question_answer

Water is coming out from a tap of cross-section area A with speed\[{{v}_{0}}\]. Area of cross-section of water stream changes as it moves down. Which of the following graph can best represent cross-section area 'a' of stream with depth h?

A)         

B)

C)

D)

Correct Answer: C

Solution :

[c] Velocity of stream at height h will be given as \[{{v}^{2}}={{v}_{0}}^{2}+2gh\]    or \[v=\sqrt{v_{0}^{2}+2gh}\] From continuity law, \[{{v}_{0}}A=va\]  or   \[a=\frac{{{v}_{0}}A}{v}\] or  \[a=\frac{{{v}_{0}}A}{\sqrt{v_{0}^{2}+2gh}}\]