Question

water (density $\rho$) is flowing through the uniform tube of cross-sectional area A with a constant speed v. as shown in the figure. The magnitude of force exerted by the water on the curved corner of the tube is (neglect viscous forces)

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

Answer 1

The correct option is A $\sqrt{3}\rho A{v}^2$

$FBD$ of curved part of tube.

$\begin{array}{c}\rho A{V}^2=k\\ F_{res}=\sqrt{k^2+k^2+2k^2.\frac{1}{2}}\\ =k\sqrt{3}\\ =\sqrt{3}\rho A{V}^2\end{array}$