Various Flow Section Channels and their Geometric Relationships
Geometric relationships like area, wetted perimeter and hydraulic diameter
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Area, wetted perimeter and hydraulic diameter for some common geometric sections like
- rectangular channels
- trapezoidal channels
- triangular channels
- circular channels
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 y) (1c)
where
Rh = hydraulic radius (m, in)
Trapezoidal Channel
Flow Area
Flow area of a trapezoidal channel can be expressed as
A = (a + z h) h (2)
where
z = see figure above (m, in)
Wetted Perimeter
Wetted perimeter of a trapezoidal channel can be expressed as
P = a + 2 h (1 + z2)1/2 (2b)
Hydraulic Radius
Hydraulic radius of a trapezoidal channel can be expressed as
Rh = (a + z h) h / a + 2 h (1 + z2)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)
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