Rising Main Design Methodology Report

Reference Document for Official Pipeline Design Optimization

This document details the mathematical framework, formulas, and parameters utilized by the Rising Main Design Tool to calculate the most economical pipeline size based on CPHEEO guidelines.

1. Design Parameters & Flow Calculation

The tool designs the pipeline for a 30-year lifecycle, operating in two stages to meet future demand without overcapitalizing immediately.

Target Population (P): Expected ultimate population.
Per Capita Demand (D_lpcd): Standard water demand (e.g., 135 LPCD).
Pumping Hours (T): Number of daily hours the pumps operate.

Stage I Design Flow (Q_15)

Designed for a 15-year horizon using a CPHEEO peak factor of 1.28.

Q_15 (m³/s) = [P × D_lpcd × 1.28] / [1000 × (T × 3600)]

Stage II Design Flow (Q_30)

Designed for the ultimate 30-year horizon using a CPHEEO peak factor of 1.64.

Q_30 (m³/s) = [P × D_lpcd × 1.64] / [1000 × (T × 3600)]

2. Hydraulic Design & Pressure Checks

The tool uses the Modified Hazen-Williams Formula to evaluate friction head loss (h_f).

h_f = [L × (Q / C_R)^1.81] / [994.62 × D^4.81]

Where:

L = Length of the pipeline (m)
D = Internal diameter of the pipe (m)
C_R = Pipe roughness coefficient ratio (C / 140)
Q = Flow rate (Q_15 for Stage I, Q_30 for Stage II)

Total Head Calculation & Constraint:

Total Head (H) = Static Head + h_f

Safety Check: If the Total Head at Stage II exceeds the specified safe operating pressure of the pipe class (e.g., 180 meters for DI K-9), the pipe is disqualified to prevent pipeline failure.

3. Capital & Energy Cost Estimation

Capital Cost

The initial capital outlay is calculated linearly with the length of the pipeline, plus the required pumping infrastructure.

Pipe Cost = L × Material Cost per meter
Earthwork Cost = L × Trenching Cost per meter
Machinery Cost = Power_30 × Cost per kW
Miscellaneous = 5% added to the subtotal for contingencies.

Energy Cost (30-Year Lifecycle)

Energy cost is proportional to the hydraulic power required to overcome Total Head.

Power (kW) = (9.81 × Q × H × 1000) / (1000 × Pump Efficiency)

Total Energy Cost is calculated as the sum of Stage I and Stage II consumption:

Stage I (Years 1-15): Power_15 × T × 365 × Tariff × 15 years
Stage II (Years 16-30): Power_30 × T × 365 × Tariff × 15 years

4. Sample Calculation

Given Inputs:

Population: 50,000 | LPCD: 135 | Pumping: 22 Hrs | Length: 20,000 m | Static Head: 40 m | Energy Tariff: 8 Rs/kWh | Pump Efficiency: 65%

Pipe Evaluated: DI K-9 400mm (D = 0.4m, C = 130)

Material Rate: 7,525 Rs/m | Earthwork Rate: 224 Rs/m

Step A: Flow Rates

Daily Demand = 50,000 × 135 = 6.75 MLD
Q_30 = (6,750,000 × 1.64) / (1000 × 22 × 3600) = 0.1398 m³/s
Q_15 = (6,750,000 × 1.28) / (1000 × 22 × 3600) = 0.1091 m³/s

Step B: Head Loss & Power

C_R = 130/140 = 0.9286
h_f(30) = [20000 × (0.1398 / 0.9286)^1.81] / [994.62 × 0.4^4.81] = 51.56 m
H_Total(30) = 40 + 51.56 = 91.56 m (Safe: < 180m limit)
Power_30 = (9.81 × 0.1398 × 91.56) / 0.65 = 193.1 kW

Step C: Costing

Capital Cost = (20000 × 7525) + (20000 × 224) + (193.1 × 9000) = 15.67 Cr + 5% = 16.45 Crores
Energy Cost (Stage II) = 193.1 kW × 22 hr × 365 d × 8 Rs × 15 yr = 1.86 Crores (Calculated similarly for Stage I)
Total Lifecycle Cost = Capital + Energy = ~19.46 Crores

5. The Concept of Economic Diameter

The fundamental principle of the tool is finding the optimum point where the rising capital cost of larger pipes intersects with the rapidly falling energy cost caused by friction reduction. This results in a classic "U-Shaped" total cost curve.

Graph Interpretation:

As pipeline diameter increases, the Capital Cost (Blue) rises steadily due to more expensive pipes and earthwork.
Simultaneously, the Energy Cost (Orange) plummets because larger pipes drastically reduce friction losses.
The Total Cost (Green) forms a distinct "U" shape. The lowest point on this curve identifies the most economically efficient pipe diameter over the 30-year lifecycle.