Question

There is a $90^\circ $ bend in a pipe line in which water is flowing at speed $v$ . The cross sectional area of pipe is $A$ . The force exerted by pipe walls on water at bend is

• A. $\sqrt{3}Av^{2}\rho $
• B. $\sqrt{2}Av^{2}\rho $
• C. $Av^{2}\rho $
• D. $\sqrt{5}Av\rho $

Answer 1

Answer: (B)

$F=\frac{d p}{d t}=\left(\sqrt{2} V\right)\frac{d m}{d t}=\left(\sqrt{2} V \rho \right)\frac{d \left(\text{volume}\right)}{d t}=\left(\sqrt{2} V \rho \right)\left(A V\right)$