A streamline flow of a liquid of density ' $\rho$ ' is passing through a horizontal pipe of cross-sectional…
A streamline flow of a liquid of density ' $\rho$ ' 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
$\mathrm{P}-\frac{3}{4} \rho v^2$
$P-2 \rho v^2$
$\mathrm{P}-3 \rho v^2$
$P-4 \rho v^2$
Solution
Using Bernoulli's equation,
$\begin{aligned}
& P_1+\frac{1}{2} \rho v_1^2+\rho g h_1=P_2+\frac{1}{2} \rho v_2^2+\rho g h_2 \\
& P_1+\frac{1}{2} \rho v_1^2=P_2+\frac{1}{2} \rho v_2^2 \quad ext{...(given horizontal pipe)}
\end{aligned}$
Substituting the given values,
$\begin{aligned} & P+\frac{1}{2} \rho v_1^2=P_2+\frac{1}{2} \rho(3 v)^2 \\ & P_2=P+\left(\frac{1}{2} \rho v^2-\frac{9}{2} \rho v^2\right)=P-4 \rho v^2\end{aligned}$