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# Pipe Line Sizing Calculator Documentation

Note: This documentation is based on standard fluid dynamics principles. The actual implementation in the code may vary.

# 1. Objective

The Pipe Line Sizing Calculator is used to determine the pressure drop and fluid velocity for a given flow rate through a pipe of a specified diameter and length. It helps engineers select an appropriate pipe size that balances pressure loss (operating cost) and pipe diameter (capital cost).

# 2. Design Basis & Methodology

The calculator uses the Darcy-Weisbach equation to calculate frictional pressure loss in the pipe.

# Key Formulas:

  1. Reynolds Number (Re): To determine the flow regime (laminar or turbulent).

    Re = (ρ * v * D) / μ

  2. Darcy Friction Factor (f):

    • For laminar flow (Re < 2300): f = 64 / Re
    • For turbulent flow (Re > 4000): Calculated using an empirical correlation, such as the Colebrook-White equation or the explicit Swamee-Jain equation. This requires the pipe's absolute roughness (ε).

  3. Darcy-Weisbach Equation (Pressure Drop):

    ΔP = f * (L/D) * (ρ * v² / 2)

    Where L is pipe length, D is diameter, ρ is density, and v is velocity. The total pressure drop also includes losses from fittings and elevation changes.

# 3. Input Parameters

  • Fluid Properties: Flow Rate, Density (ρ), and Viscosity (μ).
  • Pipe Properties: Internal Diameter (D), Length (L), and Absolute Roughness (ε).
  • Fittings: Number and type of fittings (e.g., elbows, valves) to calculate minor losses.

# 4. Output Results

  • Fluid Velocity: To check against erosional velocity limits.
  • Reynolds Number: To identify the flow regime.
  • Friction Factor: The calculated Darcy friction factor.
  • Pressure Drop: The total frictional pressure loss across the pipe length, including minor losses from fittings.

# 5. Limitations and Assumptions

  • Assumes steady-state, incompressible, single-phase flow.
  • The accuracy of the pipe roughness value can significantly affect the friction factor in turbulent flow.
  • Does not handle non-Newtonian fluids without modification.

# 6. Example Calculation

Goal: Calculate the pressure drop for water flowing through a pipe.

Given:

  • Fluid (Water): ρ = 998 kg/m³, μ = 0.001 Pa·s
  • Flow Rate (Q): 50 m³/hr = 0.0139 m³/s
  • Pipe: 100 m long, 4-inch Sch. 40 (ID D = 0.1023 m), commercial steel (ε = 0.046 mm)

Calculation Steps:

  1. Calculate Fluid Velocity (v):
    Area = π * D² / 4 = π * (0.1023)² / 4 = 0.00821 m²
    v = Q / Area = 0.0139 m³/s / 0.00821 m² ≈ 1.69 m/s

  2. Calculate Reynolds Number (Re):
    Re = (ρ * v * D) / μ = (998 * 1.69 * 0.1023) / 0.001 ≈ 172,300
    Since Re > 4000, the flow is turbulent.

  3. Calculate Friction Factor (f) using Swamee-Jain:
    Relative Roughness = ε / D = 0.000046 m / 0.1023 m = 0.00045
    f = 0.25 / [log10( (ε/D)/3.7 + 5.74/Re^0.9 )]²
    f = 0.25 / [log10( 0.00045/3.7 + 5.74/172300^0.9 )]²
    f = 0.25 / [log10( 0.000121 + 0.000098 )]² = 0.25 / (-3.66)² ≈ 0.0186

  4. Calculate Pressure Drop (ΔP):
    (Ignoring minor losses for this example)
    ΔP = f * (L/D) * (ρ * v² / 2)
    ΔP = 0.0186 * (100 / 0.1023) * (998 * 1.69² / 2)
    ΔP = 18.18 * 1424 ≈ 25,890 Pa ≈ 0.26 bar

Result: The frictional pressure drop over 100m of pipe is approximately 0.26 bar (or 3.8 psi).

# Reference Standards

  • ASME B31.3: Process Piping design code.
  • Crane Technical Paper No. 410: Flow of Fluids Through Valves, Fittings, and Pipe.
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