Pipe Flow Calculator
Use this pipe flow calculator to analyze the properties of water flowing in a gravityfed system. You only need to know the diameter of the pipe, the material it's made of, its length, and the drop in height. We then apply the HazenWilliams equation for you, which calculates the resulting velocity and discharge. Interested? Read on to discover the formulas we use and to see an easytofollow example calculation.
What is the gravity flow?
The gravity flow of water is when the flow of water in a pipe is caused by the force of gravity. The flow will happen as long as there is an altitude difference between the source water (upstream source) and the discharge point. There must also be no external energy (for example, from a pump) used to move the water forward.
Our water flow calculator takes into consideration the particular case of gravity flow, where the water flows in a closed pipe. Its velocity is influenced not only by the inclination and size of the pipe but also by the pipe material. Its roughness causes friction between the sides of the pipe and the water, decreasing the water speed.
HazenWilliams equation
The HazenWilliams equation is an empirically derived formula that describes the velocity of water in a gravity flow. Remember that the HazenWilliams equation is valid only for water – applying it for any other fluid will give you inaccurate results. It also doesn't take into account the temperature of the water, and is only accurate for the 4075 °F (425 °C) range.
You can write down this formula as:
v = k * C * R^{0.63} * S^{0.54}
where:
v
— Velocity of water flowing in the pipe (in m/s for the metric system and ft/s for the Imperial system);C
— Roughness coefficient;R
— Hydraulic radius (in meters or feet depending on the unit system);S
— Slope of the energy line (frictional head loss per length of pipe). It is unitless, but sometimes expressed in m/m; andk
— Conversion factor dependent on the unit system (k = 0.849
for the metric system andk = 1.318
for the imperial system).
You don't need to know the values of C, R, or S in order to use our pipe flow calculator – we calculate them for you!
The roughness coefficient C dependents on the material of the pipe. You can pick a material from a dropdown list or input the value of C manually if you know the roughness coefficient of your flow system. We use the following values:
Material  Roughness coefficient 

Cast iron  100 
Concrete  110 
Copper  140 
Plastic  150 
Steel  120 
The hydraulic radius, R, is the proportion between the area and the perimeter of your pipe. If the pipe is circular, you will find it according to the following equation:
R = A / P = πr² / 2πr = r / 2 = d / 4
where r
is the pipe radius, and d
is the pipe diameter. In this pipe flow calculator's Advanced mode
, you can view and modify all these parameters (area, perimeter, hydraulic radius).
To calculate the slope S
, you must divide the pipe length by the drop (height difference between the beginning and endpoints). Remember that if the pipe slope is not constant but changes all the time, the actual water flow speed will differ from the obtained result.
Once you know the velocity of the gravity flow, you can also find the discharge, Q
, by multiplying the crosssectional area of the pipe by the flow speed:
Q = A * v
Make sure to use our flow rate calculator to convert between the discharge (volumetric flow rate) and the mass flow rate.
Velocity of water flow in a pipe: an example
Let's use the pipe flow calculator to determine the velocity and discharge of a plastic pipe, 0.5 feet in diameter. The pipe is 12 feet long, and the difference in height between the beginning and endpoints of the pipe is equal to 3 feet.

Divide the diameter by 2 to find the radius of the pipe.
r = d/2 = 0.5 / 2 = 0.25 ft

Find the crosssectional area of the pipe.
A = πr² = π * 0.25² ≈ 0.1963 ft²

Determine the perimeter of the pipe.
P = 2πr = 2π * 0.25 ≈ 1.57 ft

Divide the area by the perimeter to find the hydraulic radius of the pipe.
R = A/P = 0.1963 / 1.57 ≈ 0.125 ft

Pick "Plastic" from the dropdown list and write down its roughness coefficient.
C = 150

Divide the drop by the length of the pipe to calculate the slope.
S = y / L = 3 / 12 = 0.25

Use the HazenWilliams equation to find the velocity of the gravity flow.
v = 1.318 * C * R^{0.63} * S^{0.54} = 1.318 * 150 * 0.125^{0.63} * 0.25^{0.54} = 25.23 ft/s

Multiply this value with the crosssectional area of the pipe to find the discharge:
Q = A * v = 0.1963 * 25.23 = 4.95 cu ft/s
That's it! You just found the speed and discharge of a gravity flow.
FAQ
How do you calculate gravity flow through a pipe?
First use the HazenWilliams equation to find the velocity of the fluid: v = k × C × R^{0.63} × S^{0.54}
. In this equation, k
is either 0.489 for metric or 1.318 if using imperial units, C
is the roughness coefficient of the pipe material, R
is the hydraulic radius (crosssectional area divided by perimeter), and S
is the slope of the pipe.
You can then calculate the volume that flows through the pipe per second by multiplying v
by the crosssectional area of the pipe.
Does flow rate change with pipe diameter?
Yes. The flow rate will increase with pipe diameter squared since it depends on the pipe's crosssectional area. It then follows that the flow rate will decrease with the square of the pipe diameter.
How to calculate volume flow rate in a pipe?
You multiply the speed of the liquid flowing through the pipe by the pipe's crosssectional area.
What is the roughness coefficient of a plastic pipe?
For a typical plastic pipe, its roughness coefficient is 150. The higher the roughness coefficient, the slower the gravityfed flow through a pipe will be.