Enter the pipe diameter (or the depth of flow) into the calculator to calculate the other value. This calculator assumes a circular pipe flowing full to the crown under free-surface (gravity) flow, so the depth of flow equals the pipe’s internal diameter (DF = PD). If a pipe is pressurized, a free-surface “depth of flow” is not applicable.

Depth Of Flow In Pipe Calculator

Enter either Pipe Diameter or Depth of Flow to calculate the other (full-pipe assumption: DF = PD)

Depth of Flow Formula

The following formula is used to calculate the depth of flow in a circular pipe when it is flowing full to the crown under free-surface (gravity) flow.

DF = PD

Variables:

  • DF is the depth of flow in the pipe (a length, e.g., feet or meters)
  • PD is the pipe’s internal diameter (a length, e.g., feet or meters)

To calculate the depth of flow in a pipe that is flowing full (to the crown), the depth of flow equals the pipe diameter. For partial (partially full) gravity flow, the depth depends on additional factors (such as slope/energy gradient and roughness, e.g., Manning’s n) and is typically solved using open-channel flow relationships (often iteratively), not from flow rate and diameter alone.

What is Depth of Flow in a Pipe?

Depth of flow in a pipe refers to the vertical distance from the bottom (invert) of the pipe to the surface of the flowing water (the free surface). It is an important parameter in hydraulic and civil engineering for designing and analyzing gravity (free-surface) pipe systems. The depth of flow can vary depending on whether the pipe is flowing full or partially full.

How to Calculate Depth of Flow?

The following steps outline how to calculate the Depth of Flow in a Pipe.

  1. First, confirm the situation is free-surface (gravity) flow and the pipe is flowing full to the crown.
  2. Next, determine the pipe’s internal diameter (PD).
  3. Next, gather the formula from above: DF = PD.
  4. Finally, calculate the Depth of Flow (DF) using DF = PD (in consistent units).
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

flow rate (Q) = 2 cubic feet per second (not needed when assuming the pipe is flowing full to the crown under free-surface conditions)

pipe diameter (PD) = 1 foot

Depth of flow (DF) = 1 foot