Question 10.9.1: The water is supplied at the rate of 3000 l/min from a heigh......
The water is supplied at the rate of 3000 l/min from a height of 4 m to a hydraulic ram, which raises 300 l/min to a height of 30 m from the ram. The length and diameter of the delivery pipe is 100 m and 70 mm respectively. Calculate the efficiency of the hydraulic ram if the coefficient of friction is 0.009.
Given: Q = 3000 \ l/\min = 0.05 m^3/s, q = 300 l/\min = 0.005 m^3/s, h_2 = 30 m, L = 100 m, d = 0.07 m, f = 0.009
Velocity in discharge pipe =q/a=\frac{0.005}{{\pi}/{4} \times 0.07^2}=1.3 m/s
Head loss due to pipe friction =\frac{4\times 0.009 \times 100}{0.07}\times \frac{1.3^2}{2\times 9.81} =4.43 m
Effective pressure head developed at the discharge valve = h_2 + 4.43 = 34.43 m
From Eq. 10.8.1
Efficiency of fluied coupling = P_m/P_p=(\tau \omega )_m/(\tau \omega )_p (10.8.1)
D′ Aubuisson efficiency =\frac{q\times \mathrm{effective head}}{Q\times h_1} =\frac{0.005 \times 34.43}{0.05 \times }=0.8607 or, 86.07 %
Rankine efficiency =\frac{q\times (\mathrm{effective head} -h_1)}{Q\times h_1} =\frac{0.005 \times 34.43 -4}{0.05 \times } = 0.8453 or,84.53%