A streamline flow of a liquid of density ' ρ ' is passing through a horizontal pipe of cross-sectional area A 1 and A 2 at two ends. If the pressure of liquid is ' P ' at a poi

Question

A streamline flow of a liquid of density ' ρ ' is passing through a horizontal pipe of cross-sectional area A 1 ​ and A 2 ​ at two ends. If the pressure of liquid is ' P ' at a point where flow speed is ' v ', then pressure at another point where the flow of speed becomes 3 v is

TestHub · Accepted Answer

Using Bernoulli's equation for a horizontal pipe:

$P_{1} + \frac{1}{2} ρ v_{1}^{2} = P_{2} + \frac{1}{2} ρ v_{2}^{2}$

Substituting the given values $P_{1} = P$ , $v_{1} = v$ , and $v_{2} = 3 v$ :

$P + \frac{1}{2} ρ v^{2} = P_{2} + \frac{1}{2} ρ (3 v)^{2}$

$P + \frac{1}{2} ρ v^{2} = P_{2} + \frac{9}{2} ρ v^{2}$

$P_{2} = P + \frac{1}{2} ρ v^{2} - \frac{9}{2} ρ v^{2}$

$P_{2} = P - 4 ρ v^{2}$

Answer: $P - 4 ρ v^{2}$

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