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Atmospheric Pressure

What gauge pr...

Question

What gauge pressure must the pump provide to achieve the same volume flow rate for a pipe with a diameter of $4.0 c m$ ?

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Solution

$Q_{1} = Q_{2}$
$∴$ ${[(p_{1} - p_{2}) R^{4}]}_{i}^{4} = {[(p_{1} - p_{2}) R^{4}]}_{f}^{4}$
Since dialneter or radius has decreased to half. Therefore gauge pressure should become 16 times.
or ${(p_{1} - p_{2})}_{f} = 16 \times 1400$
$= 2.24 \times 10^{4}$ Pa

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