Question

The head difference between the inlet and outlet of a 1km long pipe discharging 0.1 m^3/s of water is 0.53 m. If the diameter is 0.6m, what is the friction factor? Is a) 0.01 b) 0.02 c) 0.03 d) 0.04 e) 0.05

Answer 1

Answer:

The correct option is 'e': f = 0.05.

Explanation:

The head loss as given by Darcy Weisbach Equation is as

$h_{l}=\frac{flv^{2}}{2gD}$

where

$h_{l}$ is head loss in the pipe

'f' is the friction factor

'l' is the length of pile

'v' is the velocity of flow in pipe

'D' is diameter of pipe

From equation of contuinity we have $v=\frac{Q}{A}$

Thus using this in darcy's equation we get

$h_{l}=\frac{flQ^{2}}{2gDA}$

where

'Q' is discharge in the pipe

'A' is area of the pipe $A=\frac{\piD^2}{4}$

Applying the given values we get

$h_{l}=\frac{8flQ^{2}}{\pi ^{2}gD^{5}}$

Solving for 'f' we get

$f=\frac{0.53\times \pi ^{2}\times 9.81\times 0.6^{5}}{1000\times 0.1^{2}\times 8}\\\\f=0.05$