Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is $P$ at a point where flow speed is $v$ , the pressure at another point where the flow speed is $2v$ , is (Take density of water as $\rho $ )
Medium
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Applying Bernoullis's Equation at two points$:$
$p_{1}+\frac{\rho v_{1}^{2}}{2}=p_{2}+\frac{\rho v_{2}^{2}}{2}$
Given, $p_{1}=p, \quad v_{1}=v \quad v_{2}=2 v$
$p_{2}=p+\frac{\rho v^{2}}{2}-\frac{4 \rho v^{2}}{2}$
$p_{2}=p-\frac{3 \rho v^{2}}{2}$
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