Self-Cleansing Calculator
Check flow velocity and boundary shear stress against your self-cleansing criteria.
Inputs
Results
Flow velocity at this condition
0.91m/s
Boundary shear stress 3.98 Pa
Criteria are those entered above. No sediment transport model is applied.
Calculation details
Engineering equations
V = (1 / n) · R^(2/3) · S^(1/2)
τ = ρ · g · R · S
Flow depth for a design discharge is found by solving Q(y) numerically
Variables
- V
- Mean flow velocity (m/s)
- τ
- Boundary shear stress (Pa)
- ρ
- Water density, 1000 kg/m³
- g
- Gravitational acceleration, 9.81 m/s²
- R
- Hydraulic radius at the flow depth (m)
- S
- Pipe grade (m/m)
- v_min
- User-defined minimum velocity criterion (m/s)
- τ_min
- User-defined minimum shear stress criterion (Pa)
Assumptions
- Criteria are user-defined: a minimum velocity and a minimum boundary shear stress.
- No sediment transport model is applied; flow parameters are compared with the criteria entered.
- Boundary shear stress uses the hydraulic radius computed at the flow depth.
- Where a design flow is entered, the depth is solved from the Manning relationship for that pipe.
Worked example
D = 225 mm, S = 1% (0.010), n = 0.013, design flow 10 L/s
Depth solving gives y ≈ 72 mm (d/D ≈ 0.32), R ≈ 0.041 m
V ≈ 0.91 m/s, τ = 1000 × 9.81 × 0.041 × 0.010 ≈ 4.0 Pa
Against v_min = 0.75 m/s and τ_min = 1.0 Pa both criteria are satisfied.
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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.