Question

Water flows steadily through a horizontal tube of variable cross-section. If the pressure of water is $P$ at a point where the velocity of flow is $v$, what is the pressure at another point where the velocity of flow is $2v$; $\rho$ being the density of water?

• A. $P-\frac{3}{2}\rho v^2$
• B. $P+\frac{3}{2}\rho v^2$
• C. $P-2p{v}^2$
• D. $P+\frac{1}{2}\rho v^2$

Answer 1

The correct option is A $P-\frac{3}{2}\rho v^2$

Applying Bernoulli's equation at two points, we get
$P_1+\frac{\rho v_1^2}{2}=P_2+\frac{\rho v_2^2}{2}$
Horizontal pipe, $[\because h_1=h_2]$
Given, $P_1=P,v_1=v$ and $v_2=2v$
So, $P+\frac{\rho v^2}{2}=P_2+\frac{\rho (2v{)}^2}{2}$
$\Rightarrow P_2=P-\frac{3}{2}\rho v^2$