Pipe Flow Rate Calculator

What the pipe flow rate calculator does

Flow rate is how much fluid moves past a point each second, the figure behind sizing pipes, channels, and pumps. This works it out. You pick the cross-section, enter its size and the speed the fluid moves, and it returns the volume flow rate and the mass flow rate.

It handles a full pipe, a part-full one, a rectangular channel, or any shape by its area. Below is how it works and what the two flow figures mean.

How to use it

1. Pick the cross-section: a full circular pipe, a partially filled pipe, a rectangular channel, or other by its area.
2. Enter the size for that shape, each measurement with its unit.
3. Enter the velocity in meters per second, then press Calculate, or Reset to clear it.

How the flow rate is worked out

Flow rate rests on one simple idea: the amount passing a point is the area of the opening times how fast the fluid moves through it:

Flow rate = cross-sectional area × velocity

So a wider pipe or a faster flow both carry more. The calculator works out the cross-sectional area for the shape you pick, multiplies by the velocity, and gives the volume flow rate in cubic meters per second. Everything comes down to getting that area right, which is where the shapes differ.

The four cross-sections

The shapes are four ways of finding the area the fluid flows through. A full circular pipe uses pi times the radius squared, the whole circle. A rectangular channel is width times height. The other option lets you enter a cross-sectional area directly, for any shape you have worked out yourself.

The clever one is the partially filled pipe, a pipe running part full, as a drain often does. The water fills only the bottom of the circle, a shape called a segment, and the calculator works out that exact segment area from the diameter and the depth of water. It is a calculation many tools skip or fudge, so getting the real part-full area is what makes this one trustworthy for drains and channels, not just full pipes.

Flow rate and mass flow rate

The calculator gives two figures, and the difference is worth understanding. The volume flow rate is how much space of fluid passes each second, in cubic meters per second. The mass flow rate is how much weight of fluid passes each second, in kilograms per second, found by multiplying the volume by the fluid's density.

Volume flow is what you want for filling and draining, where space is the thing. Mass flow matters when weight is what counts, in heating, process work, and anywhere the fluid's density comes into the engineering. The calculator works in water, so the mass flow is for water moving through the pipe.

A worked example: a 100 mm pipe

Say water flows through a full 100 millimeter pipe at 2 meters per second.

The radius is 50 millimeters, so the area is π × 0.05², about 0.00785 square meters. Times the 2 meters per second velocity, the flow rate is about 0.0157 cubic meters per second, which is roughly 15.7 litres a second. The mass flow rate is about 15.7 kilograms per second, since a litre of water weighs about a kilogram.

So that pipe shifts around 940 litres a minute, which is the kind of figure pump and pipe sizing turns on.

Questions people ask

How do I calculate flow rate in a pipe?

Multiply the cross-sectional area by the velocity. A full 100 millimeter pipe at 2 meters per second flows about 0.0157 cubic meters per second, or 15.7 litres a second.

How do I find the flow in a part-full pipe?

You need the area of the water, which fills only a segment of the circle. The calculator works out that segment area from the diameter and the depth of water.

What is the difference between flow rate and mass flow rate?

Volume flow rate is the space of fluid per second; mass flow rate is the weight per second, found by multiplying by the fluid's density.

What units does the velocity need to be in?

Meters per second, and the flow rate comes out in cubic meters per second to match.

References

A quick note on the numbers. The flow rate is the continuity relationship from fluid mechanics, the cross-sectional area times the velocity, and the part-full pipe uses the geometry of a circular segment. The mass flow rate multiplies by the density of water. The unit conversions follow the US National Institute of Standards and Technology guide.

1. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811