Question

Water is flowing in streamline motion through a horizontal tube. The pressure at a point in the tube is $p$ where the velocity of flow is $v$. At another point, where the pressure is $p/2$, the velocity of flow is [density of water = $?$]

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

Answer 1

Answer: (A)

$\sqrt{v^{2}+\frac{p}{\rho}}$

Answer 2

As the water is flowing through the horizontal tube, so in the streamline flow of water, the sun of static pressure and dynamic pressure is constant i.e.,
$P+\frac{1}{2} \rho v^{2}=\frac{P}{2}+\frac{1}{2} \rho v_{1}^{2}$
$\Rightarrow v_{1} =\sqrt{\frac{P}{\rho}+v^{2}}$