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Stormwater Drainage Calculation

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Designing 🌧️ Stormwater Drainage systems is essential to ensure the efficient collection and disposal of surface runoff from rainfall. Proper pipe sizing ensures that the stormwater is carried safely without causing flooding, ponding, or structural damage.

📘 1. Key Formula: Rational Method

The Rational Method is widely used for stormwater pipe sizing in small urban drainage systems: Q=C ⋅ i ⋅ A

Where:

  • Q = Peak runoff (m³/s or cfs)
  • C = Runoff coefficient (depends on surface type)
  • i = Rainfall intensity (mm/hr or in/hr)
  • A = Catchment area (hectares or acres)

📐 2. Step-by-Step Pipe Sizing Procedure

🔹 Step 1: Define Catchment Area

Measure the area contributing runoff to the pipe. Use site drawings or GIS tools.

  • Units: hectares (ha) or square meters (m²)

🔹 Step 2: Assign Runoff Coefficient (C)

Based on surface type:

SurfaceC value
Paved / Asphalt0.85–0.95
Roof surface0.75–0.95
Lawn / grass area0.10–0.35
Concrete surface0.90–0.95

🔹 Step 3: Determine Rainfall Intensity (i)

Use local IDF curves or rainfall data for the required return period (e.g., 10-year, 25-year storm).

  • Units: mm/hr or in/hr

🔹 Step 4: Calculate Peak Flow (Q)

Q = (C⋅i⋅A) / 360

  • Result in m³/s if using mm/hr and hectares
  • Adjust for multiple catchments if needed

🔹 Step 5: Select Pipe Diameter

Use Manning’s Formula for flow in pipes: Q = 1/ n ⋅ A ⋅ R ^ 2/3 ⋅ S ^1/2

Where:

  • n = Manning’s roughness coefficient (typically 0.013 for concrete, 0.011 for PVC)
  • A = Cross-sectional area of pipe
  • R = Hydraulic radius = A / P (P = wetted perimeter)
  • S = Slope of pipe

🧰 Example Calculation

  • Catchment Area (A) = 0.5 ha
  • Surface = Pavement ⇒ C = 0.90`
  • Rainfall Intensity (i) = 75 mm/hr
  • Pipe Slope (S) = 0.005 (0.5%)
  • Manning’s n = 0.013

Q = 0.9 ⋅ 75 ⋅ 0.5 / 360 = 0.094 m3/s

Use Manning’s formula to back-calculate required pipe diameter that will carry 0.094 m³/s.

f = arc sin (0.4r/r) = 0.412 radians = 23.578 degrees

q = 180+2*f = 3.965 radians = 227.156 degrees

Sample Calculation for an 8″ (0.203mm) pipe.        D =         0.203

FLOW AREA                                                                                                 

Method 1

=             0.102^2*(227.156*pi/180-SIN(227.156))/2                                          

=             0.024     m2                                                                    

Method 2

=             0.102^2*(3.965/2+COS(0.412)*SIN(0.412)                                           

=             0.024     m2                                                                    

WETTED PERIMETER                                                                                 

=             0.102*3.965                                                                  

=             0.402     m                                                                       

B. CALCULATION OF DISCHARGE CAPACITY, Qc                               

Manning’s Formula                                                                     

Assume flow depth equal to 0.7 times the pipe diameter for the max. design flow rate.

Qc =       3600 * A * R2/3 * S 1/2 / n                                                                 

Where,                                                                                           

D =         Pipe Diameter, m                                                                         

A =         Flow Area, m2                                                               

P =          Wetted Perimeter, m                                                                  

S =          Bed Gradient                                                                 

n =          Roughness Coefficient                                                               

R =         Hydraulic Radius, m                                                                    

=             A/P                                                                                   

C.CALCULATION OF VELOCITIES                                                            

Qc =       V * A                                                                                

Where ,                                                                                          

v =          velocity, m/s                                                                  

A =         Flow Area, m2                                                               

 vmax ≤ 3             m/s                                                                   

vmin ≥   0.75       m/s                                                                    Qcmin =               0.2         x Qcmax             

✅ Design Tips

  • Always check full flow capacity (pipe not surcharged)
  • Include minimum self-cleansing velocity (≥ 0.6 m/s)
  • Consider future expansion (use 25–50% extra capacity)
  • Provide manholes and catchpits at changes in slope or direction

📚 Codes & References

  • IS 1172, IS 2065, IS 3370, and SP 35
  • US EPA SWMM software
  • StormCAD / Civil 3D for advanced modeling
  • Local municipal design manuals
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