Calculate Drain Time

Calculator after Torricelli's law for the time it takes for water to flow out of a container with an orifice. The shape of the container and of the orifice must be an generalized cylinder, this is a continuously straight, perpendicular form. This calculation applies to all thin fluids (those with low viscosity), so not only to water. The cross section area of the container must be much larger than that of the orifice. Then, this formula is a good approximation for the calculation of the drain time.

Area container A₁:
Area orifice A₂:
Height h:		m
Gravitational acceleration g:		m/s²
Drain time t:		s

Round to decimal places.

Please enter every value except for one. This one will be calculated. The height is the height of the water above the orifice. The units for both areas must be identical, e.g. square centimeters or square meters. The height is in meters, the time is in seconds. Often, the cross section of the container and of the orifice is a circle.

The formula for the calculation is: t = A₁/A₂ * √ 2h/g
Hereby, area A₁ is the base area of the container, and area A₂ is the base area of the orifice. The height is the water level in the container. The gravitational acceleration is a measure of the Earth's gravity, which causes the water to flow downward, more precisely toward the Earth's center.

Example: a container with a cross section area of 250 cm², an orifice cross section of 2 cm² and a height of 1.50 meters will be empty or at orifice level about 69 seconds after opening the orifice.

For conical containers or other containers whose cross-sectional area changes upwards, such a calculation is way more complicated. For the cylindrical cross-section assumed here, the volume of the container is the cross-sectional area multiplied by the water level. The drain velocity is then the drained volume divided by the drain time.