Water enters and leaves a pump in pipelines of the same diameter and approximately the same elevation. If the pressure on the inlet side of the pump is 30 kPa and a pressure of 500 kPa is desired for the water leaving the pump, what is the head that must be added by the pump

The head added by the pump is approximately 51.8 meters

Explanation:

The given parameters of the water are;

The initial diameter of the pump ≈ The final diameter of the pump

The inlet side pressure, p₁ = 30 kPa

The intended outlet side pressure, p₂ = 500 kPa

The power of the pump, P = ρ·g·Q·H

Where, the pressure added by the pump, Δp = p₂ - p₁ = ρ·g·H

ρ = The density of the water ≈ 997 kg/m³

g = The acceleration due to gravity ≈ 9.81 m/s²

H = The head added by the pump

Therefore, we have;

500 kPa - 30 kPa = 997 kg/m³ × 9.81 m/s² × H

H = (500 kPa - 30 kPa)/(997 kg/m³ × 9.1 m/s²) ≈ 51.8 m

The head added by the pump, H ≈ 51.8 meters.

answer:

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