Mercado de capitales

flow rate of water and the head loss caused by the nozzle meter.

8–111E The volume flow rate of liquid refrigerant-134a at 10°F (r ⫽ 83.31 lbm/ft3_{) is to be measured with a horizontal}

Venturi meter with a diameter of 5 in at the inlet and 2 in at the throat. If a differential pressure meter indicates a pressure drop of 7.4 psi, determine the flow rate of the refrigerant. Take the discharge coefficient of the Venturi meter to be 0.98. Review Problems

8–112 The compressed air requirements of a manufacturing facility are met by a 150-hp compressor that draws in air from the outside through an 8-m-long, 20-cm-diameter duct made of thin galvanized iron sheets. The compressor takes in air at a rate of 0.27 m3_{/s at the outdoor conditions of 15°C}

and 95 kPa. Disregarding any minor losses, determine the useful power used by the compressor to overcome the fric- tional losses in this duct. Answer: 9.66 W

tion of a circular stainless-steel duct of 20-cm diameter passes through the water. Air flows through the underwater section of the duct at 3 m/s at an average temperature of 15°C. For an overall fan efficiency of 62 percent, determine the fan power needed to overcome the flow resistance in this section of the duct.

8–114 The velocity profile in fully developed laminar flow in a circular pipe, in m/s, is given by u(r) ⫽ 6(1 ⫺ 100r2_),

where r is the radial distance from the centerline of the pipe in m. Determine (a) the radius of the pipe, (b) the average velocity through the pipe, and (c) the maximum velocity in the pipe.

8–115E The velocity profile in a fully developed laminar flow of water at 40°F in a 80-ft-long horizontal circular pipe, in ft/s, is given by u(r) ⫽ 0.8(1 ⫺ 625r2_{), where r is the radial}

distance from the centerline of the pipe in ft. Determine (a) the volume flow rate of water through the pipe, (b) the pressure drop across the pipe, and (c) the useful pumping power required to overcome this pressure drop.

8–116E Repeat Prob. 8–115E assuming the pipe is inclined 12° from the horizontal and the flow is uphill.

8–117 Consider flow from a reservoir through a horizontal pipe of length L and diameter D that penetrates into the side wall at a vertical distance H from the free surface. The flow rate through an actual pipe with a reentrant section (KL ⫽ 0.8) will be considerably less than the flow rate through the hole calculated assuming “frictionless” flow and thus zero loss. Obtain a relation for the “equivalent diameter” of the reentrant pipe for use in relations for frictionless flow through a hole and determine its value for a pipe friction fac- tor, length, and diameter of 0.018, 10 m, and 0.04 m, respec- tively. Assume the friction factor of the pipe to remain con- stant and the effect of the kinetic energy correction factor to be negligible.

8–118 Water is to be withdrawn from a 5-m-high water reservoir by drilling a well-rounded 3-cm-diameter hole with negligible loss at the bottom surface and attaching a horizon- tal 90° bend of negligible length. Taking the kinetic energy correction factor to be 1.05, determine the flow rate of water through the bend if (a) the bend is a flanged smooth bend

8 m 20 cm Air, 0.27 m3_/s 15°C, 95 kPa Air compressor 150 hp FIGURE P8–112

8–113 A house built on a riverside is to be cooled in sum- mer by utilizing the cool water of the river. A 15-m-long sec-

River Air Air, 3 m/s FIGURE P8–113 5 m FIGURE P8–118

and (b) the bend is a miter bend without vanes. Answers:

(a) 0.00603 m3_{/s, (b) 0.00478 m}3_/s

8–119 In a geothermal district heating system, 10,000 kg/s of hot water must be delivered a distance of 10 km in a horizontal pipe. The minor losses are negligi- ble, and the only significant energy loss will arise from pipe friction. The friction factor can be taken to be 0.015. Specify- ing a larger-diameter pipe would reduce water velocity, velocity head, pipe friction, and thus power consumption. But a larger pipe would also cost more money initially to pur- chase and install. Otherwise stated, there is an optimum pipe diameter that will minimize the sum of pipe cost and future electric power cost.

Assume the system will run 24 h/day, every day, for 30 years. During this time the cost of electricity will remain con- stant at $0.06/kWh. Assume system performance stays con- stant over the decades (this may not be true, especially if highly mineralized water is passed through the pipeline— scale may form). The pump has an overall efficiency of 80 percent. The cost to purchase, install, and insulate a 10-km pipe depends on the diameter D and is given by Cost ⫽ $106_D2_{, where D is in m. Assuming zero inflation and}

interest rate for simplicity and zero salvage value and zero maintenance cost, determine the optimum pipe diameter. 8–120 Water at 15°C is to be discharged from a reservoir at a rate of 18 L/s using two horizontal cast iron pipes con- nected in series and a pump between them. The first pipe is 20 m long and has a 6-cm diameter, while the second pipe is 35 m long and has a 4-cm diameter. The water level in the reservoir is 30 m above the centerline of the pipe. The pipe entrance is sharp-edged, and losses associated with the con- nection of the pump are negligible. Neglecting the effect of the kinetic energy correction factor, determine the required pumping head and the minimum pumping power to maintain the indicated flow rate.

FLUID MECHANICS

8–121 Reconsider Prob. 8–120. Using EES (or other) software, investigate the effect of the second pipe diameter on the required pumping head to maintain the

Water tank Pump 35 m 20 m 30 m 6 cm 4 cm FIGURE P8–120 500 m 30 cm 800 m 3 m3_/s Oil A B 45 cm FIGURE P8–123

indicated flow rate. Let the diameter vary from 1 to 10 cm in increments of 1 cm. Tabulate and plot the results.

8–122 Two pipes of identical diameter and material are connected in parallel. The length of pipe A is twice the length of pipe B. Assuming the flow is fully turbulent in both pipes and thus the friction factor is independent of the Reynolds number and disregarding minor losses, determine the ratio of the flow rates in the two pipes. Answer: 0.707

8–123 A pipeline that transports oil at 40°C at a rate of 3 m3_{/s branches out into two parallel pipes}

made of commercial steel that reconnect downstream. Pipe A is 500 m long and has a diameter of 30 cm while pipe B is 800 m long and has a diameter of 45 cm. The minor losses are considered to be negligible. Determine the flow rate through each of the parallel pipes.

60 psig

50 ft _{20 gpm}

Water main

FIGURE P8–125E

8–124 Repeat Prob. 8–123 for hot-water flow of a district heating system at 100°C.

8–125E A water fountain is to be installed at a remote loca- tion by attaching a cast iron pipe directly to a water main through which water is flowing at 70°F and 60 psig. The entrance to the pipe is sharp-edged, and the 50-ft-long piping system involves three 90° miter bends without vanes, a fully open gate valve, and an angle valve with a loss coefficient of 5 when fully open. If the system is to provide water at a rate of 20 gal/min and the elevation difference between the pipe and the fountain is negligible, determine the minimum diam- eter of the piping system. Answer: 0.76 in

CHAPTER 8