Flow Section Channels - Geometric Relationships

Area, wetted perimeter and hydraulic diameter for geometric sections like

• rectangular channels
• trapezoidal channels
• triangular channels
• circular channels

Rectangular Channel

Flow Area

Flow area of a rectangular channel:

A = b h                               (1)

where

A = flow area (m², in²)

b = width of channel (m, in)

h = height of flow (m, in)

Wetted Perimeter

Wetted perimeter of a rectangular channel:

P = b + 2 h                         (1b)

where

P = wetted perimeter (m, in)

Hydraulic Radius

Hydraulic radius of a rectangular channel:

R_h = b h / (b + 2 h)                   (1c)

where

R_h = hydraulic radius (m, in)

• Hydraulic diameter

Trapezoidal Channel

Flow Area

Flow area of a trapezoidal channel:

A = h (b + T) / 2                      (2)

Wetted Perimeter

Wetted perimeter of a trapezoidal channel:

P = b + 2 (((T - b) / 2)² + h²)^1/2                       (2b)

Hydraulic Radius

Hydraulic radius of a trapezoidal channel:

R_h = (h (b + T) / 2) / (b + 2 (((T - b) / 2)² + h²)^1/2)                       (2c)

• Hydraulic diameter

Triangular Channel

Flow Area

Flow area of a triangular channel:

A = z h²                     (3)

where

z = see figure above (m, in)

Wetted Perimeter

Wetted perimeter of a triangular channel:

P = 2 h (1 + z²)^1/2                      (3b)

Hydraulic Radius

Hydraulic radius of a triangular channel:

R_h = z h / 2 (1 + z²)^1/2                      (3c)

• Hydraulic diameter

Circular Channel

Flow Area

Flow area of a circular channel:

A = D²/4 (α - sin(2 α)/2)                      (4)

where

D = diameter of channel

α = cos^-1(1 - h/r)

Wetted Perimeter

Wetted perimeter of a circular channel:

P = α D                      (4b)

Hydraulic Radius

Hydraulic radius of a circular channel:

R_h = D/4 [1 - sin(2 α) / (2 α)]                     (4c)

• Hydraulic diameter

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