# Flow Section Channels - Geometric Relationships

## Geometric relationships in flow channels - area, wetted perimeter and hydraulic diameter

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 of a rectangular channel:

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

where

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 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)

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 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)

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 of a circular channel:

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

## Related Topics

• Fluid Mechanics - The study of fluids - liquids and gases. Involves velocity, pressure, density and temperature as functions of space and time

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