Hydraulic Radius

R = \frac{A}{P}

Hydraulic radius is the flow area divided by the wetted perimeter. It is the characteristic length in Manning and Hazen–Williams. For a full (or half-full) circular pipe R = D/4; for a very wide rectangle R ≈ y.

$R$ (m): Hydraulic radius
$A$ (m²): Cross-sectional flow area
$P$ (m): Wetted perimeter

Step-by-step solved example

Rectangular channel 4.0 m wide and 1.5 m deep. Find R.

R = A/P_wetted. Rectangle: by/(b+2y).

1. Area and perimeter
A = 4.0×1.5 = 6.00 m². P = 4.0 + 2×1.5 = 7.00 m (bed plus two walls).
2. Divide
R = A/P = 6.00/7.00 = 0.857 m.
$R = 0.857 m$

Answer: R = 0.857 m

10 practice questions

0/10 correct

1.Hydraulic radius of a full circular conduit is

2.A 3 m wide × 1 m deep rectangle has R =

3.Wetted perimeter of a rectangle of width b and depth y is

4.For a very wide rectangular channel, R is nearest

5.Trapezoid with A = 12 m² and P = 10 m: R =

6.A half-full circular pipe of diameter D has R =

7.Increasing depth in a narrow rectangle (fixed b) makes R

8.Most-efficient rectangle (b = 2y) has R =

9.Hydraulic radius is the length scale in

10.If A doubles while P is unchanged, R