Pipe Slope & Drainage Gradient Calculator
Calculate pipe slope (gradient), fall over length, and estimated flow velocity using Manning's equation for partially or fully filled circular pipes.
Formulas Used
Manning's Equation (full or partial flow in circular pipe):
V = (1 / n) × R2/3 × S1/2
Q = V × A
Where:
- V = mean flow velocity (m/s)
- n = Manning's roughness coefficient (dimensionless)
- R = hydraulic radius = A / P (m)
- S = pipe slope (dimensionless, e.g. 0.01 for 1%)
- A = cross-sectional flow area (m²)
- P = wetted perimeter (m)
- Q = volumetric flow rate (m³/s)
Partial fill geometry (central angle θ):
θ = 2 × arccos(1 − 2 × fill ratio)
A = (D² / 8) × (θ − sin θ)
P = (D / 2) × θ
Slope relationships:
S = Fall / Length | Slope% = S × 100 | Gradient ratio = 1 : (1/S)
Solving for slope from known velocity:
S = (V × n / R2/3)2
Assumptions & References
- Self-cleansing velocity minimum of 0.6 m/s is per BS EN 752 and AS/NZS 3500.3 for foul drainage.
- Maximum velocity of 3.0 m/s is a general guideline to prevent pipe erosion (concrete pipes).
- Typical minimum slope for 100 mm foul drain: 1:60 (≈ 1.67%) per BS EN 12056-2.
- Typical minimum slope for 150 mm drain: 1:150 (≈ 0.67%) per AS/NZS 3500.3.
- Manning's n values sourced from Chaudhry (2008) Open-Channel Hydraulics and ASCE manuals.