Calculate ideal liquid outflow speed, circular-orifice flow rate, optional mass flow from an entered density, or constant-area tank drain time. This incompressible-liquid model assumes equal surface/outlet pressure, a small outlet and negligible surface velocity. It does not model gas flow or pressurized tanks.

Incompressible liquid, equal surface/outlet pressure and a small outlet. Ignores surface velocity, pipe friction and changing discharge coefficient. Not a gas or pressurized-tank model.

Default: standard Earth gravity. Planetary suggestions are approximate.

Torricelli's Law Formula

The following formula is used to calculate the speed of fluid flowing out of an orifice under the force of gravity according to Torricelli's Law.

v = √(2gh)

Variables:

  • v is the speed of the outflow (m/s)
  • g is the acceleration due to gravity (m/s²)
  • h is the vertical distance between the liquid surface and the outlet (m)

To calculate the ideal outflow speed, use v = √(2gh). Circular-orifice flow is Q = Cd × (πd²/4) × √(2gh); optional mass flow is density × Q. For a constant-area tank, t = 2A(√h₀ − √h₁)/(Cd × a × √(2g)), with heights above the outlet and no inflow. The previous drain implementation omitted the factor 2. The assumed Cd defaults to 0.61; geometry and density suggestions are illustrative, so use values suitable for the actual system. Default gravity is standard Earth gravity, 9.80665 m/s².

What Is Torricelli's Law?

Torricelli's Law is a principle in fluid dynamics that describes the speed of fluid flowing out of an orifice under the force of gravity. It states that the speed (v) of the outflow is proportional to the square root of the vertical distance (h) between the liquid surface and the outlet, or v = √(2gh), where g is the acceleration due to gravity. This law is essentially a specific application of Bernoulli's principle, and is named after the Italian scientist Evangelista Torricelli.

How to Calculate Torricelli's Law?

The following steps outline how to calculate the speed of the outflow using Torricelli's Law.

  1. First, determine the value of acceleration due to gravity (g) in meters per second squared (m/s²).
  2. Next, determine the vertical distance between the liquid surface and the outlet (h) in meters (m).
  3. Next, gather the formula from above: v = √(2gh).
  4. Finally, calculate the speed of the outflow (v) using the formula.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

acceleration due to gravity (g) = 9.8 m/s²

vertical distance (h) = 5 m. The ideal speed is √(2 × 9.8 × 5) ≈ 9.89949494 m/s.