Question

Water flows steadily through a horizontal pipe of a 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. $p-2\rho v^2$
• D. $p+2\rho v^2$

Answer 1

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

Applying Bernoulli's equation for a horizontal flow at a height $h$ from ground level,
$p_1+\frac{1}{2}\rho v_1^2+\rho hg=p_2+\frac{1}{2}\rho v_2^2+\rho gh$
or $p_2=p_1+\frac{1}{2}\rho (v_1^2-v_2^2)$
Since $p_1=p$, (given)
$\Rightarrow p_2=p+\frac{1}{2}\rho (v^2-(2v{)}^2)$
$\therefore p_2=p-\frac{3}{2}\rho v^2$
Hence the correct choice is $\left(a\right)$.