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Water flows between two points 1, 2. The volumetric flow rate is 20 litres/min. Point 2 is 50 m higher than point 1. The pipe internal diameters are 0.5 cm at point 1 and 1 cm at point 2. The pressure at point 2 is 1 atm. Calculate the pressure at point 1.

Water flows between two points 1, 2. The volumetric flow rate is 20 litres/min. Point 2 is 50 m higher than point 1. The pipe internal diameters are 0.5 cm at point 1 and 1 cm at point 2. The pressure at point 2 is 1 atm. Calculate the pressure at point 1. Correct Answer 4.6 bar

ΔP/ρ + Δv2/2 + gΔh + F = W ΔP = P2 – P1 (Pa) Δv2 = v22 – v12 Δh = h2 – h1 (m) F = frictional energy loss (mechanical energy loss to system) (J/kg) W = work done on system by pump (J/kg) ρ = 1000 kg/m3 Volumetric flow is 20/ (1000.60) m3/s = 0.000333 m3/s v1 = 0.000333/(π(0.0025)2) = 16.97 m/s v2 = 0.000333/ (π(0.005)2) = 4.24 m/s (101325 – P1)/1000 + /2 + 9.81.50 = 0 P1 = 456825 Pa (4.6 bar).

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