How To Calculate Equivalent Hydraulic Diameter

If you want to calculate the pressure drop, or Reynolds Number, in fluid passages that have non-circular cross-sections, this can be approximated pretty close if the shear stress at the wall of this “non-circular passage” is equated to the shear stress at the wall of an equivalent round passage. By using the following equation, we can calculate an equivalent diameter for the non-circular passage.

The equation for calculating the equivalent hydraulic diameter is:

Deq = 4A/P

Where;
Deq indicates the equivalent hydraulic diameter.
A is the cross-sectional flow area.
P is the perimeter of the fluid passage.

Example: Let's calculate the equivalent hydraulic diameter of a rectangular passage. If the rectangle measures .500 inches tall by 1.000 inches wide, what is the equivalent hydraulic diameter?

Area = .500 x 1.000 = .500

Perimeter = (.500 x 2) + (1.000 x 2) = 3.000

Equivalent Hydraulic Diameter (Deq) = (4(.5))/3

Deq = 2/3 = .667 inches

This means that this particular shaped rectangular passage will have the same pressure drop and Reynolds Number as a .667 diameter hole.

As you can see, this is a very simple calculation. As the shape of the fluid passage deviates from round, the ratio of the wall surface area to the flow surface area gets larger. This exhibits more shear stress on the flowing fluid, and causes a greater pressure drop. The passage cause the fluid to experience conditions similar to what it would experience in an equivalent hydraulic diameter, or more simply, a smaller round diameter.

The calculation of pressure drop in a non-circular passage involves calculation of the equivalent diameter and using it to obtain the friction factor. The equivalent hydraulic diameter is also used in Reynolds Number calculations. Poor results can occur when using the equation for shapes that are substantially different from round. Also, the equation is best used for turbulent flow situations. Large errors can occur in laminar flow situations.