Question

A large open tank has two holes in its wall. One is a square of side a at a depth x from the top and the other is a circular hole of radius r at depth 4x fron the top. When the tank is completely filled with water,the quantities of water flowing out per second from both holes are the same. Then r is equal to

Answer 1

Answer on Question #38356, Physics, Mechanics

Question:

A large open tank has two holes in its wall. One is a square of side at a depth $x$ from the top and the other is a circular hole of radius $r$ at depth $4x$ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then $r$ is equal to

Answer:

Speed of water in hole equals:

$$v = \sqrt{2gh}$$

where $g$ is acceleration due to gravity, $h$ - depth

Water flow equals:

$$f = \frac{V}{t} = \frac{vtS}{t} = vS = \sqrt{2gh} S$$

where $S$ is area of hole.

Therefore:

$$\sqrt{2gx} a^2 = \sqrt{2g4x} \pi r^2$$ $$r = \frac{a}{2\sqrt{\pi}}$$

Answer: $r = \frac{a}{2\sqrt{\pi}}$