FUNDAMENTALS OF THERMAL-FLUID SCIENCESY. A. Çengel, R. H. Turner, J. M. Cimbala

McGraw Hill, 3rd edition2-14 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.

z, km r, kg/m36377 1.2256378 1.1126379 1.0076380 0.90936381 0.81946382 0.73646383 0.66016385 0.52586387 0.41356392 0.19486397 0.088916402 0.04008

*2–34 The water in a tank is pressurized by air, and the pressure is measured by a multifluid manometer as shown in Fig. P2–34. Determine the gage pressure of air in the tank if h1 _ 0.2 m, h2 _ 0.3 m, and h3 _ 0.46 m. Take the densities of water, oil, and mercury to be 1000 kg/m3, 850 kg/m3, and 13,600 kg/m3, respectively.

*2–39 The diameters of the pistons shown in Fig. P2–39 are D1 _ 8 cm and D2 _ 5 cm. Determine the pressure in chamber 3, in kPa, when the other pressures are P1 _ 1050 kPa and P2 _ 1400 kPa.

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2–51 Both a gage and a manometer are attached to a gas tank to measure its pressure. If the reading on the pressure gage is 80 kPa, determine the distance between the two fluid levels of the manometer if the fluid is (a) mercury (r _ 13,600 kg/m3) or (b) water (r _ 1000 kg/m3).

*2–67 The top part of a water tank is divided into two compartments, as shown in Fig. P2–67. Now a fluid with an unknown density is poured into one side, and the water level rises a certain amount on the other side to compensate for this effect. Based on the final fluid heights shown on the figure, determine the density of the fluid added. Assume the liquid does not mix with water.

2–87 A glass tube is attached to a water pipe, as shown in Fig. P2–87. If the water pressure at the bottom of the tube is 115 kPa and the local atmospheric pressure is 92 kPa, determine how high the water will rise in the tube, in m. Take the density of water to be 1000 kg/m3.

2–95 Pressure transducers are commonly used to measure pressure by generating analog signals usually in the range of 4 mA to 20 mA or 0 V-dc to 10 V-dc in response to applied pressure. The system whose schematic is shown in Fig. P2–95 can be used to calibrate pressure transducers. A rigid container is filled with pressurized air, and pressure is measured by the manometer attached. A valve is used to regulate the pressure in the container. Both the pressure and the electric signal are measured simultaneously for various settings, and the results are tabulated. For the given set of measurements, obtain the calibration curve in the form of P _ aI _ b, where a and b are constants, and calculate the pressure that corresponds to a signal of 10 mA.

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*9–9 In a piping system, the water temperature remains under 40_C. Determine the minimum pressure allowed in the system to avoid cavitation.*9–10 The analysis of a propeller that operates in water at 20_C 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.9–11 A pump is used to transport water to a higher reservoir. If the water temperature is 25_C, determine the lowest pressure that can exist in the pump without cavitation.*9–16 Determine the speed of sound in air at (a) 300 K and (b) 1000 K. Also determine the Mach number of an aircraft moving in air at a velocity of 240 m/s for both cases.9–17 Assuming ideal gas behavior, determine the speed of sound in refrigerant-134a at 0.1 MPa and 60°C.9–19 Air expands isentropically from 1.5 MPa and 60°C to 0.4 MPa. Calculate the ratio of the initial to final speed of sound. Answer: 1.219–26C How does the kinematic viscosity of (a) liquids and (b) gases vary with temperature?9–29 A thin 20-cm _ 20-cm flat plate is pulled at 1 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. P9–29. The dynamic viscosity of 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.

*9–35 The viscosity of a fluid is to be measured by a viscometer constructed of two 75-cm-long concentric cylinders. The outer diameter of the inner cylinder is 15 cm, and the gap between the two cylinders is 0.12 cm. The inner cylinder is rotated at 200 rpm, and the torque is measured to be 0.8 N _ m. Determine the viscosity of the fluid.

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9–43 A 0.8-mm-diameter glass tube is inserted into kerosene at 20°C. The contact angle of kerosene with a glass surface is 26°. Determine the capillary rise of kerosene in the tube. Answer: 16 mm

9–44 A 1.9-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. *9–45 Determine the gage pressure inside a soap bubble of diameter (a) 0.2 cm and (b) 5 cm at 20°C.*9–46 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 0.005-mm-diameter tube as a result of the capillary effect. Treat the solution as water at 20°C with a contact angle of 15°. Answer: 5.75 m

9–47 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 0.012 N, determine the surface tension of this liquid in air.9–48 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 20°C. 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.

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10–13 A 5-m-high, 5-m-wide rectangular plate blocks the end of a 4-m-deep freshwater channel, as shown in Fig. P10–13. The plate is hinged about a horizontal axis along its upper edge through a point A and is restrained from opening by a fixed ridge at point B. Determine the force exerted on the plate by the ridge.

10–14 Reconsider Prob. 10–13. Using EES (or other) software, investigate the effect of water depthon the force exerted on the plate by the ridge. Let the water depth vary from 0 m to 5 m in increments of 0.5 m. Tabulate and plot your results.

*10–15 The flow of water from a reservoir is controlled by a 1.5-m-wide L-shaped gate hinged at point A, as shown in Fig. P10–15. If it is desired that the gate open when the water height is 3.6 m, determine the mass of the required weight W. Answer: 131,100 N

10–16 Repeat Prob. 10–15 for a water height of 2.4 m.*10–17 A water trough of semicircular cross section of radius 0.5 m consists of two symmetric parts hinged to each other at the bottom, as shown in Fig. P10–17. The two parts are held together by a cable and turnbuckle placed every 3 m along the length of the trough. Calculate the tension in each cable when the trough is filled to the rim.

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*10–18 The two sides of a V-shaped water trough are hinged to each other at the bottom where they meet, as shown in Fig. P10–18, making an angle of 45° with the ground from both sides. Each side is 0.75 m wide, and the two parts are held together by a cable and turnbuckle placed every 6 m along the length of the trough. Calculate the tension in each cable when the trough is filled to the rim. Answer: 5510 N

10–20 A retaining wall against a mud slide is to be constructed by placing 0.8-m-high and 0.2-m-wide rectangular concrete blocks (r _ 2700 kg/m3) side by side, as shown in Fig. P10–20. The friction coefficient between the ground and the concrete blocks is f _ 0.3, and the density of the mud is about 1800 kg/m3. There is concern that the concrete blocks may slide or tip over the lower left edge as the mud level rises. Determine the mud height at which (a) the blocks will overcome friction and start sliding and (b) the blocks will tip over.

10–21 Repeat Prob. 10–20 for 0.4-m-wide concrete blocks.

10–22 A 4-m-long quarter-circular gate of radius 3 m and of negligible weight is hinged about its upper edge A, as shown in Fig. P10–22. The gate controls the flow of water over the ledge at B, where the gate is pressed by a spring. Determine the minimum spring force required to keep the gate closed when the water level rises to A at the upper edge of the gate.

*10–23 Repeat Prob. 10–22 for a radius of 4 m for the gate. Answer: 314 Kn

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*10–37 The 200-kg, 5-m-wide rectangular gate shown in Fig. P10–37 is hinged at B and leans against the floor at A making an angle of 45° with the horizontal. The gate is to be opened from its lower edge by applying a normal force at its center. Determine the minimum force F required to open the water gate. Answer: 522 kN

10–38 Repeat Prob. 10–37 for a water height of 1.2 m above the hinge at B.

10–39 A 3-m-high, 6-m-wide rectangular gate is hinged at the top edge at A and is restrained by a fixed ridge at B. Determine the hydrostatic force exerted on the gate by the 5-m-high water and the location of the pressure center.

10–40 Repeat Prob. 10–39 for a total water height of 2 m.

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12–5 Consider a river flowing toward a lake at an average velocity of 3 m/s at a rate of 500 m3/s at a location 90 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. Answer: 444 MW

12–6 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.

12–7 At a certain location, wind is blowing steadily at 12 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/m3.12–8 Reconsider Prob. 12–7. Using EES (or other) software, investigate the effect of wind velocity and the blade span diameter on wind power generation. Let the velocity vary from 5 to 20 m/s in increments of 5 m/s, and the diameter to vary from 20 to 80 m in increments of 20 m. Tabulate the results, and discuss their significance.12–9 Water is pumped from a lake to a storage tank 20 m above at a rate of 70 L/s while consuming 20.4 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.

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*12–22C A glass manometer with oil as the working fluid is connected to an air duct as shown in Fig. P12–22C. Will the oil levels in the manometer be as in Fig. P12–22Ca or b? Explain. What would your response be if the flow direction is reversed?

12–25 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.12–27 The drinking water needs of an office are met by large water bottles. One end of a 0.6-cmdiameter plastic hose is inserted into the bottle placed on a high stand, while the other end with an on/off valve is maintained 0.6 m below the bottom of the bottle. If the water level in the bottle is 0.45 m when it is full, determine how long it will take at the minimum to fill a 0.25-L glass (a) when the bottle is first opened and (b) when the bottle is almost empty. Neglect frictional losses.

*12–30 A pressurized tank of water has a 10-cm-diameter orifice at the bottom, where water discharges to the atmosphere. The water level is 3 m above the outlet. The tank air pressure above the water level is 300 kPa (absolute) while the atmospheric pressure is 100 kPa. Neglecting frictional effects, determine the initial discharge rate of water from the tank. Answer: 0.168 m3/s

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12–39 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.

12–40 Air is flowing through a venturi meter whose diameter is 6.6 cm at the entrance part (location 1) and 4.6 cm at the throat (location 2). The gage pressure is measured to be 84 kPa at the entrance and 81 kPa at the throat. Neglecting frictional effects, show that the volume flow rate can be expressed as

and determine the flow rate of air. Take the air density to be 1.2 kg/m3.

*12–43 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 cover is airtight, and the air pressure above the water surface is 2 atm gage. The system is at sea level. Determine the maximum height to which the water stream could rise. Answer: 40.7 m

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*12–44 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.

12–45 The air velocity in a duct is measured by a Pitotstatic probe connected to a differential pressure gage. If the air is at 92 kPa absolute and 20°C and the reading of the differential pressure gage is 1.0 kPa, determine the air velocity. Answer: 42.8 m/s*12–52 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 and 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 of the fan–motor unit to be purchased, (b) the diameter of the 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.

12–53 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 7 m, determine the mechanical efficiency of the pump. Answer: 78.5 percent

12–57 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.

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12–58 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.*12–60 Water flows at a rate of 20 L/s through a horizontal pipe whose diameter is constant at 3 cm as shown in Fig. P12–60. 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. Answers: 0.204 m, 40 W

12–61 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.

12–62 The velocity profile for turbulent flow in a circular pipe is usually approximated as u(r) _ umax(1 _ r/R)1/n, where n _ 7. Determine the kinetic energy correction factor for this flow. Answer: 1.0612–63 An oil pump is drawing 35 kW of electric power while pumping oil with r _ 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 400 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.

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12–64 A 73-percent efficient 8.9-kW pump is pumping water from a lake to a nearby pool at a rate of 0.035 m3/s through a constant-diameter pipe. The free surface of the pool is 11 m above that of the lake. Determine the irreversible head loss of the piping system, in m, and the mechanical power used to overcome it.

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