Minimum Pipe Grade Calculator
Required grade for a circular pipe to achieve a target velocity or target discharge.
Inputs
Results
Required minimum grade
0.757%
Equivalent to 1 in 132
Grade as 1 in X1 in 132
Velocity at this grade0.75m/s
Discharge at this grade13.3L/s
Hydraulic radius0.0375m
MethodTarget velocity
Assumes full-bore flow. The grade returned is the theoretical minimum to just achieve the target.
Calculation details
Engineering equations
S = [ (V · n) / R^(2/3) ]²
V = Q / A, A = πD² / 4, R = D / 4
Variables
- S
- Required grade (m/m), shown also as a percentage and 1 in X
- V
- Target velocity (m/s) or velocity produced by the target discharge
- Q
- Target discharge (m³/s)
- n
- Manning's roughness coefficient
- R
- Hydraulic radius, full-bore (m)
- D
- Internal pipe diameter (m)
Assumptions
- Full-bore flow is assumed for both methods.
- The result is the theoretical minimum grade to just achieve the target, without freeboard or design factor.
- A target discharge is converted to velocity through the full-bore flow area.
- Local losses and longitudinal profile constraints are not considered.
Worked example
D = 150 mm, n = 0.013, target velocity 0.75 m/s
R = 0.0375 m, R^(2/3) = 0.1120
S = [(0.75 × 0.013) / 0.1120]² = 0.00758
Required grade = 0.76% ≈ 1 in 132
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Results are preliminary engineering estimates based on the stated assumptions. Confirm inputs, assumptions and requirements against the applicable standards and authority requirements before use in design or construction.