Question

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 $\rho$ )

Answer 1

using bernoulli equation$:$

$\frac{\rho }{s}+\frac{v^2}{2}=\frac{{\rho }^{\prime }}{s}+\frac{{\left(2v\right)}^2}{2}$

$\Rightarrow \frac{\rho }{s}+\frac{v^2}{2}=\frac{{\rho }^{\prime }}{s}+2v^2$

$\Rightarrow \frac{{\rho }^{\prime }}{s}=\frac{\rho }{s}-\frac{3v^2}{2}$

${\rho }^{\prime }=\rho -\frac{3s{v}^2}{2}.$