Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 14, Problem 137P
To determine
The correct option for the net head produced by the centrifugal blower in
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A Francis radial-flow hydroturbine has the following dimensions, where location 2 is the inlet and location 1 is the outlet: r2 = 6.60 ft, r1 = 4.40 ft, b2 = 2.60 ft, and b1 = 7.20 ft. The runner blade angles are ?2 = 82° and ?1 = 46° at the turbine inlet and outlet, respectively. The runner rotates at n. = 120 rpm. The volume flow rate at design conditions is 4.70 ×106 gpm. Irreversible losses are neglected in this preliminary analysis. Calculate the angle ?2 through which the wicket gates should turn the flow, where ?2 is measured from the radial direction at the runner inlet. Calculate the swirl angle ?1, where ?1 is measured from the radial direction at the runner outlet. Does this turbine have forward or reverse swirl? Predict the power output (hp) and required net head (ft).
Two identical centrifugal pumps connected in series are used to pump water between two storage tanks that are open to the atmosphere, through a cylindrical pipe with ID of 0.1 m on both the discharge and suction side. The total equivalent length on the suction and discharge sides are 20m and 40m respectively. The change in static head is 7m.
Pump Data:
Q( m3/s)
0
0.01
0.02
0.03
0.04
Δh (m)
23
21.5
18.5
11
3
Assume the friction factor f to be 0.02 and is constant throughout the range of flowrates.
a) Determine the operating point of the system.
b) Determine the power requirement for the pumping system if the pump efficiency is 75%.
A Francis radial-flow hydroturbine is being designed with the following dimensions: r2 = 2.00 m, r1 = 1.42 m, b2 = 0.731 m, and b1 = 2.20 m. The runner rotates at n. = 180 rpm. The wicket gates turn the flow by angle ?2 = 30° from radial at the runner inlet, and the flow at the runner outlet is at angle ?1 = 10° from radial. The volume flow rate at design conditions is 340 m3 /s, and the gross head provided by the dam is Hgross = 90.0 m. For the preliminary design, irreversible losses are neglected. Calculate the turbine specific speed of the turbine. Provide answers in both dimensionless form and in customary U.S. units. Is it in the normal range for a Francis turbine? If not, what type of turbine would be more appropriate?
Chapter 14 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 14 - What is the more common term for an...Ch. 14 - What the primary differences between fans,...Ch. 14 - List at least two common examples of fans, of...Ch. 14 - Discuss the primary difference between a porn...Ch. 14 - Explain why there is an “extra” term in the...Ch. 14 - For a turbine, discuss the difference between...Ch. 14 - Prob. 7CPCh. 14 - Prob. 8PCh. 14 - Prob. 9PCh. 14 - Prob. 10CP
Ch. 14 - There are three main categories of dynamic pumps....Ch. 14 - For each statement about cow cetrifugal the...Ch. 14 - Prob. 13CPCh. 14 - Consider flow through a water pump. For each...Ch. 14 - Write the equation that defines actual (available)...Ch. 14 - Consider a typical centrifugal liquid pump. For...Ch. 14 - Prob. 17CPCh. 14 - Consider steady, incompressible flow through two...Ch. 14 - Prob. 19CPCh. 14 - Prob. 20PCh. 14 - Suppose the pump of Fig. P1 4-19C is situated...Ch. 14 - Prob. 22PCh. 14 - Prob. 23EPCh. 14 - Consider the flow system sketched in Fig. PI 4-24....Ch. 14 - Prob. 25PCh. 14 - Repeat Prob. 14-25, but with a rough pipe-pipe...Ch. 14 - Consider the piping system of Fig. P14—24. with...Ch. 14 - The performance data for a centrifugal water pump...Ch. 14 - For the centrifugal water pump of Prob. 14-29,...Ch. 14 - Suppose the pump of Probs. 14-29 and 14-30 is used...Ch. 14 - Suppose you are looking into purchasing a water...Ch. 14 - The performance data of a water pump follow the...Ch. 14 - For the application at hand, the flow rate of...Ch. 14 - A water pump is used to pump water from one large...Ch. 14 - For the pump and piping system of Prob. 14-35E,...Ch. 14 - A water pump is used to pump water from one large...Ch. 14 - Suppose that the free surface of the inlet...Ch. 14 - Calculate the volume flow rate between the...Ch. 14 - Comparing the results of Probs. 14-39 and 14-43,...Ch. 14 - Prob. 45PCh. 14 - The performance data for a centrifugal water pump...Ch. 14 - Transform each column of the pump performance data...Ch. 14 - 14-51 A local ventilation system (a hood and duct...Ch. 14 - Prob. 52PCh. 14 - Repeat Prob. 14-51, ignoring all minor losses. How...Ch. 14 - Suppose the one- way of Fig. P14-51 malfunctions...Ch. 14 - A local ventilation system (a hood and duct...Ch. 14 - For the duct system and fan of Prob. 14-55E,...Ch. 14 - Repeat Prob. 14-55E, ignoring all minor losses....Ch. 14 - A self-priming centrifugal pump is used to pump...Ch. 14 - Repeat Prob. 14-60. but at a water temperature of...Ch. 14 - Repeat Prob. 14-60, but with the pipe diameter...Ch. 14 - Prob. 63EPCh. 14 - Prob. 64EPCh. 14 - Prob. 66PCh. 14 - Prob. 67PCh. 14 - Prob. 68PCh. 14 - Prob. 69PCh. 14 - Two water pumps are arranged in Series. The...Ch. 14 - The same two water pumps of Prob. 14-70 are...Ch. 14 - Prob. 72CPCh. 14 - Name and briefly describe the differences between...Ch. 14 - Discuss the meaning of reverse swirl in reaction...Ch. 14 - Prob. 75CPCh. 14 - Prob. 76CPCh. 14 - Prob. 77PCh. 14 - Prob. 78PCh. 14 - Prob. 79PCh. 14 - Prob. 80PCh. 14 - Wind ( =1.204kg/m3 ) blows through a HAWT wind...Ch. 14 - Prob. 82PCh. 14 - Prob. 84CPCh. 14 - A Francis radial-flow hydroturbine has the...Ch. 14 - Prob. 87PCh. 14 - Prob. 88PCh. 14 - Prob. 89PCh. 14 - Prob. 90CPCh. 14 - Prob. 91CPCh. 14 - Discuss which dimensionless pump performance...Ch. 14 - Prob. 93CPCh. 14 - Prob. 94PCh. 14 - Prob. 95PCh. 14 - Prob. 96PCh. 14 - Prob. 97PCh. 14 - Prob. 98PCh. 14 - Prob. 99PCh. 14 - Prob. 100EPCh. 14 - Prob. 101PCh. 14 - Calculate the pump specific speed of the pump of...Ch. 14 - Prob. 103PCh. 14 - Prob. 104PCh. 14 - Prob. 105PCh. 14 - Prob. 106PCh. 14 - Prob. 107EPCh. 14 - Prob. 108PCh. 14 - Prob. 109PCh. 14 - Prob. 110PCh. 14 - Prove that the model turbine (Prob. 14-109) and...Ch. 14 - Prob. 112PCh. 14 - Prob. 113PCh. 14 - Prob. 114PCh. 14 - Prob. 115CPCh. 14 - Prob. 116CPCh. 14 - Prob. 117CPCh. 14 - Prob. 118PCh. 14 - For two dynamically similar pumps, manipulate the...Ch. 14 - Prob. 120PCh. 14 - Prob. 121PCh. 14 - Prob. 122PCh. 14 - Calculate and compare the turbine specific speed...Ch. 14 - Prob. 124PCh. 14 - Prob. 125PCh. 14 - Prob. 126PCh. 14 - Prob. 127PCh. 14 - Prob. 128PCh. 14 - Prob. 129PCh. 14 - Prob. 130PCh. 14 - Prob. 131PCh. 14 - Prob. 132PCh. 14 - Prob. 133PCh. 14 - Prob. 134PCh. 14 - Prob. 135PCh. 14 - A two-lobe rotary positive-displacement pump moves...Ch. 14 - Prob. 137PCh. 14 - Prob. 138PCh. 14 - Prob. 139PCh. 14 - Prob. 140PCh. 14 - Which choice is correct for the comparison of the...Ch. 14 - Prob. 142PCh. 14 - In a hydroelectric power plant, water flows...Ch. 14 - Prob. 144PCh. 14 - Prob. 145PCh. 14 - Prob. 146PCh. 14 - Prob. 147PCh. 14 - Prob. 148PCh. 14 - Prob. 149PCh. 14 - Prob. 150PCh. 14 - Prob. 151P
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- A Francis radial-flow hydroturbine is being designed with the following dimensions: r2 = 2.00 m, r1 = 1.42 m, b2 = 0.731 m, and b1 = 2.20 m. The runner rotates at n. = 180 rpm. The wicket gates turn the flow by angle ?2 = 30° from radial at the runner inlet, and the flow at the runner outlet is at angle ?1 = 10° from radial. The volume flow rate at design conditions is 340 m3 /s, and the gross head provided by the dam is Hgross = 90.0 m. For the preliminary design, irreversible losses are neglected. Calculate the inlet and outlet runner blade angles ?2 and ?1, respectively, and predict the power output (MW) and required net head (m). Is the design feasible?arrow_forwardA converging elbow turns water through an angle of 135º in a vertical plane. The flow cross-sectional diameter is 400 mm at the elbow inlet, section (1), and 200 mm at the elbow outlet,section (2). The elbow flow passage volume is 0.2 m3between sections (1) and (2). The water volume flowrate is 0.4 m3/s, and the elbow inlet and outlet pressures are 150 kPa(gage) and 90 kPa(gage). The empty elbow mass is 12 kg. Calculate the horizontal and vertical anchoring forces required to hold the elbow in place. Assume: a) Steady, Incompressible, Uniform fluid flow at inlet/ outlet. ρwater= 1000 kg/m3.arrow_forwardThe dimensions of a Francis radial-flow hydroturbine are r2 = 2.00 m, r1 = 1.30 m, b2 = 0.85 m, and b1 = 2.10 m, where location 2 is the inlet and location 1 is the outlet. At the turbine inlet and outflow, the runner blade angles are β2 = 71.4° and β1 = 15.3°, respectively. The runner rotates at a rate of ń = 160 rpm. At design conditions, the volume flow rate is 80.0 m3 /sarrow_forward
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- A centrifugal blower rotates at 1400 rpm. Air enters the impeller normal to the blades (?1 = 0°) and exits at an angle of 25° (?2 = 25°). The inlet radius is r1 = 6.5 cm, and the inlet blade width b1 = 8.5 cm. The outlet radius and blade width are r2 = 12 cm and b2 = 4.5 cm, respectively. The volume flow rate is 0.22 m3 /s. What is the net head produced by this blower in meters of air? (a) 12.3 m (b) 3.9 m (c) 8.8 m (d) 5.4 m (e) 16.4 marrow_forwardThe centrifugal pump in Fig. has r1 = 15 cm,r2 = 25 cm, b1 =b2 = 6 cm, and rotates counterclockwiseat 600 r/min. A sample blade is shown. Assume α1 = 90°.Estimate the theoretical flow rate and head produced, forwater at 20°C, and comment.arrow_forwardThe dimensions of a Francis radial-flow hydroturbine are r2 = 2.00 m, r1 = 1.30 m, b2 = 0.85 m, and b1 = 2.10 m, where location 2 is the inlet and location 1 is the outlet. At the turbine inlet and outflow, the runner blade angles are β2 = 71.4° and β1 = 15.3°, respectively. The runner rotates at a rate of ń = 160 rpm. At design conditions, the volume flow rate is 80.0 m3 /s. (a) State the necessary assumptions and calculate the angle α2 at which the wicket gates should turn the flow (Figure Q1), with α2 measured from the radial direction at the runner inlet. (b) Calculate the swirl angle α1 (Figure Q1), where α1 is the angle measured from the radial direction at the runner output. (c) Calculate the needed net head and power output. (d) Discuss the actual power output and head required for actual case of the turbine (irreversibility not neglected). (Properties For water at 20oC, ρ = 998.0 kg/m3)arrow_forward
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