- A Francis radial-flow hydroturbine has the following dimensions, where location 2 is the inlet and location 1 is the outlet: r2 = 2.00 m, r1 = 1.30 m, b2 = 0.85 m, and b1 = 2.10 m. The runner blade
- Repeat the calculations of Prob. 15–52 for several angles of attack of the heating elements, from 0 (horizontal) to 90° (vertical). Use identical inlet conditions and wall conditions for each
- Calculate the turbine specific speed of the turbine in Prob. 14–85. Provide answers in both dimensionless form and in customary U.S. units. Is it in the normal range for a Francis turbine? If not,
- Comparing the results of Probs. 14–43 and 14–47, the volume flow rate increases as expected when one doubles the inner diameter of the pipe. One might expect that the Reynolds number increases as
- In the section on wind turbines, an expression was derived for the ideal power coefficient of a wind turbine, CP = 4a(1 – a)2. Prove that the maximum possible power coefficient occurs when a = 1/3.
- Look up the word affinity in a dictionary. Why do you suppose some engineers refer to the turbomachinery scaling laws as affinity laws?
- Calculate the fan specific speed of the fan of Probs. 14–51 and 14–96 at the best efficiency point for the case in which the BEP occurs at 13,600 Lpm. Provide answers in both dimensionless form
- Consider the pump of Prob. 14–43. The pump diameter is 1.80 cm, and it operates at ṅ = 4200 rpm. Nondimensionalize the pump performance curve, i.e., plot CH versus CQ. Show sample calculations of
- Calculate the pump specific speed of the pump of Prob. 14–102 at the best efficiency point for the case in which the BEP occurs at 14.0 Lpm. Provide answers in both dimensionless form and in
- Calculate the turbine specific speed of the turbine in Prob. 14–86E using customary U.S. units. Is it in the normal range for a Francis turbine? If not, what type of turbine would be more
- The prototype turbine corresponding to the onefifth scale model turbine discussed in Prob. 14–114 is to operate across a net head of 50 m. Determine the appropriate rpm and volume flow rate for
- Prove that the model turbine (Prob. 14–114) and the prototype turbine (Prob. 14–115) operate at homologous points by comparing turbine efficiency and turbine specific speed for both cases.Data
- In Prob. 14–116, we scaled up the model turbine test results to the full-scale prototype assuming exact dynamic similarity. However, as discussed in the text, a large prototype typically yields
- A hydraulic turbine operates at the following parameters at its best efficiency point: ṅ = 90 rpm, V̇ = 200 m3/s, H = 55 m, bhp = 100 MW. The turbine specific speed of this turbine is(a) 0.71 (b)
- Experiments on an existing turbine (A) yield the following data: DA = 86.0 cm, HA =22.0 m,V̇A = 69.5 m3/s, ρA = 998.0 kg/m3, ṅA = 240 rpm, bhpA = 11.4 MW. You are to design a new turbine (B) that
- Calculate and compare the efficiency of the two turbines of Prob. 14–156. They should be the same since we are assuming dynamic similarity. However, the larger turbine will actually be slightly
- Anita runs a CFD code using the computational domain and grid developed in Probs. 15–22 and 15–23. Unfortunately, the CFD code has a difficult time converging and Anita realizes that there is
- Choose one of the room geometries of Probs. 15–32 and 15–34, and add the energy equation to the calculations. In particular, model a room with air-conditioning, by specifying the supply air as
- In this chapter, we make a statement that the boundary layer approximation “bridges the gap” between the Euler equation and the Navier–Stokes equation. Explain.
- Paul realizes that the pump being used in Prob. 14–39E is not well-matched for this application, since its shutoff head (125 ft) is much larger than its required net head (less than 30 ft), and its
- Repeat Prob. 15–42, except for several values of the Mach number, ranging from 1.10 to 3.0. Plot the calculated Mach angle as a function of Mach number and compare to the theoretical Mach angle
- Generate a computational domain to study Mach waves in a two-dimensional supersonic channel (Fig. P15–42). Specifically, the domain should consist of a simple rectangular channel with a supersonic
- Repeat Prob. 15–40, except for turbulent, rather than laminar, flow. Compare to the laminar case. Which has the lower drag coefficient? Discuss.Data from Problem 15-40.Repeat Prob. 15–39, except
- Repeat Prob. 15–39, except for an axisymmetric, rather than a two-dimensional, body. Compare to the two dimensional case. For the same sectional slice shape, which has the lower drag coefficient?
- Repeat Prob. 15–28, except for turbulent flow of air with a uniform inlet velocity of 10.0 m/s. In addition, set the turbulence intensity at the inlet to 10 percent with a turbulent length scale of
- Choose one of the grids generated in Prob. 15–27, and run a CFD solution for laminar flow of air with a uniform inlet velocity of 0.02 m/s. Set the outlet pressure at both outlets to the same
- Consider the two-dimensional wye of Fig. P15–27. Dimensions are in meters, and the drawing is not to scale. Incompressible flow enters from the left, and splits into two parts. Generate three
- Sketch a structured multiblock grid with four sided elementary blocks for the computational domain of Prob. 15–25. Each block is to have four-sided structured cells, but you do not have to sketch
- As a follow-up to the heat exchanger design of Prob. 15–22, suppose Anita’s design is chosen based on the results of a preliminary single-stage CFD analysis. Now she is asked to simulate two
- A water pump is used to pump water from one large reservoir to another large reservoir that is at a higher elevation. The free surfaces of both reservoirs are exposed to atmospheric pressure, as
- For the pump and piping system of Prob. 14–43, plot required pump head Hrequired (m of water column) as a function of volume flow rate V̇(Lpm). On the same plot, compare available pump head
- Suppose that the free surface of the inlet reservoir in Prob. 14–43 is 3.0 m lower in elevation, such that z2 – z1 = 10.85 m. All the constants and parameters are identical to those of Prob.
- Sketch a coarse structured multiblock grid with four sided elementary blocks and four-sided cells for the computational domain of Prob. 15–22.Data from Problem 15-22A new heat exchanger is being
- A new heat exchanger is being designed with the goal of mixing the fluid downstream of each stage as thoroughly as possible. Anita comes up with a design whose cross section for one stage is sketched
- Suppose your CFD code can handle nonelementary blocks. Combine as many blocks of Fig. 15–12b as you can. The only restriction is that in any one block, the number of i-intervals and the number of
- Redraw the structured multiblock grid of Fig. 15–12b for the case in which your CFD code can handle only elementary blocks. Renumber all the blocks and indicate how many i- and j-intervals are
- Suppose that the two reservoirs in Prob. 14–39E are 1000 ft farther apart horizontally, but at the same elevations. All the constants and parameters are identical to those of Prob. 14–39E except
- For the pump and piping system of Prob. 14–39E, plot the required pump head Hrequired (ft of water column) as a function of volume flow rate V̇(gpm). On the same plot, compare the available pump
- A water pump is used to pump water from one large reservoir to another large reservoir that is at a higher elevation. The free surfaces of both reservoirs are exposed to atmospheric pressure, as
- A manufacturer of small water pumps lists the performance data for a family of its pumps as a parabolic curve fit, Havailable = H0 – aV̇2, where H0 is the pump’s shutoff head and a is a
- For the application at hand, the flow rate of Prob. 14–36 is not adequate. At least 9 Lpm is required. Repeat Prob. 14–36 for a more powerful pump with H0 = 8.13 m and a = 0.0297 m/(Lpm)2.
- Suppose the pump of Probs. 14–31E and 14–33E is used in a piping system that has the system requirement Hrequired = (z2 – z1) 1 bV̇2, where elevation difference z2 – z1 = 11.3 ft, and
- For the centrifugal water pump of Prob. 14–31E, plot the pump’s performance data: H (ft), bhp (hp), and ηpump (percent) as functions of V̇ (gpm), using symbols only (no lines). Perform linear
- For the centrifugal water pump of Prob. 14–28, plot the pump’s performance data: H (m), bhp (W), and ηpump (percent) as functions of V̇ (Lpm), using symbols only (no lines). Perform linear
- The performance data for a centrifugal water pump are shown in Table P14–28 for water at 20°C (Lpm = liters per minute). (a) For each row of data, calculate the pump efficiency (percent). Show
- Repeat Prob. 14–26, but instead of a smooth pipe, let the pipe roughness = 0.12 mm. Compare to the smooth pipe case and discuss—does the result agree with your intuition?Data from Problem
- Consider the piping system of Fig. P14–23, with all the dimensions, parameters, minor loss coefficients, etc., of Prob. 14–24. The pump’s performance follows a parabolic curve fit, Havailable =
- Repeat Prob. 14–24, but with a rough pipe—pipe roughness ε = 0.12 mm. Assume that a modified pump is used, such that the new pump operates at its free delivery conditions, just as in Prob.
- Suppose the pump of Fig. P14–23 is operating at free delivery conditions. The pipe, both upstream and downstream of the pump, has an inner diameter of 2.0 cm and nearly zero roughness. The minor
- Suppose the pump of Fig. P14–19C is situated between two large water tanks with their free surfaces open to the atmosphere. Explain qualitatively what would happen to the pump performance curve if
- In Fig. P14–19C is shown a plot of pump net head as a function of pump volume flow rate, or capacity. On the figure, label the shutoff head, the free delivery, the pump performance curve, the
- Consider the flow system sketched in Fig. P14–23. The fluid is water, and the pump is a centrifugal pump. Generate a qualitative plot of the pump net head as a function of the pump capacity. On the
- Suppose the pump of Fig. P14–19C is situated between two water tanks with their free surfaces open to the atmosphere. Which free surface is at a higher elevation—the one corresponding to the tank
- Suppose the pump of Fig. P14–19C is situated between two large water tanks with their free surfaces open to the atmosphere. Explain qualitatively what would happen to the pump performance curve if
- List at least two common examples of fans, of blowers, and of compressors.
- What are the primary differences between fans, blowers, and compressors? Discuss in terms of pressure rise and volume flow rate.
- What is the more common term for an energy producing turbomachine? How about an energy-absorbing turbomachine? Explain this terminology. In particular, from which frame of reference are these terms
- Discuss the primary difference between a positive displacement turbomachine and a dynamic turbomachine. Give an example of each for both pumps and turbines.
- Explain why there is an “extra” term in the Bernoulli equation in a rotating reference frame.
- For a turbine, discuss the difference between brake horsepower and water horsepower, and also define turbine efficiency in terms of these quantities.
- For a pump, discuss the difference between brake horsepower and water horsepower, and also define pump efficiency in terms of these quantities.
- An air compressor increases the pressure (Pout > Pin) and the density (rout > rin) of the air passing through it (Fig. P14–8). For the case in which the outlet and inlet diameters are equal
- A water pump increases the pressure of the water passing through it (Fig. P14–9). The flow is assumed to be incompressible. For each of the three cases listed below, how does average water speed
- Define net positive suction head and required net positive suction head, and explain how these two quantities are used to ensure that cavitation does not occur in a pump.
- For each statement about centrifugal pumps, choose whether the statement is true or false, and discuss your answer briefly:(a) A centrifugal pump with radial blades has higher efficiency than the
- Figure P14–12C shows two possible locations for a water pump in a piping system that pumps water from the lower tank to the upper tank. Which location is better? Why?FIGURE P14–12C
- There are three main categories of dynamic pumps. List and define them.
- Consider flow through a water pump. For each statement, choose whether the statement is true or false, and discuss your answer briefly:(a) The faster the flow through the pump, the more likely that
- Write the equation that defines actual (available) net positive suction head NPSH. From this definition, discuss at least five ways you can decrease the likelihood of cavitation in the pump, for the
- Consider a typical centrifugal liquid pump. For each statement, choose whether the statement is true or false, and discuss your answer briefly:(a) V̇ at the pump’s free delivery is greater than
- Explain why it is usually not wise to arrange two (or more) dissimilar pumps in series or in parallel
- Consider steady, incompressible flow through two identical pumps (pumps 1 and 2), either in series or in parallel. For each statement, choose whether the statement is true or false, and discuss your
- Suppose the pump of Probs. 14–28 and 14–29 is used in a piping system that has the system requirement Hrequired 5 (z2 – z1) + bV̇2, where the elevation difference z2 – z1 = 21.7 m, and
- The performance data for a centrifugal water pump are shown in Table P14–31E for water at 77°F (gpm = gallons per minute). (a) For each row of data, calculate the pump efficiency (percent). Show
- Transform each column of the pump performance data of Prob. 14–31E to metric units: V̇ into Lpm (liters per minute), H into m, and bhp into W. Calculate the pump efficiency (percent) using these
- Suppose you are looking into purchasing a water pump with the performance data shown in Table P14–35. Your supervisor asks for some more information about the pump. (a) Estimate the shutoff head
- The performance data of a water pump follow the curve fit Havailable = H0 – aV̇2, where the pump’s shutoff head H0 = 7.46 m, coefficient a = 0.0453 m/(Lpm)2, the units of pump head H are meters,
- A CFD code is used to simulate flow over a two dimensional airfoil at an angle of attack. A portion of the computational domain near the airfoil is outlined in Fig. P15–16 (the computational domain
- For the airfoil of Prob. 15–16, sketch a coarse hybrid grid and explain the advantages of such a grid.Data from Problem 15-16.A CFD code is used to simulate flow over a two dimensional airfoil at
- An incompressible CFD code is used to simulate the flow of water through a two-dimensional rectangular channel in which there is a circular cylinder (Fig. P15–18). A time-averaged turbulent flow
- An incompressible CFD code is used to simulate the flow of gasoline through a two-dimensional rectangular channel in which there is a large circular settling chamber (Fig. P15–19). Flow enters from
- A two-lobe rotary positive-displacement pump, similar to that of Fig. 14–30, moves 3.64 cm3 of tomato paste in each lobe volume V̇lobe. Calculate the volume flow rate of tomato paste for the case
- A vane-axial flow fan is being designed with the stator blades upstream of the rotor blades (Fig. P14–70). To reduce expenses, both the stator and rotor blades are to be constructed of sheet metal.
- Repeat Prob. 14–60, but at a water temperature of 80°C. Repeat for 90°C. Discuss.Data from Problem 14–60A self-priming centrifugal pump is used to pump water at 25°C from a reservoir whose
- Consider the gear pump of Fig. 14–26c. Suppose the volume of fluid confined between two gear teeth is 0.350 cm3. How much fluid volume is pumped per rotation?Fig. 14–26c O
- Repeat Prob. 14–63E for the case in which the pump has three lobes on each rotor instead of two, and V̇lobe = 0.0825 gal.Data from Problem 14-63The two-lobe rotary pump of Fig. P14–63E moves
- Repeat Prob. 14–60, but with the pipe diameter increased by a factor of 2 (all else being equal). Does the volume flow rate at which cavitation occurs in the pump increase or decrease with the
- The two-lobe rotary pump of Fig. P14–63E moves 0.110 gal of a coal slurry in each lobe volume V̇lobe. Calculate the volume flow rate of the slurry (in gpm) for the case where ṅ = 175 rpm.FIGURE
- A centrifugal pump rotates at ṅ = 750 rpm. Water enters the impeller normal to the blades (α1 = 0°) and exits at an angle of 35° from radial (α2 = 35°). The inlet radius is r1 = 12.0 cm, at
- Suppose the pump of Prob. 14–67 has some swirl at the inlet such that α1 = 7° instead of 0°. Calculate the net head and required horsepower and compare to Prob. 14–67. Discuss. In particular,
- Suppose the pump of Prob. 14–67 has some reverse swirl at the inlet such that α1 = –10° instead of 0°. Calculate the net head and required horsepower and compare to Prob. 14–67. Discuss. In
- Two water pumps are arranged in series. The performance data for both pumps follow the parabolic curve fit Havailable = H0 – aV̇2. For pump 1, H0 = 6.33 m and coefficient a = 0.0633 m/Lpm2; for
- The same two water pumps of Prob. 14–71 are arranged in parallel. Calculate the shutoff head and free delivery of the two pumps working together in parallel. At what combined net head should pump 1
- A self-priming centrifugal pump is used to pump water at 25°C from a reservoir whose surface is 2.2 m above the centerline of the pump inlet (Fig. P14–60). The pipe is PVC pipe with an ID of 24.0
- Repeat Prob. 14–58E, but at a water temperature of 113°F. Discuss.Data from Prob. 14–58A centrifugal pump is used to pump water at 77°F from a reservoir whose surface is 20.0 ft above the
- A centrifugal pump is used to pump water at 77°F from a reservoir whose surface is 20.0 ft above the centerline of the pump inlet (Fig. P14–58E). The piping system consists of 67.5 ft of PVC pipe
- For the duct system and fan of Prob. 14–55E, partially closing the damper would decrease the flow rate. All else being unchanged, estimate the minor loss coefficient of the damper required to
- Repeat Prob. 14–55E, ignoring all minor losses. How important are the minor losses in this problem? Discuss.Data from Problem 14–55EA local ventilation system (a hood and duct system) is used to
- A local ventilation system (a hood and duct system) is used to remove air and contaminants produced by a welding operation (Fig. P14–55E). The inner diameter (ID) of the duct is D = 9.06 in, its
- Suppose the one-way valve of Fig. P14–51 malfunctions due to corrosion and is stuck in its fully closed position (no air can get through). The fan is on, and all other conditions are identical to

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