Shape
circular (pipe) Diameter (d)
in
Velocity
ft/s
Density
lb/cu ft
Flow rate
(Volumetric) flow rate
ft³/s
Mass flow rate
lb/s

# Flow Rate Calculator

By Hanna Pamuła, PhD candidate

Believe it or not, our flow rate calculator is not only useful in fluid mechanics, but also in everyday problems. It will not only help you if you want to find the flow rate of a garden hose or shower head, but also if you're curious how much blood your heart pumps every minute (it's cardiac output). It may also serve as simple pipe velocity calculator.

For a complete understanding of the topic, you can find a section explaining what the flow rate is below, as well as a paragraph helping to understand how to calculate the flow rate. Be careful, as the term "flow rate" itself may be ambiguous! Luckily for you, we've implemented two flow rate formulas, so you're covered in both cases. This means that our tool may serve as both a volumetric flow rate calculator and a mass flow rate calculator.

## What is flow rate? Volumetric and mass flow rate

When we talk about flow rate, you most likely picture the concept of volumetric flow rate (also known as rate of liquid flow, volume flow rate or volume velocity). The volumetric flow rate can be defined as the volume of a given fluid that passes through a given cross-sectional area per unit of time. It's usually represented by the symbol Q (sometimes V̇ - V with a dot)

`Volumetric flow rate = V / t = Volume / time`

Another related concept is mass flow rate, sometimes called mass flux or mass current. This time it's not the volume, but mass of a substance that passes through a given cross-sectional area per unit of time.

`Mass flow rate = m / t = mass / time`

Mass flow rate is commonly used in the specifications of fans and turbines, amongst other things.

If you're interested in fluid mechanics, you should also have a look at the Bernoulli equation calculator to determine the speed and pressure of an incompressible fluid. Also, the hydrostatic pressure and buoyancy calculators may be helpful.

## How to calculate flow rate? Flow rate formulas

TL;DR version

• Volumetric flow rate formula: `Volumetric flow rate = A * v`

where `A` - cross-sectional area, `v` - flow velocity

• Mass flow rate formula: `Mass flow rate = ρ * Volumetric flow rate = ρ * A * v`

where `ρ` - fluid density

Longer explanation:

The volumetric flow rate formula may be written in the alternative (read: way more useful) form. You can first calculate the volume of a portion of the fluid in a channel as:

`Volume = A * l`

Where `A` is a cross-sectional area of the fluid and `l` is the width of a given portion of the fluid. If our pipe is circular, it's just the formula for cylinder volume. Substituting the above formula to the equation from the flow rate definition, we obtain:

`Volumetric flow rate = V / t = A * l / t`

As `l / t` is the volume length divided by time, you can see that it's just the flow velocity. So, the volumetric flow rate formula boils down to:

`Volumetric flow rate = A * v`

Most pipes are cylindrical, so the formula for volumetric flow rate will look as follows:

`Volumetric flow rate for cylindrical pipe = π * (d/2)² * v` where `d` is the pipe diameter

The equation can be rearranged to find the formula for pipe velocity.

To find the mass flow rate formula, we need to remind ourselves of the density definition first:

`ρ = m / V` and `m = ρ * V`

As mass flow rate is the mass of a substance passing per unit of time, we can write the formula as:

`Mass flow rate = m / t = ρ * V / t = ρ * Volumetric flow rate = ρ * A * v`

`Mass flow rate = ρ * A * v`

## How to use the flow rate calculator

Now that you know what the flow rate is, let's check it out with a simple example:

1. First, select a shape from the drop-down list. For this example, we'd like to know the flow rate of water in a circular pipe, so we will select the `circular (full)` option.

2. Input the measurements needed to compute cross-sectional area. If the cross-section is a circle or square/rectangle, you'll find that option on the list. In every other case, you can type the area value directly into the calculator (you can use our comprehensive area calculator to help you). Let's choose a pipe with in internal diameter of 3 inches.

3. Enter the average velocity of the flow. Let's pick 10 ft/s.

4. And there it is, the first part of the calculations is done: the tool has worked as a volumetric flow rate calculator. We've found out that the volumetric flow rate is 0.4909 ft³/s. Remember, you can always change the units, so don't worry if you need to work in gallons/minute or liters/hour.

5. If you know the density, you can calculate the mass flow rate as well, just input the density of the flow material. In our example, water has a flow rate of approximate 998 kg/m³ (the density of water at 68°F / 20°C). However, if you want to be super accurate, check out our water density calculator, as the density changes with temperature, salinity, and pressure.

6. The tool displayed a mass flow rate of 30.58 lbs/s. Great!

Don't forget that our tools are flexible, so you can use it as pipe velocity calculator. You can, for example, determine the water velocity of your faucet, given the diameter (e.g., 0.5 in) and flow rate of a kitchen faucet (usual range is 1-2.2 gallons per minute, depending on the aerator type). By the way, have you seen our tap water calculator which shows your savings if you were to switch from bottled to tap water?

Hanna Pamuła, PhD candidate