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. $p-2\rho v^2$
• D. $p+2\rho v^2$

Answer 1

Answer: (A)

$p-\frac{3}{2}\rho v^2$

Applying Bernoullis's Equation at two points:

$p_1+\frac{\rho {v_1}^2}{2}=p_2+\frac{\rho {v_2}^2}{2}$

Given, $p_1=p,v_1=v{v}_2=2v{p}_2=p+\frac{\rho v^2}{2}-\frac{4\rho v^2}{2}{p}_2=p-\frac{3\rho v^2}{2}$