20. The flow of river is \( 19 \mathrm{~m}^{3} / \mathrm{sec} \) produces a total brake power of \( 7000 \mathrm{~kW} \). It is proposed to install two turbines, one of which is twice the capacity of the other. The efficiency and specific speed of both units are assumed to be \( 80 \% \) and \( 61 \mathrm{rpm} \), respectively. Find the rotative speed of each unit if the measure of the head is \( 47 \mathrm{~m} \). A. \( 526 \mathrm{rpm}, 761 \mathrm{rpm} \) C. \( 110 \mathrm{rpm}, 155 \mathrm{rpm} \) B. \( 412 \mathrm{rpm}, 981 \mathrm{rpm} \) D. \( 348 \mathrm{rpm}, 616 \mathrm{rpm} \) ANS: C PTS: 1
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An impulse turbine under a net head of 33 ft was tested at a variety of speeds. The flow rate and the brake force needed to set the impeller speed were recorded: $$\begin{array}{ccc} \text { Wheel Speed } & \text { Flow rate } & \text { Brake Force (lbf) } \\ (\mathrm{rpm}) & (\mathrm{cfm}) & (R=0.5 \mathrm{ft}) \\ 0 & 7.74 & 2.63 \\ 1000 & 7.74 & 2.40 \\ 1500 & 7.74 & 2.22 \\ 1900 & 7.44 & 1.91 \\ 2200 & 7.02 & 1.45 \\ 2350 & 5.64 & 0.87 \\ 2600 & 4.62 & 0.34 \\ 2700 & 4.08 & 0.09 \end{array}$$ Calculate and plot the machine power output and efficiency as a function of water turbine speed.
Water drives a waterwheel (or turbine) of radius $R = 3.0 m$ as shown in Fig. 8-66. The water enters at a speed $\upsilon_1 = 7.0 m/s$ and exits from the waterwheel at a speed $\upsilon_2 = 3.8 m/s$. $(a)$ If 85 kg of water passes through per second, what is the rate at which the water delivers angular momentum to the waterwheel? $(b)$ What is the torque the water applies to the waterwheel? $(c)$ If the water causes the waterwheel to make one revolution every 5.5 s, how much power is delivered to the wheel? FIGURE 8-66(Figure Cant copy)
Dimensions of a centrifugal pump impeller are $$\begin{array}{lcc} \text { Parameter } & \text { Inlet, Section }(1) & \text { Outlet, Section }(2) \\ \text { Radius, } r \text { (in.) } & 15 & 45 \\ \text { Blade width, } b \text { (in.) } & 4.75 & 3.25 \\ \text { Blade angle, } \beta(\operatorname{deg}) & 40 & 60 \end{array}$$ The pump is driven at 575 rpm and the fluid is water. Calculate the theoretical head and mechanical power if the flow rate is 80,000 gpm.
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