Answer:
a) the power loss due to irreversible head loss is 4.57 kW
b) the efficiency of the piping is 95%
c) the electric power output is 72.9918 kW
Explanation:
Given the data in the question below;
Irreversible loses = 7m
Total head, H = 140 m
flow rate Q = 4000 L/min = 0.0666 m³/s
Generator efficiency n₀ = 84% = 0.84
we know that density of water is 1000 kg/m³
g = 9.81 m/s²
a) power loss due to irreversible head loss is;
= p × Q × g ×
we substitute
= 1000 × 0.0666 × 9.81 × 7
= 4573.422 W
= 4573.422 / 1000
= 4.57 kW
Therefore, the power loss due to irreversible head loss is 4.57 kW
b) the efficiency of the piping n is;
n = (Actual head / maximum head) × 100
n = (( H - ) / H) × 100
so we substitute
n = (( 140 - 7 ) / 140) × 100
n = (133/140) × 100
n = 0.95 × 100
n = 95%
Therefore, the efficiency of the piping is 95%
c) the electric power output if the turbine-generator efficiency is 84 percent;
n₀ = /
= n₀ ×
= n₀ × ( pQg( H - ))
so we substitute
= 0.84 × ( 1000 × 0.0666 × 9.81( 140 - 7 ))
= 0.84 × 653.346( 133)
= 0.84 × 86895.018
= 72991.815 W
= 72991.815 / 1000
= 72.9918 kW
Therefore, the electric power output is 72.9918 kW