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 = $\rho$]

• 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

The correct option is A $\sqrt{v^2+\frac{p}{\rho }}$

Given : $P_1=p$ $v_1=v$ $P_2=p/2$

Using Bernoulli's equation, $P_1+\rho g{h}_1+\frac{1}{2}\rho v_1^2=P_2+\rho g{h}_2+\frac{1}{2}\rho v_2^2$

As water flows in a horizontal tube i.e. $h_1=h_2$

We get $P_1+\frac{1}{2}\rho v_1^2=P_2+\frac{1}{2}\rho v_2^2$

OR $p+\frac{1}{2}\rho v^2=\frac{p}{2}+\frac{1}{2}\rho v_2^2$

OR $\frac{1}{2}\rho (v_2^2-v^2)=\frac{p}{2}$ $⟹v_2=\sqrt{v^2+\frac{p}{\rho }}$