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Torricelli's Law Calculator

Find how fast fluid jets from a hole below the surface.

Result

5.42 m/s
19.53 km/h

How it is calculated

The speed of a liquid leaving a small hole is v = √(2 × g × h), where h is the depth of the hole below the free surface in metres and g is gravitational acceleration in m/s². If you leave g empty, zero or negative, the tool uses 9.81 m/s². The speed is given in m/s and also in km/h (multiplied by 3.6), rounded to two decimals. The depth must be above zero. This is the ideal speed: it assumes a wide tank, a small hole and no friction. A real jet is somewhat slower, and the tool does not compute flow rate, which also needs the hole area and a discharge coefficient.

Worked example

A tank has a small hole 1.5 m below the water surface, with the default g of 9.81 m/s². Inside the root: 2 × 9.81 × 1.5 = 29.43. Square root: √29.43 ≈ 5.425, shown as 5.42 m/s. In km/h: 5.425 × 3.6 ≈ 19.53 km/h. This is the same speed a stone reaches after falling freely 1.5 m. On the Moon (g = 1.62), the same depth would give about 2.20 m/s.

Try this example →

Common mistakes

  • Using the total height of the tank instead of the depth of the hole below the water surface. Only the vertical distance from the surface down to the hole counts.
  • Entering depth in centimetres or inches. The result assumes metres together with g in m/s², so 150 cm typed as 150 gives a speed more than ten times too high.
  • Expecting the speed to depend on the liquid. Density cancels out, so water, oil and syrup leave at the same ideal speed (viscosity only matters in real conditions).
  • Treating the result as flow rate. Volume per second also needs the hole area and an allowance for the contraction of the jet.
  • Assuming the speed stays constant. As the tank drains, h falls and so does the speed, so the number is valid only for the depth you entered.

About this calculator

This calculator finds the efflux velocity of liquid escaping through a hole using Torricelli's law: v = √(2gh), where g is gravitational acceleration and h is the depth of the hole below the fluid's surface. Torricelli derived this in 1643 by applying Bernoulli's principle (before Bernoulli formalized it), showing that the exit speed matches what an object would reach falling freely from height h.

Engineers use it to estimate drain and tank discharge rates, size orifices for irrigation and industrial fluid systems, and it's a classic demonstration in fluid mechanics courses of energy conservation in a flowing liquid. Enter the depth of the hole below the surface to get the jet's exit velocity.

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