Please help me! :(

Question

How fast does water flow from a hole at the bottom of a very wide 5.8 m deep storage tank filled with water? Ignore viscosity.   (The density of water is 1000 kg/m³)  

  

Answer 1

Hi Bristan

For flowing water you can use Bernoulli's equation:

P_top+ρgh_top+ρv_top²/2=P_bottom+ρgh_bottom+ρv_bottom²/2

In your case:

1. pressure at the top and bottom are the same 1 atm (atmospheric pressure, since both are open to atmosphere),
2. velocity at the top is the speed by which the liquid level will drop. Since it is very wide container, the speed of the water level dropping there will be close to zero.
3. You can set h_bottom as zero height, and your equation simplifies to:

ρgh_top=ρv_bottom²/2

You don't even need to know the density of your fluid because it cancels:

gh_top=v_bottom²/2

Solve for v_bottom

v_bottom=(2gh_top)^1/2

You can also get this equation from conservation of energy for an object freely falling a distance h: this is why we sometimes refer Bernoulli's law as conservation of energy for fluids. I will leave the last part for you to do: just plug in the height (h_top=5.8 m) and the value of g=9.8 m, and you should get your answer.

Remember that this works only if you are told that the area of the container ("very wide") is much larger than the cross sectional area of the opening (hole) through which the liquid flows.