# Flow Rate Calculator

Created by Gabriela Diaz
Last updated: Jun 29, 2022

Use the flow rate calculator to determine a moving fluid's volumetric flow rate and mass flow rate.

• What is flow rate?;
• The difference between volumetric flow rate and mass flow rate;
• How to calculate them using the volumetric flow rate equation and the mass flow rate formula; and
• How to go from the volume flow rate to the mass flow rate.

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

Flow rate is the amount of fluid that moves per unit of time. Because this amount can be represented as either volume or mass, it is essential to distinguish between volumetric flow rate and mass flow rate.

Volumetric flow rate, often referred to as flow rate, represents the volume of fluid passing through a given cross-sectional area per time. It's usually denoted by the symbol Q or sometimes as V̇ (a V with a dot).

$\small \text{Volumetric flow rate} = \cfrac{\text{Volume}}{\text{time}}$

Mass flow rate, on the other hand, describes the amount of mass that passes through a given cross-sectional area per unit of time. It is often symbolized as (m-dot):

$\small \text{Mass flow rate} = \cfrac{\text{Mass}}{\text{time}}$

## How to calculate flow rate — Volumetric flow rate equation and mass flow rate equation

To calculate the volumetric flow rate, we must first be able to relate the volume of fluid that's in a length of pipe to its retention time. This is, how long it takes for that volume to move that given distance. In the case of a pipe, this volume would correspond to the volume of a cylinder. As previously stated, this ratio is expressed as:

$\small Q = \cfrac{\text{Volume}}{\text{time}}$

Since $\text{Volume} = \text{Area} \times \text{length}$ and $\text{velocity} = \text{length}/\text{time}$, the volumetric flow rate equation is give by:

$\small Q = v \cdot A$

where:

• $Q$ — Volumetric flow rate, usually in m3/s or ft3/s;
• $v$ — Average flow velocity, in m/s or ft/s; and
• $A$ — Cross-sectional area, in m2 or ft2. If you want to learn more about area units and area conversion, you might like to take a look at our area conversion calculator.

To calculate mass flow rate you can start from the volumetric flow rate if this one is known:

$\small \dot{m} = Q \cdot \rho$

where:

• $\dot{m}$ — Mass flow rate, usually in kg/s or lb/s;
• $Q$ — Volumetric flow velocity, in m3/s or ft3/s; and
• $\rho$ — Density of the fluid, in kg/m3 or lb/ft3.

Alternately, suppose the volumetric flow rate $Q$ is unknown. In that case, you can determine the mass flow rate using the cross-sectional area $A$ and average velocity of the flow $v$ with this mass flow rate formula:

$\small \dot{m} = v \cdot A\cdot \rho$

Another concept that's of great importance in fluid mechanics is pressure. You can calculate the pressure that a fluid exerts over a surface by substituting the acceleration of gravity in the and dividing by the area of the applied force 🌊

## How to use the flow rate calculator

Let's see how to use the flow rate calculator to determine the volumetric flow rate and mass flow rate of a moving fluid passing through a pipe or any other shape:

1. Begin by selecting the shape that you'd like to evaluate. To do so, click on the drop-down menu in the Shape field. Choose 'other' if the geometry is irregular or you already know the cross-sectional area.

2. Proceed to input the corresponding cross-sectional dimensions or area if known. For example, the 'Diameter (d)' in the case of a pipe or Width (w) and Height (h) if the shape is rectangular.

3. Enter the average velocity of the flow in the Velocity row.

4. At this point, the calculator will be able to determine the (Volumetric) flow rate by just using these inputs.

5. To determine the mass flow rate, you'll need to enter the density of the flowing substance. The calculator is prefilled with water's density (998 kg/m3) since it's the most commonly used fluid. But please change this value to the corresponding of your fluid.

6. Finally, after specifying the density, the calculator will display the Mass flow rate. And you're finished! 😎

Gabriela Diaz
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
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