Enter the pipe diameter, pipe material, pipe length, and total elevation change to calculate the flow velocity and mass flow rate of a gravity-fed pipe flow.

Pipe Flow Formula

The following formula is used to calculate the volumetric flow of water through a pipe of a certain diameter, length, and height.

v = k * C * R0.63 * S0.54

  • Where k is a constant (.849)
  • C is the roughness coefficient (dependent on the material of pipe)
  • R is the hydraulic radius
  • S is the slope of the pipe
  • v is the velocity of water (m/s)

From this, the mass flow rate can be determined by multiplying the volume flow rate times the density.

m= p * v

  • Where p is the density of the fluid
  • v is the volumetric flow rate

Pipe Flow Definition

The pipe flow is defined as either the total mass or total volume of fluid moving through a pipe section at any point.

How to calculate pipe flow velocity?

How to calculate pipe flow velocity.

  1. First, determine the roughness coefficient.

    This should be available based on the material used.

  2. Next, determine the hydraulic radius.

    Calculate the hydraulic radius.

  3. Next, determine the slope of the pipe.

    Calculate the slope of the pipe.

  4. Finally, calculate the flow velocity.

    Using the formula above, calculate the flow velocity.


What factors affect the flow velocity in a pipe?

The flow velocity in a pipe is affected by several factors including the pipe diameter, the roughness of the pipe’s interior surface, the slope of the pipe, the length of the pipe, and the viscosity and density of the fluid being transported.

How does the slope of the pipe impact the flow rate?

The slope of the pipe impacts the flow rate by influencing the gravitational force component acting on the fluid. A steeper slope increases the gravitational force, which can increase the flow rate, assuming all other factors remain constant.

Can the pipe flow formula be used for any fluid type?

The pipe flow formula provided is generally used for calculating the flow of water. However, it can be adapted for other fluids by adjusting the roughness coefficient and ensuring accurate values for the fluid’s density and viscosity are used. For gases or highly viscous fluids, additional factors may need to be considered.