Sewage lifting station, wet well sizing, pipe sizing and pump head calculation

Sewage Lifting Station (or Pump Station) is used to transport wastewater from a lower elevation to a higher elevation when gravity flow is not possible. It consists of a wet well (collection chamber), pumps, piping, and control systems.

Key Components & Design Calculations

1. Wet Well Sizing

The wet well stores incoming sewage before pumping. Its size depends on:

• Inflow rate (Q) – Peak sewage flow (typically calculated based on population or industrial discharge).

• Pump cycle time – To avoid frequent pump starts/stops (min 5-10 min cycle).

Design Steps:

1. Determine Peak Flow (Q):

   • For residential areas:

     $$Q=\text{Population}\times \text{Per capita sewage flow}\times \text{Peak factor}$$

   • Peak factor = 2–4 (depends on local standards).

2. Minimum Wet Well Volume (V):

   • Based on pump runtime and cycle time:

     $$V=\frac{Q\times T}{4}$$

     Where:

     • $Q$ = Peak flow (m³/min or GPM)

     • $T$ = Minimum pump cycle time (min) (typically 5–10 min)

     • Divide by 4 because the pump runs only when the level reaches a certain point (between start & stop levels).

3. Wet Well Dimensions:

   • Depth = Pump stop level – pump start level + freeboard (0.3–0.5 m).

   • Diameter/Width depends on available space (typically 1.5–3 m for small stations).

2. Pipe Sizing

Pipes must handle peak flow with minimal friction losses.

Design Steps:

1. Select Velocity (V):

   • Recommended: 0.6–2.4 m/s (to avoid sedimentation & erosion).

   • Typical: 0.9–1.5 m/s for sewage.

2. Calculate Pipe Diameter (D):

   $$Q=A\times V$$$$A=\frac{\pi D^2}{4}$$$$D=\sqrt{\frac{4Q}{\pi V}}$$

   • Round up to the nearest standard pipe size (e.g., 100 mm, 150 mm, 200 mm).

3. Check Friction Loss (Darcy-Weisbach or Hazen-Williams):

   $$h_f=\frac{fL{V}^2}{2gD}$$

   Where:

   • $h_f$ = Head loss (m)

   • $f$ = Friction factor

   • $L$ = Pipe length (m)

   • $g$ = Gravity (9.81 m/s²)

3. Pump Head Calculation

Total Dynamic Head (TDH) = Static Head + Friction Loss + Velocity Head

Design Steps:

1. Static Head (Hₛ):

   $$H_s=\text{Discharge elevation}-\text{Wet well pump start level}$$

2. Friction Loss (Hₗ):

   • From pipe, fittings, valves (use Darcy-Weisbach or manufacturer charts).

3. Velocity Head (Hᵥ):

   $$H_v=\frac{V^2}{2g}$$

   (Usually negligible in sewage systems).

4. Total Dynamic Head (TDH):

   $$TDH=H_s+H_l+H_v$$

5. Pump Power (P):

   $$P=\frac{Q\times TDH\times \rho \times g}{\eta }$$

   Where:

   • $\rho$ = Density of sewage (~1000 kg/m³)

   • $\eta$ = Pump efficiency (0.6–0.8)

Example Calculation

Given:

• Peak flow (Q) = 0.05 m³/s (50 L/s)

• Static lift (Hₛ) = 10 m

• Pipe length (L) = 50 m

• Velocity (V) = 1.2 m/s

1. Pipe Diameter (D):

$$D=\sqrt{\frac{4\times 0.05}{\pi \times 1.2}}=0.23\text{m}\approx 250\text{mm}$$

2. Friction Loss (Hₗ):
Assuming $f=0.02$:

$$h_f=\frac{0.02\times 50\times (1.2{)}^2}{2\times 9.81\times 0.25}=0.29\text{m}$$

3. TDH:

$$TDH=10+0.29+0.07(\text{velocity head})\approx 10.36\text{m}$$

4. Pump Power (η = 0.7):

$$P=\frac{0.05\times 10.36\times 1000\times 9.81}{0.7}=7.25\text{kW}$$