01 How to calculate the discharge and the velocity of flow

Problem 1
Compute the discharge of water through 75 mm pipe if the mean velocity is 2.5 m/sec.

Solution:

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$Q = vA = 2.5[ \, \frac{1}{4}\pi (0.075^2) \, ]$

$Q = 0.011 \, \text{ m}^3\text{/sec}$ answer

Problem 2
The discharge of air through a 600-mm pipe is 4 m³/sec. Compute the mean velocity in m/sec.

Solution

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$Q = vA$

$4 = v [ \, \frac{1}{4} \pi (0.6^2) \, ]$

$v = 14.15 \, \text{ m/sec}$ answer

Problem 3
A pipe line consists of successive lengths of 380-mm, 300-mm, and 250-mm pipe. With a continuous flow through the line of 250 Lit/sec of water, compute the mean velocity in each size of pipe.

Solution

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For continuous flow
$Q_1 = Q_2 = Q_3 = Q$

$v_1A_1 = v_2A_2 = v_3A_3 = Q$

$v_1 [ \, \frac{1}{4}\pi (0.380^2) \, ] = v_2 [ \, \frac{1}{4}\pi (0.300^2) \, ] = v_3 [ \, \frac{1}{4}\pi (0.250^2) \, ] = 0.25$

$v_1 = \dfrac{4(0.25)}{\pi (0.380^2)} = 2.20 \, \text{ m/sec}$ answer

$v_2 = \dfrac{4(0.25)}{\pi (0.300^2)} = 3.54 \, \text{ m/sec}$ answer

$v_3 = \dfrac{4(0.25)}{\pi (0.250^2)} = 5.09 \, \text{ m/sec}$ answer

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