Hydraulic diameter

The hydraulic diameter, D_H, is a commonly used term when handling flow in noncircular tubes and channels. Using this term one can calculate many things in the same way as for a round tube.

Definition:

$D_H = \frac {4A}{P}$

where A is the cross sectional area and P is the wetted perimeter of the cross-section.

For a round tube, this checks as:

$D_H = \frac{4 \frac {\pi D^2}{4}}{\pi D} = D$

The Manning formula contains a quantity called the hydraulic radius. Despite what the name may suggest, the hydraulic diameter is not twice the hydraulic radius, but four times.

For an annulus the hydraulic diameter is

$D_H = \frac{4 \cdot 0.25 \pi (D_o^2 - D_i^2)} {\pi (D_o + D_i)} = D_o - D_i$

and for a rectangular duct, if completely filled with fluid:

$D_H = \frac {4 L W} {2 (L + W)} = \frac{2LW}{L+W}$

And for a rectangular duct, if partly filled with fluid:

$D_H = \frac {4 L W} {2L + W}$

For the special case of a square duct, where L=W, then D_H = L. For the other limiting case of a very wide duct, i.e. a slot of width W where L ≫ W', then D_H = 2W.

For a fully filled duct or pipe whose cross section is a regular polygon, the hydraulic diameter is equivalent to the diameter of a circle inscribed within the wetted perimeter.

Hydraulic diameter is mainly used for calculations involving turbulent flow. Secondary flows can be observed in non-circular ducts as a result of turbulent shear stress in the turbulent flow. These secondary flows force the fluid into the "corners" of the pipe.

When the flow is laminar, secondary flows do not occur, and therefore the entire cross section of the pipe is not filled. This will result in errors in calculations.

Hydraulic diameter is also used in calculation of heat transfer in internal flow problems.

See also

• Equivalent spherical diameter
• Hydraulic radius
• Darcy friction factor