The method
Before using the result
- Use consistent fluid properties at the operating temperature. Results do not select equipment or establish code compliance.
- Steady fully developed incompressible flow in a circular pipe; entrance and fitting losses are excluded. Transition: 2,300 ≤ Re < 4,000.
Worked examples
These original training examples illustrate the method for United States: Fundamentals of Engineering (FE) Examination. Use the matching “Load example” button above to explore a variation; example values are not equipment settings or prescribed criteria.
1. Worked example
Build the FE fluid-mechanics calculation chain from pipe area to velocity, Reynolds number and energy loss. Recognise when the flow regime prevents a single confident friction-factor result.
- Actual internal diameter
- 50 mm
- Straight pipe length
- 30 m
- Absolute roughness
- 0.045 mm
- Volume flow
- 2 L/s
- Fluid density
- 1,000 kg/m³
- Dynamic viscosity
- 1 mPa·s
- v = 1.0185916357881302 m/s; Re = 50929.58178940651.
- Darcy f = 0.023681658475296158 (not the Fanning factor).
- h = 0.023681658475296158 × (30 / 0.05) × 1.0185916357881302² / (2 × 9.80665) = 0.7516452270693483 m.
- Δp = 1000 × 9.80665 × 0.7516452270693483 Pa.
- Velocity: 1.018592 m/s
- Reynolds number: 50,929.58
- Flow regime: Turbulent
- Darcy friction factor: 0.02368166
- Head loss: 0.7516452 m
- Pressure loss: 7,371.122 Pa
2. Comparison example
Compare a different supplied condition using the same method. For Engin Exam, the important check is that the input meaning, units and method assumptions still match the problem.
- Actual internal diameter
- 50 mm
- Straight pipe length
- 30 m
- Absolute roughness
- 0.045 mm
- Volume flow
- 1 L/s
- Fluid density
- 1,000 kg/m³
- Dynamic viscosity
- 1 mPa·s
- v = 0.5092958178940651 m/s; Re = 25464.790894703256.
- Darcy f = 0.02650391014873954 (not the Fanning factor).
- h = 0.02650391014873954 × (30 / 0.05) × 0.5092958178940651² / (2 × 9.80665) = 0.21030555759804953 m.
- Δp = 1000 × 9.80665 × 0.21030555759804953 Pa.
- Velocity: 0.5092958 m/s
- Reynolds number: 25,464.79
- Flow regime: Turbulent
- Darcy friction factor: 0.02650391
- Head loss: 0.2103056 m
- Pressure loss: 2,062.393 Pa
Check your understanding
1. Which relationship is used?
v = Q/A; Re = ρvD/μ; h = f(L/D)v²/(2g); Δp = ρgh. Laminar f = 64/Re; turbulent f solves Colebrook–White.
2. Which assumption should you check first?
Use consistent fluid properties at the operating temperature. Results do not select equipment or establish code compliance.
3. How should you verify a different unit system?
Convert every input to the displayed calculation units first. Equivalent physical inputs must give equivalent results; a unit label alone does not convert a number.
Continue with the matching exam topic
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