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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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