Question

A fluid is flowing through a horizontal pipe of varying cross-section, with speed $vm{s}^{-1}$ at a point where the pressure is $P$ Pascal. At another point where pressure is $\frac{P}{2}$ Pascal its speed is $Vm{s}^{-1}$. If the density of the fluid is $\rho kg{m}^{-3}$ and the flow is streamline, then $V$ is equal to :

• A. $\sqrt{\frac{P}{2\rho }+v^2}$
• B. $\sqrt{\frac{P}{\rho }+v^2}$
• C. $\sqrt{\frac{2P}{\rho }+v^2}$
• D. $\sqrt{\frac{P}{\rho }+v}$

Answer 1

Answer: (B)

Applying Bernoulli's Equation
$P_1+\frac{1}{2}\rho v_1^2+\rho g{y}_1=P_2+\frac{1}{2}\rho v_2^2+\rho g{y}_2$
$P+\frac{1}{2}\rho v^2=\frac{P}{2}+\frac{1}{2}\rho V^2$
$\frac{2P}{2\rho }+\frac{1}{2}\frac{\rho v^2}{\rho }\times 2=V^2$
$\sqrt{\frac{P}{\rho }+v^2}=V$