The frictionless converging stationary nozzle of the hydraulic turbine shown in Fig. P12.46 has an inlet pressure \(p_{0}=480 \mathrm{kPa}\), a negligible inlet velocity \(V_{0}\), and an exit pressure \(p_{1}=101 \mathrm{kPa}\). The velocity \(V_{1}\) is used to drive the axial flow turbine, which has a rotational speed of \(185.7 \mathrm{rpm}\), an outside radius of \(R=1.20 \mathrm{~m}\), and a blade height of \(h=0.40 \mathrm{~m}\). Determine velocities \(V_{1}\) and \(V_{2}\) and the power transmitted to the turbine in terms of \(\alpha_{1}\) and \(\alpha_{2}\). The fluid density is constant and the velocities of the fluid relative to the blade are directed as shown in Fig. P12.46. Assume that the velocities are uniform over the flow inlet and outlet areas and use an average blade velocity at the blade midheight \((r=1.00 \mathrm{~m})\) and a water temperature of \(20^{\circ} \mathrm{C}\).

Figure P12.46

Transcribed Image Text:

Blades Flow area Vo Po Nozzle U Bi W W2 B Section AA U R h Nozzles BzU 012 V2 A P1 P2 P1