First slide

Fluid dynamics

Question

A rectangular vessel when full of water takes 10 minutes to be emptied through an orifice in its bottom. How much time will it take to be emptied
when half filled with water ?

Moderate

A

9 minutes
B

7 minutes
C

5 minutes
D

3 minutes

Solution

We know that velocity (v) of outflow through an orifice is given by
$v = \sqrt{(2 g h)}$
$IatA be the area of cross - section of the a n d a b e t h e a r e a o f c r o s s s e c t i o n o f t h e orifice . The tirne o f e m p t y t i s g i v e n b y t = \frac{A}{a} \sqrt{\frac{2 h}{g}} T h e r e f o r e \frac{t'}{t} = \sqrt{\frac{h'}{h}} \Rightarrow \frac{t'}{10} = \sqrt{\frac{h / 2}{h}} \Rightarrow t' = \frac{10}{\sqrt{2}} s = 7 m i n$

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