The integration of a flux over an area gives the volumetric flow rate.

Another unit used is standard cubic centimetres per minute (SCCM).

In US customary units and imperial units, volumetric flow rate is often expressed as cubic feet per second (ft3/s) or gallons per minute (either US or imperial definitions).

In oceanography, the sverdrup (symbol: Sv, not to be confused with the sievert) is a non-SI metric unit of flow, with 1 Sv equal to 1 million cubic metres per second (260,000,000 US gal/s);[1][2] it is equivalent to the SI derived unit cubic hectometer per second (symbol: hm3/s or hm3⋅s−1).

Named after Harald Sverdrup, it is used almost exclusively in oceanography to measure the volumetric rate of transport of ocean currents.

The change in volume is the amount that flows after crossing the boundary for some time duration, not simply the initial amount of volume at the boundary minus the final amount at the boundary, since the change in volume flowing through the area would be zero for steady flow.

The amount passing through the cross-section is reduced by the factor cos θ.

This occurs when θ = ⁠π/2⁠ and so this amount of the volumetric flow rate is zero: These results are equivalent to the dot product between velocity and the normal direction to the area.

When the mass flow rate is known, and the density can be assumed constant, this is an easy way to get

: where In internal combustion engines, the time area integral is considered over the range of valve opening.

The time lift integral is given by where T is the time per revolution, R is the distance from the camshaft centreline to the cam tip, r is the radius of the camshaft (that is, R − r is the maximum lift), θ1 is the angle where opening begins, and θ2 is where the valve closes (seconds, mm, radians).