Fluid Mechanics-1

Classical Mechanics Level 4

A rectangular tank of height $10 \text{ m}$ filled with water, is placed near the bottom of an incline of angle ${ 30 }^{ \circ }$ . At a height $h$ from bottom a small hole is made as shown, such that stream coming out from hole strikes the inclined plane normally. Find $h$ .

Try Fluid Mechanics-2 and Fluid Mechanics-3

The answer is 8.333.

2 solutions

Murlidhar Sharma
Apr 2, 2015

For simplicity I assume x and y as rightwards and downwards directions.

Velocity of strean of water in x-direction will remain $\sqrt{2*g*(10-h)}$

If the stream is perpendicular to the incline then it makes an angle of \pi/3 with the horizontal. Therefore,

Velocity of strean of water in y-direction will be $\sqrt{6*g*(10-h)}$ at that point. I assumed that 't' time has passed,

Distance travelled in x-direction 'x' = $\sqrt{2*g*(10-h)}*t$

Distance travelled in y-direction = $(g*t^2)/2 = h-x*tan(\pi/6)$

Solving it we get the correct answer

Ashutosh Sharma
Jan 28, 2018

use translation of axes and bit trigo