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Flow Section Channels - Geometric Relationships

Geometric relationships like area, wetted perimeter and hydraulic diameter.

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Area, wetted perimeter and hydraulic diameter for geometric sections like

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

Various Flow Section Channels and their Geometric Relationships

Rectangular Channel

Flow Area

Flow area of a rectangular channel:

A = b h                               (1)


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)


P = wetted perimeter (m, in)

Hydraulic Radius

Hydraulic radius of a rectangular channel:

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


Rh = hydraulic radius (m, in)

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:

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

Triangular Channel

Flow Area

Flow area of a triangular channel:

A = z h2                     (3)


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:

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

Circular Channel

Flow Area

Flow area of a circular channel:

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


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:

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

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  • Engineering ToolBox, (2005). Flow Section Channels - Geometric Relationships. [online] Available at: [Accessed Day Mo. Year].

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