Will it move?

Classical Mechanics Level 2

Fill in the blank:

There are two identical small holes on the opposite sides of a tank containing a liquid as shown below. The tank is open at the top. The difference in heights between the two holes is $h$ . As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to $\text{\_\_\_\_\_\_\_\_\_\_\_}$ .

\sqrt{h}

h^{1.5}

h^2

2 solutions

Gautam Sharma
Sep 12, 2015

From Toricelli's theorem we know that velocity of efflux $v$ $v=\sqrt{2gh}$

(area of orifice is $\ll$ Cross section area of tank $A$ )

here $h$ is depth of orifice from surface.

We know $F=\rho Av^2$

Hence Force by deeper orifice will be greater as $v$ will be greater and hence due to unequal force the tank will move.

Moderator note:

Great insight in finding the imbalance. Your writeup would be clearer if you were more explicit with your calculation.

Siddhant Chaudhari
Dec 23, 2015

P=hdg. Pressure is exerted equally in all directions about a point. So on the walls,pressure will reduce as height reduces. Force is directly proportional to pressure. Job done.

Will it move?

2 solutions

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