Flow Rate Calculator

This flow rate calculator uses flow velocity and cross-sectional flow area data to determine the volumetric flow rate of liquid.

You can calculate the flow rate in five simple steps:

  1. Select the shape of the cross-section of the channel
  2. Input all the measurements required to compute the cross-sectional area
  3. Input the average velocity of the flow
  4. Choose the unit of the flow rate
  5. Click on the "Calculate" button to compute the flow rate.
Liquid Flow Rate Calculator

What is Volumetric Flow Rate?

The volumetric flow rate, which is also commonly referred to as the rate of liquid flow or volume flow rate, is the volume of a given fluid that flows within a unit of time. It is usually denoted by the Q symbol.

The rate at which a liquid flows will vary according to area of the pipe or channel through which it is passing and the velocity of the liquid.

Units that are commonly used to measure volumetric flow rate are: m3/s (cubic meter per second), L/min (liters per minute), ft3/sec (cubic feet per second), ft3/min (cubic feet per minute, or CFM), and gal/min (gallons per minute, or GPM).

The volumetric flow rate (Q) can be computed as the product of the cross-sectional area (A) for flow and the average flow velocity (v) as follows:

Q = A * v

Example:

Let's say we have a circular channel that has an inner diameter of 8 inches. Water is flowing through the channel at an average velocity of 16 feet per second. We can determine the volumetric flow rate as follows:

The flow rate will vary according to the cross-sectional area of the channel:

Area = π * (Diameter)2 / 4

Area = 3.1415926 * (8/12 ft)2 / 4

Area = 0.349 ft2

The area of the pipe is 0.349 ft2. Using this information, we can determine the flow rate (Q) as follows:

Q = Area * Velocity

Q = (0.349 ft2) * (16 ft/s)

Q = 5.584 ft3/s

Answer: In this example, the water flows through the circular channel at a rate of 5.584 ft3/s.

Formulas for Calculating Flow Rate

The channel or pipe through which a liquid flows will commonly have a circular, rectangular, or trapezoidal cross-sectional shape. The formula that is used to determine flow rate will vary according to this cross-sectional shape. Common approaches are outlined below.

Calculating the Flow Rate in a Circular/Partially Full Circular Pipe

The cross-sectional area of a full circular pipe can be determined as follows:
A = π * (Diameter)2 / 4

The flow rate (Q) can be written as:
Q = (Velocity) * π * (Diameter)2 / 4

The cross-sectional area of a partially full circular pipe can be determined as follows:
A = (Diameter)2 * (theta - sin(theta)) / 8

Where, theta [in radians] is the central angle between the lines drawn from the center of the pipe to the water surface at each side.

The flow rate (Q), is thus as follows:

Q = (Velocity) * (Diameter)2 * (theta - sin(theta)) / 8

Calculating the Flow Rate of a Rectangular Channel

The cross-sectional area of a rectangular channel can be determined as follows:
A = (Width) * (Depth)

The flow rate (Q), is thus as follows:
Q = (Velocity) * (Width) * (Depth)

Calculating the Flow Rate of a Trapezoidal Channel

The cross-sectional area of a trapezoidal channel can be determined as follows:
A = (Depth) * (Top Width + Bottom Width) / 2

The flow rate (Q), is thus as follows:
Q = (Velocity) * (Depth) * (Top Width + Bottom Width) / 2

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