How can I calculate the volume (cubic meter per second) of water flowing out a tank? (or the velocity in meter per second)

A horizontal pipe with a diameter of 1 meter is mounted (within the tank) 10 meters below the surface (that is 10 meter for the center line of the pipe). What's the formula to calculate the water volume flowing out the tank?

Is the volume of the tank important? Let's say one tank with a diameter of 5 meter and another with a diameter of 20 meter, the volume of the water flowing out at the beginning is the same I guess? Off course for the first tank volume will decrease quicker than for the second tank.

Is there a difference if the pipe is mounted within or outside the tank?

  • $\begingroup$ If you could add a sketch we could help you a lot more. $\endgroup$
    – rul30
    Dec 10, 2017 at 13:35

1 Answer 1


The pressure driving the flow is down to the height of water above the pipe - the diameter will have no effect : pressure = density * gravity * height, you should be able to take it from here - this does seem like a homework question...

One thing to consider is how the pipe connects to the tank : sharp edge joint, rounded edge, pipe extends into tank...

Edit: If the pipe is small relative to the height of the tank then the following where A is the area:

V = Cd A (2 g H)^1/2

If the pipe is large then use the following where b is the width of the outlet in m :

V = 2/3 Cd b (2 g)^1/2 (H^3/2 - h^3/2) 

and H is the height from the liquid surface to the top of the pipe and h is the height from the liquid surface to the bottom of the pipe.

  • $\begingroup$ The configuration of the pipe is also important - is it a short straight discharge to an open area, or a long pipe with lots of tirns, valves, and other restrictions? $\endgroup$
    – Mark
    Dec 3, 2017 at 22:28
  • $\begingroup$ @Mark if those details are specified then the loss factor for each bend, constriction, valve, even change of material and surface roughness can be included... $\endgroup$
    – Solar Mike
    Dec 4, 2017 at 8:33

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