Question

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.

(a) 4.6 bar

(b) 5.6 bar

(c) 4.1 bar

(d) 5.1 bar

The question was asked in an interview for internship.

The doubt is from Basic Energy Concepts in section Energy Balance of Bioprocess Engineering

Answer 1

The correct choice is (a) 4.6 bar

The best explanation: ΔP/ρ + Δv^2/2 + gΔh + F = W

ΔP = P2 – P1 (Pa)

Δv^2 = v2^2 – v1^2

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/m^3

Volumetric flow is 20/ (1000.60) m^3/s

= 0.000333 m^3/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 + [(4.24)^2 – (16.97)^2]/2 + 9.81.50 = 0

P1 = 456825 Pa (4.6 bar).