Pipe Diameter Optimizer

Lifecycle Cost Analysis

1. System Hydraulics
Design Flow Rate (Q)		L/s
Pipe Length (L)		m
Absolute Roughness (ε)		mm
Material Roughness Presets... 0.0015 mm - PVC / Plastic / HDPE 0.045 mm - Commercial Steel 0.15 mm - Galvanized Iron 0.26 mm - Cast Iron 1.0 mm - Concrete (Smooth) 3.0 mm - Concrete (Rough)
Allowable Head Loss (S)		m/km
Water Temp. (T)		°C
Pump System Efficiency (η)		%

2. Economic Factors
Operating Hours/Year		hrs/yr
Electricity Rate		$/kWh
Project Lifespan (n)		years
Discount/Interest Rate (i)		%

3. Installed Pipe Cost Model

Estimates total capital cost using a power curve:
Cost = BaseCost × (D / D_ref)^Exponent

Reference Dia. (Dref)		mm
Base Cost at Dref		$/m
Cost Exponent		-

Minimum Total Cost

Optimal Diameter 0 mm

Velocity at Opt. D 0.0 m/s Max Cap: 0 L/s

Capital Cost (Installed) $0

PV Energy Cost (0 yrs) $0

Target Velocity (~1.5)

Ideal Diameter 0 mm

Velocity 0.0 m/s Max Cap: 0 L/s

Friction Head 0 m

Pump Power 0 kW

The Economic Trade-off Capital vs. Operational Expense

Lifecycle Cost Optimization Curves

Detailed Analysis Table

Economic & Hydraulic Theory

1. Friction Head Loss ($H_f$)

Calculated rigorously using the Darcy-Weisbach equation and Swamee-Jain friction factor. Notice that head loss is inversely proportional to $D^5$. A small decrease in diameter causes a massive spike in required pumping energy.

$$H_f = f \cdot \frac{L}{D} \cdot \frac{v^2}{2g}$$

2. Pumping Power & Annual Energy Cost

The mechanical power ($P$) required to overcome friction is converted to annual cost based on operating hours ($h$) and the electricity rate ($R$).

$$Cost_{yr} = \frac{\rho \cdot g \cdot Q \cdot H_f}{\eta} \cdot h \cdot R$$

3. Present Worth Analysis (Lifecycle Cost)

Because energy is purchased over the lifespan of the project ($n$ years), future costs must be discounted back to today's dollars using the interest/discount rate ($i$). The optimal diameter is the discrete pipe size that minimizes the sum of immediate Capital Cost and the Present Worth of future operational energy.

$$Total Cost = Capital Cost + Cost_{yr} \cdot \left[ \frac{(1+i)^n - 1}{i(1+i)^n} \right]$$

4. Maximum Pipe Capacity ($Q_{max}$)

Determined iteratively based on an allowable head-loss gradient ($S$, e.g., 10 m/km) and fluid viscosity (derived from temperature $T$). The Darcy-Weisbach equation is rewritten and solved for velocity until convergence.

$$v = \sqrt{\frac{2g D S}{\lambda}} \quad ; \quad Q_{max} = v \cdot \frac{\pi D^2}{4}$$

Note: $\lambda$ (friction factor) depends on the Reynolds number ($Re$), which depends on $v$, requiring an iterative solver.

5. Typical Pipe Roughness ($\epsilon$)

Material	$\epsilon$ (mm)
PVC / Plastic / HDPE	0.0015
Commercial Steel	0.045
Galvanized Iron	0.15
Cast Iron	0.26
Concrete (Smooth)	1.0

6. Recommended Velocities

Application	Velocity Range (m/s)
Pump Suction	0.6 - 1.2
Gravity Mains	0.6 - 1.5
Pump Discharge	1.5 - 3.0
Max Limit (Water Hammer)	< 3.0

References

• American Water Works Association (AWWA). (2017). M32 Computer Modeling of Water Distribution Systems (3rd ed.). AWWA. Google Scholar
• Blank, L., & Tarquin, A. (2017). Engineering Economy (8th ed.). McGraw-Hill Education. Google Scholar
• Swamee, P. K., & Jain, A. K. (1976). Explicit equations for pipe-flow problems. Journal of the Hydraulics Division, 102(5), 657-664. https://doi.org/10.1061/JYCEAJ.0004542
• Munson, B. R., Young, D. F., & Okiishi, T. H. (2006). Fundamentals of fluid mechanics (5th ed.). John Wiley & Sons. Google Scholar
• Walski, P. R., Chase, D. V., Savic, D. A., Watermark, W., & Grayman, D. (2003). Advanced Water Distribution Modeling and Management. Haestad Methods. Google Scholar

Version 1.0

CivilSheets by Sothearith Seak