Water flows through a 5km long 1 2m diameter concrete e 1 m

Water flows through a 5-km long, 1, 2-m diameter concrete (e = 1 mm) penstock to a 3.2-m diameter Pelton wheel. The nozzle diameter is 25 cm, and the outlet blade angle is 165 degree. The discharge is 450 m below the reservoir level, and minor losses are K = 0.8 and 350 f_T. (a) Sketch and label a schematic for the system. (b) What is the Pelton wheel speed in rpm for maximum power extraction? What is the maximum power extracted? (c) What is the customary specific speed for this device? Is this congruent with Figure 3.11? Explain.

Solution

Given: d_p = 1.2m, h = 450m, d_n=0.25m

b) Maximum jet inlet velocity is given by,

v_i = sqrt(2*g*h) = 93.96276 m/s

For optimal wheel speed, u = v_i/2 = 46.98138 m/s

Now, u = 3.14*d_n*n/60

Therefore, n = 3589.113 rpm

Maximum power extracted = 1000*9.81*h*Q = 9810*450*(1000*3.14*0.25*0.25²*93.96276) = 20361.3789 MW

c) customary specific speed = n*sqrt(P)/(H^5/4)= 247101.3295 rpm