Hydraulic Diameter Calculator

Hydraulic diameter D_h is a single equivalent-diameter value, D_h = 4A/P, where A is the flow cross-sectional area and P is the wetted perimeter (the perimeter actually in contact with the fluid). It lets engineers apply circular-pipe formulas like Reynolds number and the Darcy friction factor to non-circular ducts and channels by substituting D_h wherever the formula calls for diameter D.

Most fluid mechanics correlations, including Reynolds number, the Moody chart friction factor, and Nusselt number heat transfer correlations, were derived and validated for circular pipes. Rectangular ducts, annular gaps, and open channels have no single natural diameter, so hydraulic diameter gives a consistent, physically motivated substitute that keeps those correlations reasonably accurate for non-circular shapes.

For a full rectangular duct with sides a and b, D_h = 2ab / (a+b). This comes from A = ab and P = 2(a+b), so D_h = 4A/P = 4ab / (2(a+b)) = 2ab/(a+b). For a square duct where a = b, this simplifies exactly to D_h = a.

For a concentric annular gap between an outer diameter D_o and inner diameter D_i, such as a shell-and-tube heat exchanger, D_h = D_o - D_i. This comes from A = pi/4 (D_o^2 - D_i^2) and P = pi(D_o + D_i), and the pi terms cancel exactly to leave a simple difference.

For a rectangular open channel with width b and flow depth h, the free top surface is excluded from the wetted perimeter because it touches air, not a solid wall. So P = b + 2h (bottom plus two sides only) and A = bh, giving D_h = 4A/P = 4bh / (b+2h). This differs from a fully enclosed rectangular duct, which includes all four sides in P.

For a full circular pipe of diameter D, D_h = D exactly. This is because A = pi D^2/4 and P = pi D, so 4A/P = 4(pi D^2/4)/(pi D) = D. Hydraulic diameter is designed so it reduces to the ordinary diameter for the circular case that all the underlying correlations were originally built for.

Yes, this is the primary use case. Compute D_h for your duct or channel shape here, then use it as the length scale D in the Reynolds Number Calculator and the Moody Chart Friction Factor Calculator. The resulting Reynolds number and friction factor are approximate for non-circular shapes but are the standard engineering practice for HVAC ducts, heat exchangers, and open channels.

As a rectangular duct becomes very elongated (aspect ratio b/a approaching zero, a thin slot), hydraulic diameter approaches 2b, twice the short side, not the long side. This is because the wetted perimeter grows almost linearly with the long side a, while the area only grows linearly with the short side b, so the 4A/P ratio collapses toward the narrow dimension.

Hydraulic diameter is exact as a geometric definition (it is always precisely 4A/P for any shape), but its use as a substitute for D in circular-pipe correlations is an approximation. It works very well for shapes reasonably close to circular or square, and less accurately for highly elongated or irregular cross-sections, where more advanced non-circular duct correlations may be needed for precise engineering work.

Hydraulic radius R_h = A/P (area over wetted perimeter, without the factor of 4), commonly used in open-channel hydraulics and the Manning equation. Hydraulic diameter D_h = 4A/P = 4R_h. The factor of 4 exists specifically so that D_h reduces to the ordinary diameter D for a full circular pipe, matching the convention used in pipe-flow formulas.