# Torricelli's speed of efflux law

Torricelli's law states that if we make a hole in a container of fluid open to atmosphere, then the speed of the fluid spouting out is:

$$\sqrt{2gh}$$

Does this velocity correspond to the horizontal velocity or the vertical velocity of the spouting water?

I would guess it is the horizontal velocity because I can see that it seems to depend on height, but it also doesn't make sense that the water comes out with zero vertical velocity after being pressurized so much.

So which one is it?

It is valid for both!! but make sure that the hole should very small compared to the upper tank's diameter. because we use an approximation for deriving.. hope this helped

• It is not valid for both. – SchrodingersCat Dec 15 '15 at 14:16
• bro! i am dam sure it is valid for both! you can check the derivation their is no direction given en.wikipedia.org/wiki/Torricelli%27s_law#Derivation – user5954246 Dec 15 '15 at 14:29
• No direction given does not imply that it is valid for both directions, is it? What does your intuition say? Is it correct? – SchrodingersCat Dec 15 '15 at 14:31
• hmmm!!! yeah it does not depend on any angle direction only difference in heights – user5954246 Dec 15 '15 at 14:33
• @Schrodinger: It is talking about velocity at the port, not some distance away. Of course if the flow is vertical it will gain kinetic energy proportional to how far it has fallen from the port, but then it is no longer in the port. – Mike Dunlavey Mar 24 '16 at 17:15

When you puncture the container I don't understand why the velocity of the water have vertical velocity. The water is falling due to the pressure of the atmosphere and the gravity.

The water will not fall in a parabola like a cannon projectile. The water will not go up and come down because this is a violation of the conservation of energy as the work will be done without the external force to do work on it.

The equation of the velocity is for the velocity of the coming water irrespective of the orientation of the opening on the container which is on the side.

It is important to remember that the velocity of the water coming out of the hole which is on the side of the container will reduce as the height of the water level will be reducing instantaneously.

But when the water is falling through the hole which is in the bottom of the container. the water will come out with constant speed. Because the velocity of the water is not dependent on the water column.

Try out this experiment using a water bottle. you will get it.

• I did not mean vertical upward velocity. I meant downward initial velocity. I guess it wasn't too clear in my question. – Mahathi Vempati Dec 15 '15 at 14:51
• Yeah dude it may happen if you are new to the site or you are tired when you are putting the question online – Vinay5forPrime Dec 15 '15 at 15:06