Question

Oil at 20°C (density = 870 kg/m³) and viscosity = 0.104 kg/m-s) flows (laminar flow) at 1.1 m³/hr through a horizontal pipe with diameter d = 2 cm and length L = 12 m. Find the power required to cause the flow
1. 29.7 W
2. 35.8 W
3. 15.7 W
4. 49.8 W

Answer 1

Correct Answer - Option 1 : 29.7 W

Concept:

Power required in a flow is given by:

\(Power = \rho gQ{h_f}\)

Where ρ = Density,

Q = Discharge = A × V

 h_f = Head loss due to friction = \(\frac{{32\mu VL}}{{\rho g{d^2}}}\)

Calculation:

Given:

ρ = 870 kg/m³, µ = 0.104 kg/m-s , Q = 1.1 m³/hour = \(\frac{{1.1}}{{3600}}\) = 3.05 × 10^-4 m³/sec, d = 2 cm = 0.02 m , L = 12 m

\(Power = \rho gQ \times \frac{{32\mu VL}}{{\rho g{d^2}}}\)

\(Power = Q \times \frac{{32\mu QL}}{{A{d^2}}}\;\)

\(P = \frac{{32\mu {Q^2}L}}{{\left( {\frac{{\pi \;}}{4}{d^2}} \right){d^2}}}\)

\(P = \frac{{32\; \times\; 0.104\; \times \;{{\left( {3.05\; \times {{10}^{ - 4}}} \right)}^2} \times \;12}}{{\left( {\frac{\pi }{4} \times {{0.02}^2}} \right)\;\times\;{{0.02}^2}}}\)

Power = 29.7 W