Pelton wheel turbines are commonly used in hydro-electric

Chapter 6, Problem 63P

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Problem 63P

Pelton wheel turbines are commonly used in hydro-electric power plants to generate electric power. In these turbines, a high-speed jet at a velocity of Vj impinges on buck ets, forcing the wheel to rotate. The buckets reverse the direction of the jet, and the jet leaves the bucket making an angle β with the direction of the jet, as shown in Fig. P13-51. Show that the power produced by a Pelton wheel of radius r rotating steadily at an angular velocity of ω is Wshaft = pωrV(Vj, ‒ ωr)(l ‒ cosβ), where ρ is the density and  is the volume flow rate of the fluid. Obtain the numerical value for ρ = 1000 kg/m3, r = 2 m, =10 m3/s, n = 150 rpm, β = 160°, and Vj = 50 m/s.