Flow Section Channels - Geometric Relationships

Geometric relationships like area, wetted perimeter and hydraulic diameter

Area, wetted perimeter and hydraulic diameter for some common 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 can be expressed as

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 can be expressed as

P = b + 2 h         (1b)

where

P = wetted perimeter (m, in)

Hydraulic Radius

Hydraulic radius of a rectangular channel can be expressed as

Rh = b h / (b + 2 h)         (1c)

where

Rh = hydraulic radius (m, in)

Trapezoidal Channel

Flow Area

Flow area of a trapezoidal channel can be expressed as

A = h (b + T) / 2          (2)

Wetted Perimeter

Wetted perimeter of a trapezoidal channel can be expressed as

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

Hydraulic Radius

Hydraulic radius of a trapezoidal channel can be expressed as

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 can be expressed as

A = z h2         (3)

where

z = see figure above (m, in)

Wetted Perimeter

Wetted perimeter of a triangular channel can be expressed as

P = 2 h (1 + z2)1/2         (3b)

Hydraulic Radius

Hydraulic radius of a triangular channel can be expressed as

Rh = z h / 2 (1 + z2)1/2         (3c)

Circular Channel

Flow Area

Flow area of a circular channel can be expressed as

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 can be expressed as

P = α D         (4b)

Hydraulic Radius

Hydraulic radius of a circular channel can be expressed as

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

Related Topics

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

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