Question

If the pipe of the previous exercise is connected to a hose and the speed there is 3.8 m/s, what is the diameter of the hose?

Answer 1

The diameter of the hose is 6.34 cm.

"Your question is not complete, it seems to be missing the following information";

the flow rate of water in the pipe is 0.012 m³/s

The given parameters;

• velocity of water in the hose, v = 3.8 m/s

• flow rate of water in the hose, Q = 0.012 m³/s

Volumetric flow rate is directly proportional to the product of the area of the hose through which the water flows and the velocity of the water flowing through the hose.

 Q = Av

where;

Q is the volumetric flow rate

A is the area of the hose

v is the velocity of flow

The area of the hose is calculated as follow;

$A = \frac{Q}{v} \\\\A = \frac{0.012}{3.8} \\\\A = 0.00316 \ m^2$

The diameter of the hose is calculated as follows;

$A = \frac{\pi D^2}{4} \\\\\pi D^2 = 4A\\\\D^2 = \frac{4 \times A}{\pi} \\\\D = \sqrt{\frac{4 \times A}{\pi} } \\\\D = \sqrt{\frac{4 \times 0.00316}{\pi} } \\\\D = 0.0634 \ m\\\\D = 6.34 \ cm$

Thus, the diameter of the hose is 6.34 cm.

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