# How to Calculate Hydraulic Diameter

The hydraulic diameter is a term used in fluid mechanics and thermodynamics. It is a measure of the efficiency of a section to pass flow by relating the cross-sectional area of flow to the wetted perimeter of the cross-section.

The hydraulic diameter of a round pipe is simply its diameter. The equations for hydraulic diameter for other cross-sections are given in the table below.

Flowing Full
Circle $latex D$
Annulus $latex D_{outside} – D_{inside}$
Square (L = side) $latex L$
Rectangle (L1 and L2 = sides) $latex \frac{2L_1L_2}{L_1 + L_2}&s=1$
Flowing partially full
Half-filled circle (d = diameter) $latex d&s=1$
Rectangle (h = height, w = width) $latex \frac{4hw}{w + 2h}&s=2$
Wide, shallow stream (d = depth) $latex 4d&s=1$
Triangle (d = depth, t = top, s = side length) $latex \frac{d\cdot t}{s}&s=2$
Trapezoid (d = depth, t = top, b = bottom, s = side length) $latex \frac{2d(t + b)}{b + 2s}&s=2$

The hydraulic diameter should not to be confused with the hydraulic radius term in the Manning equation, which is not half of the hydraulic diameter, but rather one quarter.