1.5 percent for water.

The density of seawater at a free surface where the pressure is 98 kPa is approximately 1030 kg/m3. Taking the bulk modulus of elasticity of seawater to be 2.34 3 109 N/m2 and expressing variation of pressure with depth z as dP 5 rg dz determine the density and pressure at a depth of 2500 m. Disregard the effect of temperature.

Taking the coefficient of compressibility of water to be 7 3 105 psia, determine the pressure increase required to reduce the volume of water by (a) 1 percent and (b) 2 percent.

Ignoring any losses, estimate how much energy (in units of Btu) is required to raise the temperature of water in a 75-gallon hot-water tank from 60F to 110F.

Prove that the coefficient of volume expansion for an ideal gas is bideal gas 5 1/T.

The ideal gas equation of state is very simple, but its range of applicability is limited. A more accurate but complicated equation is the Van der Waals equation of state given by P 5 RT v 2 b 2 a v 2 where a and b are constants depending on critical pressure and temperatures of the gas. Predict the coefficient of compressibility of nitrogen gas at T 5 175 K and v5 0.00375 m3/kg, assuming the nitrogen to obey the Van der Waals equation of state. Compare your result with the ideal gas value. Take a 5 0.175 m6?kPa/kg2 and b 5 0.00138 m3/kg for the given conditions. The experimentally measured pressure of nitrogen is 10,000 kPa.

A frictionless piston-cylinder device contains 10 kg of water at 20C at atmospheric pressure. An external force F is then applied on the piston until the pressure inside the cylinder increases to 100 atm. Assuming the coefficient of compressibility of water remains unchanged during the compression; estimate the energy needed to compress the water isothermally. Answer: 29.4 J FIGURE P253 Water Pressure gauge

Reconsider Prob. 253. Assuming a linear pressure increase during the compression, estimate the energy needed to compress the water isothermally.

What is sound? How is it generated? How does it travel? Can sound waves travel in a vacuum?

In which medium does a sound wave travel faster: in cool air or in warm air?

In which medium will sound travel fastest for a given temperature: air, helium, or argon?

In which medium does a sound wave travel faster: in air at 20C and 1 atm or in air at 20C and 5 atm?

Does the Mach number of a gas flowing at a constant velocity remain constant? Explain.

Is it realistic to approximate that the propagation of sound waves is an isentropic process? Explain.

Is the sonic velocity in a specified medium a fixed quantity, or does it change as the properties of the medium change? Explain.

The Airbus A-340 passenger plane has a maximum takeoff weight of about 260,000 kg, a length of 64 m, a wing span of 60 m, a maximum cruising speed of 945 km/h, a seating capacity of 271 passengers, a maximum cruising altitude of 14,000 m, and a maximum range of 12,000 km. The air temperature at the crusing altitude is about 260C. Determine the Mach number of this plane for the stated limiting conditions.

Carbon dioxide enters an adiabatic nozzle at 1200 K with a velocity of 50 m/s and leaves at 400 K. Assuming constant specific heats at room temperature, determine the Mach number (a) at the inlet and (b) at the exit of the nozzle. Assess the accuracy of the constant specific heat approximation. Answers: (a) 0.0925, (b) 3.73

Nitrogen enters a steady-flow heat exchanger at 150 kPa, 10C, and 100 m/s, and it receives heat in the amount of 120 kJ/kg as it flows through it. Nitrogen leaves the heat exchanger at 100 kPa with a velocity of 200 m/s. Determine the Mach number of the nitrogen at the inlet and the exit of the heat exchanger.

Assuming ideal gas behavior, determine the speed of sound in refrigerant-134a at 0.9 MPa and 60C.

Determine the speed of sound in air at (a) 300 K and (b) 800 K. Also determine the Mach number of an aircraft moving in air at a velocity of 330 m/s for both cases.

Steam flows through a device with a pressure of 120 psia, a temperature of 700F, and a velocity of 900 ft/s. Determine the Mach number of the steam at this state by assuming ideal-gas behavior with k 5 1.3. Answer: 0.441

Reconsider Prob. 267E. Using EES (or other) software, compare the Mach number of steam flow over the temperature range 350 to 700F. Plot the Mach number as a function of temperature.

Air expands isentropically from 170 psia and 200F to 60 psia. Calculate the ratio of the initial to final speed of sound. Answer: 1.16

Air expands isentropically from 2.2 MPa and 77C to 0.4 MPa. Calculate the ratio of the initial to the final speed of sound. Answer: 1.28

Repeat Prob. 270 for helium gas.

The isentropic process for an ideal gas is expressed as Pvk 5 constant. Using this process equation and the definition of the speed of sound (Eq. 224), obtain the expression for the speed of sound for an ideal gas (Eq. 226).

What is viscosity? What is the cause of it in liquids and in gases? Do liquids or gases have higher dynamic viscosities?

What is a Newtonian fluid? Is water a Newtonian fluid?

How does the kinematic viscosity of (a) liquids and (b) gases vary with temperature?

How does the dynamic viscosity of (a) liquids and (b) gases vary with temperature?

Consider two identical small glass balls dropped into two identical containers, one filled with water and the other with oil. Which ball will reach the bottom of the container first? Why?

The viscosity of a fluid is to be measured by a viscometer constructed of two 5-ft-long concentric cylinders. The inner diameter of the outer cylinder is 6 in, and the gap between the two cylinders is 0.035 in. The outer cylinder is rotated at 250 rpm, and the torque is measured to be 1.2 lbf?ft. Determine the viscosity of the fluid. Answer: 0.000272 lbf?s/ft2

A 50-cm 3 30-cm 3 20-cm block weighing 150 N is to be moved at a constant velocity of 0.80 m/s on an inclined surface with a friction coefficient of 0.27. (a) Determine the force F that needs to be applied in the horizontal direction. (b) If a 0.40-mm-thick oil film with a dynamic viscosity of 0.012 Pa?s is applied between the block and inclined surface, determine the percent reduction in the required force. 150 N F 30 cm 50 cm 20 V= 0.80 m/s

Consider the flow of a fluid with viscosity m through a circular pipe. The velocity profile in the pipe is given as u(r) 5 umax(1 2 rn/Rn), where umax is the maximum flow velocity, which occurs at the centerline; r is the radial distance from the centerline; and u(r) is the flow velocity at any position r. Develop a relation for the drag force exerted on the pipe wall by the fluid in the flow direction per unit length of the pipe. u(r) = umax(1 rn/Rn)

A thin 30-cm 3 30-cm flat plate is pulled at 3 m/s horizontally through a 3.6-mm-thick oil layer sandwiched between two plates, one stationary and the other moving at a constant velocity of 0.3 m/s, as shown in Fig. P281. The dynamic viscosity of the oil is 0.027 Pa?s. Assuming the velocity in each oil layer to vary linearly, (a) plot the velocity profile and find the location where the oil velocity is zero and (b) determine the force that needs to be applied on the plate to maintain this motion. Fixed wall Moving wall h1 = 1 mm = 3 m/s h2 = 2.6 mm w = 0.3 m/s V V

A rotating viscometer consists of two concentric cylinders an inner cylinder of radius Ri rotating at angular velocity (rotation rate) vi, and a stationary outer cylinder of inside radius Ro. In the tiny gap between the two cylinders is the fluid of viscosity m. The length of the cylinders (into the page in Fig. P282) is L. L is large such that end effects 30 cm Driving shaft Driven shaft SAE 30W oil 2 mm FIGURE P283 Liquid: r, m Rotating inner cylinder Stationary outer cylinder Ro Ri vi

The clutch system shown in Fig. P283 is used to transmit torque through a 2-mm-thick oil film with m 5 0.38 N?s/m2 between two identical 30-cm-diameter disks. When the driving shaft rotates at a speed of 1450 rpm, the driven shaft is observed to rotate at 1398 rpm. Assuming a linear velocity profile for the oil film, determine the transmitted torque. Driving shaft Driven shaft SAE 30W oil

Reconsider Prob. 283. Using EES (or other) software, investigate the effect of oil film thickness on the torque transmitted. Let the film thickness vary from 0.1 mm to 10 mm. Plot your results, and state your conclusions.

The dynamic viscosity of carbon dioxide at 50C and 200C are 1.612 3 1025 Pa?s and 2.276 3 1025 Pa?s, respectively. Determine the constants a and b of Sutherland correlation for carbon dioxide at atmospheric pressure. Then predict the viscosity of carbon dioxide at 100C and compare your result against the value given in Table A-10.

One of the widely used correlations to describe the variation of the viscosity of gases is the power-law equation given by m/m0 5 (T/T0)n, where m0 and T0 are the reference viscosity and temperature, respectively. Using the power and Sutherland laws, examine the variation of the air viscosity for the temperature range 100C (373 K) to 1000C (1273 K). Plot your results to compare with values listed in Table A-9. Take the reference temperature as 0C and n 5 0.666 for the atmospheric air.

For flow over a plate, the variation of velocity with vertical distance y from the plate is given as u(y) 5 ay 2 by2 where a and b are constants. Obtain a relation for the wall shear stress in terms of a, b, and m.

In regions far from the entrance, fluid flow through a circular pipe is one dimensional, and the velocity profile for laminar flow is given by u(r) 5 umax(1 2 r 2/R2), where R is the radius of the pipe, r is the radial distance from the center of the pipe, and umax is the maximum flow velocity, which occurs at the center. Obtain (a) a relation for the drag force applied by the fluid on a section of the pipe of length L and (b) the value of the drag force for water flow at 20C with R 5 0.08 m, L 5 30 m, umax 5 3 m/s, and m 5 0.0010 kg/m?s.

Repeat Prob. 288 for umax 5 7 m/s. Answer: (b) 2.64 N

A frustum-shaped body is rotating at a constant angular speed of 200 rad/s in a container filled with SAE 10W oil at 20C (m 5 0.100 Pa?s), as shown in Fig. P290. If the thickness of the oil film on all sides is 1.2 mm, determine the power required to maintain this motion. Also determine the reduction in the required power input when the oil temperature rises to 80C (m 5 0.0078 Pa?s).

A rotating viscometer consists of two concentric cylindersa stationary inner cyliner of radius Ri and an outer cylinder of inside radius Ro rotating at angular velocity (rotation rate) vo. In the tiny gap between the two cylinders is the fluid whose viscosity (m) is to be measured. The length

large plate is pulled at a constant speed of U 5 4 m/s over a fixed plate on 5-mm-thick engine oil film at 20C. Assuming a half-parabolic velocity profile in the oil film, as sketched, determine the shear stress developed on the upper plate and its direction. What would happen if a linear velocity profile were assumed?

A cylinder of mass m slides down from rest in a vertical tube whose inner surface is covered by a viscous oil of film thickness h. If the diameter and height of the cylinder are D and L, respectively, derive an expression for the velocity of the cylinder as a function of time, t. Discuss what will happen as t S q. Can this device serve as a viscometer?

A thin plate moves between two parallel, horizontal, stationary flat surfaces at a constant velocity of 5 m/s. The two stationary surfaces are spaced 4 cm apart, and the medium between them is filled with oil whose viscosity is 0.9 N?s/m2. The part of the plate immersed in oil at any given time is 2-m long and 0.5-m wide. If the plate moves through the mid-plane between the surfaces, determine the force required to maintain this motion. What would your response be if the plate was 1 cm from the bottom surface (h2) and 3 cm from the top surface (h1)?

Reconsider Prob. 294. If the viscosity of the oil above the moving plate is 4 times that of the oil below the plate, determine the distance of the plate from the bottom surface (h2) that will minimize the force needed to pull the plate between the two oils at constant velocity.

What is surface tension? What is its cause? Why is the surface tension also called surface energy?

A small-diameter tube is inserted into a liquid whose contact angle is 110. Will the level of liquid in the tube be higher or lower than the level of the rest of the liquid? Explain.

What is the capillary effect? What is its cause? How is it affected by the contact angle?

Consider a soap bubble. Is the pressure inside the bubble higher or lower than the pressure outside?

Is the capillary rise greater in small- or large-diameter tubes?

Consider a 0.15-mm diameter air bubble in a liquid. Determine the pressure difference between the inside and outside of the air bubble if the surface tension at the air-liquid interface is (a) 0.080 N/m and (b) 0.12 N/m.

A 2.4-in-diameter soap bubble is to be enlarged by blowing air into it. Taking the surface tension of soap solution to be 0.0027 lbf/ft, determine the work input required to inflate the bubble to a diameter of 2.7 in.

A 1.2-mm-diameter tube is inserted into an unknown liquid whose density is 960 kg/m3, and it is observed that the liquid rises 5 mm in the tube, making a contact angle of 15. Determine the surface tension of the liquid.

surface tension of the liquid. 2104 Determine the gage pressure inside a soap bubble of diameter (a) 0.2 cm and (b) 5 cm at 20C.

A 0.03-in-diameter glass tube is inserted into kerosene at 68F. The contact angle of kerosene with a glass surface is 26. Determine the capillary rise of kerosene in the tube. Answer: 0.65 in FIGURE P293 Oil film, h Cylinder L D FIGURE P2105E h 0.0

The surface tension of a liquid is to be measured using a liquid film suspended on a U-shaped wire frame with an 8-cm-long movable side. If the force needed to move the wire is 0.024 N, determine the surface tension of this liquid in air.

A capillary tube of 1.2 mm diameter is immersed vertically in water exposed to the atmosphere. Determine how high water will rise in the tube. Take the contact angle at the inner wall of the tube to be 6 and the surface tension to be 1.00 N/m. Answer: 0.338 m

A capillary tube is immersed vertically in a water container. Knowing that water starts to evaporate when the pressure drops below 2 kPa, determine the maximum capillary rise and tube diameter for this maximum-rise case. Take the contact angle at the inner wall of the tube to be 6 and the surface tension to be 1.00 N/m.

Contrary to what you might expect, a solid steel ball can float on water due to the surface tension effect. Determine the maximum diameter of a steel ball that would float on water at 20C. What would your answer be for an aluminum ball? Take the densities of steel and aluminum balls to be 7800 kg/m3 and 2700 kg/m3, respectively.

Nutrients dissolved in water are carried to upper parts of plants by tiny tubes partly because of the capillary effect. Determine how high the water solution will rise in a tree in a 0.0026-mm-diameter tube as a result of the capillary effect. Treat the solution as water at 20C with a contact angle of 15. Answer: 11.1 m

Derive a relation for the capillary rise of a liquid between two large parallel plates a distance t apart inserted into the liquid vertically. Take the contact angle to be f.

Consider a 55-cm-long journal bearing that is lubricated with oil whose viscosity is 0.1 kg/m?s at 20C at the beginning of operation and 0.008 kg/m?s at the anticipated steady operating temperature of 80C. The diameter of the shaft is 8 cm, and the average gap between the shaft and the journal is 0.08 cm. Determine the torque needed to overcome the bearing friction initially and during steady operation when the shaft is rotated at 1500 rpm.

The diameter of one arm of a U-tube is 5 mm while the other arm is large. If the U-tube contains some water, and both surfaces are exposed to atmospheric pressure, determine the difference between the water levels in the two arms.

The combustion in a gasoline engine may be approximated by a constant volume heat addition process, and the contents of the combustion chamber both before and after

A rigid tank contains an ideal gas at 300 kPa and 600 K. Half of the gas is withdrawn from the tank and the gas is at 100 kPa at the end of the process. Determine (a) the final temperature of the gas and (b) the final pressure if no mass were withdrawn from the tank and the same final temperature were reached at the end of the process.

The absolute pressure of an automobile tire is measured to be 320 kPa before a trip and 335 kPa after the trip. Assuming the volume of the tire remains constant at 0.022 m3, determine the percent increase in the absolute temperature of the air in the tire.

The pressure on the suction side of pumps is typically low, and the surfaces on that side of the pump are susceptible to cavitation, especially at high fluid temperatures. If the minimum pressure on the suction side of a water pump is 0.95 psia absolute, determine the maximum water temperature to avoid the danger of cavitation.

The composition of a liquid with suspended solid particles is generally characterized by the fraction of solid particles either by weight or mass, Cs, mass 5 ms/mm or by volume, Cs, vol 5 Vs/Vm where m is mass and V is volume. The subscripts s and m indicate solid and mixture, respectively. Develop an expression for the specific gravity of a waterbased suspension in terms of Cs, mass and Cs, vol.

The specific gravities of solids and carrier fluids of a slurry are usually known, but the specific gravity of the slurry depends on the concentration of the solid particles. Show that the specific gravity of a water-based slurry can be expressed in terms of the specific gravity of the solid SGs and the mass concentration of the suspended solid particles Cs, mass as SGm 5 1 1 1 Cs, mass(1/SGs 2 1)

A 10-m3 tank contains nitrogen at 25C and 800 kPa. Some nitrogen is allowed to escape until the pressure in the tank drops to 600 kPa. If the temperature at this point is 20C, determine the amount of nitrogen that has escaped. Answer: 21.5 kg

A closed tank is partially filled with water at 60C. If the air above the water is completely evacuated, determine the absolute pressure in the evacuated space. Assume the temperature to remain constant.

The variation of the dynamic viscosity of water with absolute temperature is given as T, K m, Pa?s 273.15 1.787 3 1023 278.15 1.519 3 1023 283.15 1.307 3 1023 293.15 1.002 3 1023 303.15 7.975 3 1024 313.15 6.529 3 1024 333.15 4.665 3 1024 353.15 3.547 3 1024 373.15 2.828 3 1024

newly produced pipe with diameter of 2 m and length 15 m is to be tested at 10 MPa using water at 15C. After sealing both ends, the pipe is first filled with water and then the pressure is increased by pumping additional water into the test pipe until the test pressure is reached. Assuming no deformation in the pipe, determine how much additional water needs to be pumped into the pipe. Take the coefficient of compressibility to be 2.10 3 109 Pa. Answer: 224 kg

Although liquids, in general, are hard to compress, the compressibility effect (variation in the density) may become unavoidable at the great depths in the oceans due to enormous pressure increase. At a certain depth the pressure is reported to be 100 MPa and the average coefficient of compressibility is about 2350 MPa. (a) Taking the liquid density at the free surface to be r0 5 1030 kg/m3, obtain an analytical relation between density and pressure, and determine the density at the specified pressure. Answer: 1074 kg/m3

Consider laminar flow of a Newtonian fluid of viscosity m between two parallel plates. The flow is one-dimensional, and the velocity profile is given as u(y) 5 4umax [ y/h 2 (y/h)2], where y is the vertical coordinate from the bottom surface, h is the distance between the two plates,

Two immiscible Newtonian liquids flow steadily between two large parallel plates under the influence of an applied pressure gradient. The lower plate is fixed while the upper one is pulled with a constant velocity of U 5 10 m/s. The thickness, h, of each layer of fluid is 0.5 m. The velocity profile for each layer is given by V1 5 6 1 ay 2 3y2, 20.5 # y # 0 V2 5 b 1 cy 2 9y2, 0 # y # 20.5 where a, b, and c are constants. (a) Determine the values of constants a, b, and c. (b) Develop an expression for the viscosity ratio, e.g., m1/m2 5? (c) Determine the forces and their directions exerted by the liquids on both plates if m1 5 1023 Pa?s and each plate has a surface area of 4 m2.

A shaft with a diameter of D 5 80 mm and a length of L 5 400 mm, shown in Fig. P2127 is pulled with a constant velocity of U 5 5 m/s through a bearing with variable diameter. The clearance between shaft and bearing, which varies from h1 5 1.2 mm to h2 5 0.4 mm, is filled with a Newtonian lubricant whose dynamic viscosity is 0.10 Pa?s. Determine the force required to maintain the axial movement of the shaft. Answer: 69 N

A 10-cm-diameter cylindrical shaft rotates inside a 40-cm-long 10.3-cm diameter bearing. The space between the shaft and the bearing is completely filled with oil whose viscosity at anticipated operating temperature is 0.300 N?s/m2. Determine the power required to overcome friction when the shaft rotates at a speed of (a) 600 rpm and (b) 1200 rpm.

Some rocks or bricks contain small air pockets in them and have a spongy structure. Assuming the air spaces form columns of an average diameter of 0.006 mm, determine how high water can rise in such a material. Take the surface tension of the airwater interface in that material to be 0.085 N/m.

The specific gravity of a fluid is specified to be 0.82. The specific volume of this fluid is (a) 0.00100 m3/kg (b) 0.00122 m3/kg (c) 0.0082 m3/kg (d ) 82 m3/kg (e) 820 m3/kg

The specific gravity of mercury is 13.6. The specific weight of mercury is (a) 1.36 kN/m3 (b) 9.81 kN/m3 (c) 106 kN/m3 (d ) 133 kN/m3 (e) 13,600 kN/m3

An ideal gas flows in a pipe at 20C. The density of the gas is 1.9 kg/m3 and its molar mass is 44 kg/kmol. The pressure of the gas is (a) 7 kPa (b) 72 kPa (c) 105 kPa (d ) 460 kPa (e) 4630 kPa

A gas mixture consists of 3 kmol oxygen, 2 kmol nitrogen, and 0.5 kmol water vapor. The total pressure of the gas mixture is 100 kPa. The partial pressure of water vapor in this gas mixture is (a) 5 kPa (b) 9.1 kPa (c) 10 kPa (d ) 22.7 kPa (e) 100 kPa

Liquid water vaporizes into water vapor as it flows in the piping of a boiler. If the temperature of water in the pipe is 180C, the vapor pressure of the water in the pipe is (a) 1002 kPa (b) 180 kPa (c) 101.3 kPa (d ) 18 kPa (e) 100 kPa

In a water distribution system, the pressure of water can be as low as 1.4 psia. The maximum temperature of water allowed in the piping to avoid cavitation is (a) 50F (b) 77F (c) 100F (d ) 113F (e) 140F

The thermal energy of a system refers to (a) Sensible energy (b) Latent energy (c) Sensible 1 latent energies (d ) Enthalpy (e) Internal energy

The difference between the energies of a flowing and stationary fluid per unit mass of the fluid is equal to (a) Enthalpy (b) Flow energy (c) Sensible energy (d ) Kinetic energy (e) Internal energy

The pressure of water is increased from 100 kPa to 1200 kPa by a pump. The temperature of water also increases by 0.15C. The density of water is 1 kg/L and its specific heat is cp 5 4.18 kJ/kg?C. The enthalpy change of the water during this process is (a) 1100 kJ/kg (b) 0.63 kJ/kg (c) 1.1 kJ/kg (d ) 1.73 kJ/kg (e) 4.2 kJ/kg

The coefficient of compressibility of a truly incompressible substance is (a) 0 (b) 0.5 (c) 1 (d ) 100 (e) Infinity

The pressure of water at atmospheric pressure must be raised to 210 atm to compress it by 1 percent. Then, the coefficient of compressibility value of water is (a) 209 atm (b) 20,900 atm (c) 21 atm (d ) 0.21 atm (e) 210,000 atm

When a liquid in a piping network encounters an abrupt flow restriction (such as a closing valve), it is locally compressed. The resulting acoustic waves that are produced strike the pipe surfaces, bends, and valves as they propagate and reflect along the pipe, causing the pipe to vibrate and produce a familiar sound. This is known as (a) Condensation (b) Cavitation (c) Water hammer (d ) Compression (e) Water arrest

The density of a fluid decreases by 5 percent at constant pressure when its temperature increases by 10C. The coefficient of volume expansion of this fluid is (a) 0.01 K21 (b) 0.005 K21 (c) 0.1 K21 (d ) 0.5 K21 (e) 5 K21

Water is compressed from 100 kPa to 5000 kPa at constant temperature. The initial density of water is 1000 kg/m3 and the isothermal compressibility of water is a 5 4.8 3 1025 atm21 . The final density of the water is (a) 1000 kg/m3 (b) 1001.1 kg/m3 (c) 1002.3 kg/m3 (d ) 1003.5 kg/m3 (e) 997.4 kg/m3

The speed of a spacecraft is given to be 1250 km/h in atmospheric air at 240C. The Mach number of this flow is (a) 35 .9 (b) 0.85 (c) 1.0 (d ) 1.13 (e) 2.74

The dynamic viscosity of air at 20C and 200 kPa is 1.83 3 1025 kg/m?s. The kinematic viscosity of air at this state is (a) 0.525 3 1025 m2/s (b) 0.77 3 1025 m2/s (c) 1.47 3 1025 m2/s (d ) 1.83 3 1025 m2/s (e) 0.380 3 1025 m2/s

A viscometer constructed of two 30-cm-long concentric cylinders is used to measure the viscosity of a fluid. The outer diameter of the inner cylinder is 9 cm, and the gap between the two cylinders is 0.18 cm. The inner cylinder is rotated at 250 rpm, and the torque is measured to be 1.4 N?m. The viscosity of the fluid is (a) 0.0084 N?s/m2 (b) 0.017 N?s/m2 (c) 0.062 N?s/m2 (d ) 0.0049 N?s/m2 (e) 0.56 N?s/m2

Which one is not a surface tension or surface energy (per unit area) unit? (a) lbf/ft (b) N?m/m2 (c) lbf/ft2 (d ) J/m2 (e) Btu/ft2

The surface tension of soap water at 20C is ss 5 0.025 N/m. The gage pressure inside a soap bubble of diameter 2 cm at 20C is (a) 10 Pa (b) 5 Pa (c) 20 Pa (d) 40 Pa (e) 0.5 Pa

A 0.4-mm-diameter glass tube is inserted into water at 20C in a cup. The surface tension of water at 20C is ss 5 0.073 N/m. The contact angle can be taken as zero degrees. The capillary rise of water in the tube is (a) 2.9 cm (b) 7.4 cm (c) 5.1 cm (d ) 9.3 cm (e) 14.0 cm

Design an experiment to measure the viscosity of liquids using a vertical funnel with a cylindrical reservoir of height h and a narrow flow section of diameter D and length L. Making appropriate assumptions, obtain a relation for viscosity in terms of easily measurable quantities such as density and volume flow rate.

Write an essay on the rise of the fluid to the top of trees by capillary and other effects.

Write an essay on the oils used in car engines in different seasons and their viscosities.

Consider the flow of water through a clear tube. It is sometimes possible to observe cavitation in the throat created by pinching off the tube to a very small diameter as sketched. We assume incompressible flow with negligible gravitational effects and negligible irreversibilities. You will learn later (Chap. 5) that as the duct cross-sectional area decreases, the velocity increases and the pressure decreases according to V1A1 5 V2 A2 and P1 1 r V21 2 5 P2 1 r V22 2 respectively, where V1 and V2 are the average velocities through cross-sectional areas A1 and A2. Thus, both the maximum

Even though steel is about 7 to 8 times denser than water, a steel paper clip or razor blade can be made to float on water! Explain and discuss. Predict what would happen if you mix some soap with the water.