# Flow Section Channels - Geometric Relationships

## Geometric relationships in flow channels - 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

### Rectangular Channel

#### Flow Area

Flow area of a rectangular channel:

A = b h (1)

where

A = flow area (m^{2}, in^{2})

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)

### 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}+ h^{2})^{1/2}(2b)

#### Hydraulic Radius

Hydraulic radius of a trapezoidal channel:

R_{h}= (h (b + T) / 2) /(b + 2 (((T - b) / 2)) (2c)^{2}+ h^{2})^{1/2}

### Triangular Channel

#### Flow Area

Flow area of a triangular channel:

A = z h^{2}(3)

where

z = see figure above (m, in)

#### Wetted Perimeter

Wetted perimeter of a triangular channel:

P = 2 h (1 + z^{2})^{1/2}(3b)

#### Hydraulic Radius

Hydraulic radius of a triangular channel:

R_{h}= z h / 2 (1 + z^{2})^{1/2}(3c)

### Circular Channel

#### Flow Area

Flow area of a circular channel:

A = D^{2}/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)

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