Answer:
Total power supplied to the water by the pump shaft in the absence of losses = 22.2 hp
Step-by-step explanation:
Neglecting the losses, it means the pump operates at a 100% efficiency and total power supplied by shaft = power gained by the fluid
Power gained by the fluid is converted to the power to overcome pressure difference, Power in kinetic energy form and Power in potential energy form
Power to overcome pressure difference = Q(ΔP)
Q = volumetric flow rate = 0.26 ft³/s = 0.00736 m³/s
ΔP = 180 psi = 1.241 × 10⁶ Pa
Power to overcome pressure difference = 0.00736 × 1.241 × 10⁶ = 9134.2 W
Power in kinetic energy form = ṁ(v₂² - v₁²)/2
ṁ = mass flow rate = Density × volumetric flow rate = 1000 × 0.00736 = 7.36 kg/s (Density of water = 1000 kg/m³
since the water was initially at rest, v₁ = 0m/s
v₂ = volumetric flowrate/cross sectional area
Cross sectional Area of pipe = 2πrl
r = 3/2 in = 0.0381 m, l = 2000 ft = 609.6m
v₂ = 0.00736/(2π× 0.0381 × 609.6) = 0.000504 m/s
Power in kinetic energy form = ṁ(v₂² - v₁²)/2 = 7.36(0.0000504²)/2 = (9.4 × 10⁻⁸) W
Power in potential energy = ṁg(z₂ - z₁)
z₂ - z₁ = change in elevation = (4623 - 4286) = 337 ft = 102.72 m
Power in potential energy = ṁg(z₂ - z₁) = 7.36 × 9.8 × 102.72 = 7408.99 = 7409 W
Total power gained by fluid = 9134.2 + (9.4 × 10⁻⁸) + 7409 = 16543.2 W
Total power supplied by shaft = Total power gained by fluid = 16543.2 W
In horsepower,
746 W = 1 Horsepower
16543.2 W = 22.185 hp = 22.2 hp
Hope this Helps!!!!