Question 7.P.16: A 30 cm pipe with friction factor f = 0.024 carries water to......
A 30 cm pipe with friction factor f = 0.024 carries water to a turbine at the rate of 0.25 m³/s over a distance of 160 m. The difference in levels between the water inlet and turbine inlet is 36 m. Determine the efficiency of transmission. The turbine outlet delivery is submerged into the tailrace and the velocity at the exit is 0.4 times the velocity in the pipe.
The efficiency of transmission = \frac{\mathrm{Available head for conversion to work}}{\mathrm{Difference in datum}}
The losses in this case are the friction head and the dynamic head at exit.
Flow rate = 0.25 m³/s,
∴ \quad \quad u_{m} = 0.25 × 4/π × 0.3² = 3.54\ \mathrm{m/s}.
Friction head = fLu²/2gD = [0.024 × 160 × 3.54²/(2 × 9.81 × 0.3)] = 8.176 m
Dynamic head: Exit velocity = 0.4 × 3.54 m/s.
∴ Dynamic head = (0.4 × 3.54)²/2 × 9.81 = 0.102 m
Total losses = 8.176 + 0.102 = 8.28 m
Efficiency is high but the power delivered is not maximum.
∴ Efficiency of transmission = (36 – 8.28)/36 = 0.77 or 77%