Urban Workbench: Find the loss of head when a pipe of diameter 200 mm is suddenly enlarged to a diameter of 400 mm. The rate of flow of water through the pipe is 200 lit/s.

Saturday, August 14, 2021

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

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

Solution:

Given:

Diameter of smaller pipe

$D_{1} = 200 m m = \frac{200}{1000} = 0.20 m$

Area, A 1 = π 4 × D 21 A_{1} = \frac{π}{4} \times D_{1}^{2}A 1 = π / 4 × (0.20) 2 = 0.03141 m 2Diameter
of larger pipeD 2 = 400 m m = 400 / 1000 = 0.40 mArea, A 2 = π / 4 × D 2 2A 2 = π / 4 × 0.40) 2 = 0.12564 m 2Discharge, Q = 250 l i t / s e c = 250 / 1000 = 0.25 m 3 / sVelocity, V 1 = Q / A 1 = 0.25 / 0.03141 = 7.96 m / sVelocity, V 2 = Q / A 2 = 0.25 / 0.12564 = 1.996 m / sNow
to find the loss due to enlargementh e = (V 1 − V 2) 2 / 2 × gh e = \frac{(V_{1} - V_{2})^{2}}{2 \times g}h e = (7.96 − 1.99) 2 / 2 × 9.81h e = \frac{(7.96 - 1.99)^{2}}{2 \times 9.81}h e = 1.816 m of water

Urban Workbench

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Saturday, August 14, 2021

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

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