Question

Find the loss of head when a pipe of diameter 200mm is suddenly enlarged to a diameter of 400mm . The rate of flow of water through a pipe is 250lt/sec.

Answer 1

Given:

Pipe of diameter 200mm is suddenly enlarged to a diameter of 400mm . The rate of flow of water through a pipe is 250lt/sec.

To find:

Loss of head due to sudden enlargement

Calculation:

Initial velocity of flow

$v1 = \bigg \{ \dfrac{0.25}{( \frac{\pi {(0.2)}^{2} }{4} )} \bigg \}$

$= > v1 = \dfrac{25}{\pi}$

$= > v1 = 7.95 \: m {s}^{ - 1}$

Final Velocity of flow

$v2 = \bigg \{ \dfrac{0.25}{( \frac{\pi {(0.4)}^{2} }{4} )} \bigg \}$

$= > v2 = \dfrac{25}{4\pi}$

$= > v2 = 1.98 \: m {s}^{ - 1}$

So, loss of head be H ;

$\therefore \: H = \dfrac{ {(v1 - v2)}^{2} }{2g}$

$= > \: H = \dfrac{ {(7.95 - 1.98)}^{2} }{2 \times 9.8}$

$= > \: H = \dfrac{ {(5.97)}^{2} }{2 \times 9.8}$

$= > \: H = \dfrac{ 35.64 }{2 \times 9.8}$

$= > \: H = 1.81 \: m$

So, final answer is:

$\boxed{ \bf{\large{ H = 1.81 \: m}}}$