Question

Water flows steadily through a horizontal pipe of variable cross section. If the pressure of water is P at a point where flow speed is v, the pressure at another point where the flow speed is 2v, is:

• A. $P-\frac{3\rho v^2}{2}$
• B. $P-\frac{\rho v^2}{2}$
• C. $P-\frac{3\rho v^2}{4}$
• D. $P-\rho v^2$

Answer 1

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


Apply Bernoulli’s theorem
$P=\frac{1}{2}\rho v^2+z=P_1+\frac{1}{2}\rho \left(2v^2\right)+zP=\frac{1}{2}\rho v^2=P_{1}2\rho v^2{P}_1=P-\frac{3}{2}\rho v^2$