Hydraulic Diameter

D_{h} = \frac{4 A}{P}

For Darcy friction in a noncircular closed duct, replace D by Dh = 4A/P (P = wetted perimeter). A full circular pipe: Dh = D. A square side a: Dh = a. Used with Re = V Dh / ν and f (L/Dh) V²/2g.

$D_{h}$ (m): Hydraulic diameter
$A$ (m²): Flow area
$P$ (m): Wetted perimeter

Step-by-step solved example

Square duct, side 0.20 m, flowing full. Dh?

Noncircular duct: Dh = 4A/P.

1. A,P
A=0.04 m², P=0.80 m.
2. Dh
Dh=4×0.04/0.80=0.20 m (= side).

Answer: 0.20 m

10 practice questions

0/10 correct

1.Circle full: Dh=

2.Dh vs hydraulic radius R: Dh=

3.A wide-open rectangle of depth y (free surface) uses R=A/P, not Dh of a closed duct, because

4.Annulus between D and d: A=π(D²−d²)/4, P=π(D+d), Dh=

5.Re for a duct uses

6.Square a=0.1 m full. Dh=

7.Darcy hf uses L/Dh in place of

8.A very flat closed rectangle b>>h: Dh ≈

9.Wetted perimeter for a closed full duct is

10.Units of Dh are