Question

A smooth pipe of diameter 100 mm and length 100 m carries crude oil (Kinematic viscosity = 0.4 stokes and density = 900 kg/m³ at velocity of 2 m/s. What will be the power (in W) required to maintain the flow? [ Friction factor = 0.03, g = 10 m/s²]

1.

282.7

2.

565.4

3. 848.2
4.

1130.9

Answer 1

Correct Answer - Option 3 : 848.2

Concept:

Darcy’s friction factor is given by:

\({h_f} = \frac{{fl{v^2}}}{{2gd}}\)

where

h_f = head loss, f = friction factor, l = length, v = velocity, d = diameter

Power required can be calculated by:

P = ρgQh

where

ρ = density, Q = discharge ⇒ AV

Calculation:

Given:

D = 100 mm ⇒ 0.1 m, L = 100 m, V = 2 m/s, ρ = 900 kg/m³, f = 0.03

\(Q\; = \frac{\pi }{{\;4}}{\left( {0.1} \right)^2} \times 2 \Rightarrow 0.0157\;{m^3}/s\)

Now

\({h_f} = \frac{{fl{v^2}}}{{2gd}}\)

\({h_f} = \frac{{0.03 \times 100 \times {2^2}}}{{2 \times 10 \times 0.1}}\)

hf = 6 m

Power is:

P = ρgQh

P = 900 × 10 × 0.0157 × 6

P = 847.5 W