Drain Flow Rate Calculator
Calculate the volumetric flow rate through a circular drain pipe using Manning's equation for open-channel flow, or through a drain orifice using the orifice flow equation.
Internal diameter of the circular pipe
Rise over run (e.g. 0.01 = 1%)
Depth of flow ÷ diameter (1.0 = full pipe)
Formulas Used
Manning's Equation (full or partial pipe):
Q = (1/n) × A × R2/3 × S1/2
- Q = Flow rate (m³/s)
- n = Manning's roughness coefficient
- A = Cross-sectional flow area (m²)
- R = Hydraulic radius = A / P (m), where P = wetted perimeter
- S = Pipe slope (m/m)
For a full circular pipe: A = π D² / 4, R = D / 4
For a partial circular pipe at fill ratio y/D = r:
θ = 2 × arccos(1 − 2r) [radians]
A = (D²/8)(θ − sin θ)
P = D × θ / 2
R = A / P
Orifice Flow Equation:
Q = Cd × A × √(2 × g × h)
- Cd = Discharge coefficient (dimensionless)
- A = Orifice area (m²)
- g = 9.81 m/s²
- h = Water head above drain (m)
Assumptions & References
- Manning's equation assumes steady, uniform, turbulent open-channel flow.
- Partial-pipe geometry uses the standard circular segment formula; fill ratio must be between 0.01 and 1.0.
- Maximum hydraulic efficiency for a circular pipe occurs at approximately 94% fill (y/D ≈ 0.94).
- Orifice equation assumes the orifice is fully submerged or free-discharging with a known upstream head.
- Cd = 0.61 is the classical value for a sharp-edged circular orifice (ISO 5167).
- SI units throughout: metres, seconds, m³/s.
- References: Chaudhry, M.H. – Open-Channel Hydraulics; Munson et al. – Fundamentals of Fluid Mechanics; AS/NZS 3500.3 (drainage).