Question

A 20 m high tank is full of water. A hole appears at its middle. the speed of wfflux will be ?

Answer 1

Answer:

between 4 m/s and 5 m/s

Explanation:

he main thing to know about this is that water pressure depends only on depth. The initial speed of the stream of water will come from pressure due to a one meter height of water. That pressure is the weight of a cylinder of water one meter high with a certain cross sectional area. Since pressure is force per area, You have density of water (mass/volume) times 9.8 N/Kg x one meter times cross sectional area divided by cross sectional area.

This shows that the area doesn't matter for pressure. If the density of the water (depends very slightly on temperature) is taken as one gm/cm^3, use 1000 kg/m^3. That get you a pressure of 9800 N/m^3.

From the bernoulli equation you have pressure plus (1/2) x density x v^2 in the tank equals pressure outside plus (1/2) x density x v^2 outside.

It turns out that this is one of the many times in physics problems that it would have been best to do things only algebraically first. If we start over and do it this way, a remarkable thing happens that could have been assumed in the first place on the basis of conservation of energy. But that shouldn't be a surprise since Bernoulli's equation was derived from that principle.

So pressure inside is density x height x g which equals (1/2) x density x v^2, or v^2 = 2gh.

This is the same speed that something would get in dropping one meter in the local gravitational field of g!  You should get between 4 m/s and 5 m/s.