# If the velocity of flow as well as the diameter of the flowing pipe are respectively doubled, the head loss thereafter be

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If the velocity of flow as well as the diameter of the flowing pipe are respectively doubled, the head loss thereafter be
1. Halved
2. Doubled
3. Increased 4 times
4. No change

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Correct Answer - Option 2 : Doubled

Concept-

Head loss due to flow in a pipe can be given as ${h_L} = \frac{{fL{V^2}}}{{2gd}}$

Here f = friction factor, L = Length of pipe, V = Velocity of flow

g = Acceleration due to gravity, d = diameter of pipe

Calculation-

The velocity of flow as well as the diameter of the flowing pipe are respectively doubled

So

${h_{11}} = \frac{{fLv_1^2}}{{2g{d_1}}}$

${h_{12}} = \frac{{4fLv_1^2}}{{4g{d_1}}}$

$\frac{{{h_{l1}}}}{{{h_{l2}}}} = 0.5\;$

So new head loss will be two times the initial head loss.

If the velocity of flow as well as the diameter of the flowing pipe are respectively doubled, the head loss thereafter be doubled.