Question

A fluid is flowing through a horizontal pipe of varying cross-section, with speed $v \,ms ^{-1}$ at a point where the pressure is $P$ Pascal. At another point where pressure is $\frac{ P }{2}$ Pascal its speed is $V \,ms ^{-1}$. 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. $\sqrt{\frac{2 P }{\rho}+ v ^{2}}$
• D. $\sqrt{\frac{ P }{ \rho }+ v }$

Answer 1

Answer: (B)

Applying Bernoulli's Equation
$P_{1}+\frac{1}{2} \rho v_{1}^{2}+\rho g y_{1}=P_{2}+\frac{1}{2} \rho v_{2}^{2}+\rho g y_{2}$
$P +\frac{1}{2} \rho v ^{2}=\frac{ P }{2}+\frac{1}{2} \rho V ^{2}$
$\frac{2 P}{2 \rho}+\frac{1}{2} \frac{\rho v^{2}}{\rho} \times 2=V^{2}$
$\sqrt{\frac{P}{\rho}+v^{2}}=V$