Partial Flow in Circular Pipes

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Hydraulic Properties Calculator for Partial Flow in Circular Pipes

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Formula

The velocity of flow for gravity flow is provided by mannings equation, which is as follows;
V=(1/n)*R^(2/3)*S^(1/2)

Where,

V = Velocity of Flow in m/s,

R = Hydraulic Radius in meters,

S = Slope, unitless,

n = Manning’s Coefficient

The circular channel running part-full is very commonly met with. The flow occupies a segment of the circle of total angle 2α, related to the depth y. For partially full pipe the following relations are applied:
Depth Ratio
d/D=1/2(1-cos theta/2)
Area Ratio
a/A=(theta/360-(sin theta)/2*pi)
Hydraulic Radius Ratio
r/R=(1 - (360*sin theta )/ (2*pi*theta))
Velocity Ratio
v/V = (r/R)^(2/3)
Flow Ratio
q/Q = (a/A) * (v/V)

Here, notations d,a,r,v,q are for partial flow and D,A,R,V,Q are for full pipe flow.

Mannings Coefficients

Type of material
Condition
n
Salt glazed stone ware pipeGood0.012
Fair0.015
Cement concrete pipes (with collar joints)Good0.013
Fair0.015
Spun concrete pipes (with socket and spigot joint)0.011
Masonry
Neat cement plaster0.018
Sand and cement plaster0.015
Concrete, steel trowled0.014
Concrete, wood trowled0.015
Brick in good condition0.015
Brick in rough condition0.017
Masonry in bad condition0.02
Stone work
Smooth dressed Ashlar0.015
Rubble set in cement0.017
Fine, well packed gravel0.02
Earth
Regular surface in good condition0.02
In ordinary condition0.025
With stones and weeds0.03
In poor condition0.035
Partially obstructed with debris or weeds0.05
Steel
Welded0.013
Riveted0.017
Slightly tuberculated0.02
With spun cement mortar lining0.011
Cast iron
Unlined0.013
With spun cement mortar lining0.011
Asbestos cement0.011
Plastic0.011