Created By : Naaz Fatima

Reviewed By : Phani Ponnapalli

Last Updated : Apr 10, 2023

Free Pipe Flow Calculator is used to compute the properties of water flowing in a gravity-fed system. You can know the flow speed and flow discharge by simply entering pipe diameter, material, pipe length and drop details in the input fields. This handy calculator will save you from lengthy calculations.

Pipe diameter:
Pipe length:

Steps to Get Flow Velocity & Flow Discharge

In the below-sections we have given the simple steps to find the properties of water flowing in a gravity-fed system. Follow then and learn how to solve flow velocity for the given details.

  • Get the material type of pipe, pipe diameter, length and drop values.
  • Find the hydraulic radius value i.e diameter divided by 4.
  • Calculate the slope of the energy line i.e pipe length divided by drop.
  • Get the area of the circular pipe.
  • Substitute the values in the formulas.
  • Perform the math operations to check the flow discharge and flow rate of a pipe.

Gravity Flow Definition | Hazen-Williams Equation

When the water flow in a pipe is caused by the gravitational force, then it is called the gravity flow of water. We can calculate that water flow velocity using the Hazen-Williams Equation.

Hazen-Williams equation is valid only for the water. The formula is along the lines.

v = k * C * R0.63 * S0.54


v is the water flow velocity in the pipe (m/s is for the metric system, ft/s is for the imperial system)

C is the roughness coefficient

R is the hydraulic radius

S is the slope of the energy line

k is conversion factor (k=0.849 for the metric system, k=1.318 f

or the imperial system)

The roughness coefficient depends on the material of the pipe we use. The following are the values for various pipes

Material Roughness Coefficient
Cast Iron 100
Concrete 110
Copper 140
Plastic 150
Steel 120

Hydraulic radius is defined as the ratio of area and perimeter of the pipe. As the pipe is in a circular shape,

Hydraulic radius R = A/P = πr²/2πr = r/2 = d/4

The slope of the energy line is obtained by dividing the pipe length by the drop.

The formula to get the flow discharge Q is as follows:

Q = Av


Question: Calculate the velocity and discharge of a copper pipe having 0.5 ft in diameter. The pipe is 15 ft long and the difference in height between the starting and endpoints of the pipe is 5 ft.


Given that

Diameter of pipe d = 0.5 ft

Pipe length = 15 ft

Drop = 5 ft

Radius of the pipe r = d/2 = 0.5/2 = 0.25 ft

Cross-sectional area A = πr² = 3.14 * 0.25²

= 0.1963 ft┬▓

Perimeter of the pipe P = 2πr = 2 * 3.14 * 0.25

= 1.57 ft

Hydraulic radius R = A/P

= 0.1963/1.57 = 0.125 ft

Slope S = drop/length of pipe

= 5/15 = 0.33

As the pipe material is copper, the roughness coefficient C = 140

Hazen-Williams equation for velocity v = k * C * R0.63 * S0.54

Substitute the values

v = 1.318 * 140 * (0.125)0.64 * (0.33)0.54

= 26.795 ft/s

Flow discharge Q = Av

= 0.1963 * 26.795 = 5.25 ft3/s

Therefore, the water flow rate is 26.795 ft/s and flow discharge is 5.25 ft3/s.

Check-out Physicscalc.Com to get the calculators on different physics topics like waves, optics, fluid mechanics, thermodynamics, electromagnetism, etc to make your calculations quick & easy.

Frequently Asked Questions on Pipe Flow Calculator

1. How to calculate the flow rate in a pipe?

Flow rate is nothing but the velocity of water flow in a pipe. The water flow rate can be calculated with the help of the Hazen-Williams equation. Put the values in the equation to get the result.

2. What is a gravity flow water system?

The gravity system of water supply is the system in which water flows under gravity without using any external energy to deliver water from the source to tap stand.

3. How to find pipe diameter from the water flow rate?

The square root of 4 times the flow rate divided by the pi times of velocity gives the diameter of the pipe.

4. What is the Hazen-Williams equation?

Hazen-Williams equation is a formula that is used to calculate the velocity of water in a gravity flow. The formula is v = k * C * R0.63 * S0.54.