BIZOMAT MAKEOS · Hydraulics
Pipe Friction Factor and Pressure Drop
What friction factor and pressure drop does this flow have in this pipe?
Reynolds number, Darcy friction factor (laminar 64/Re or Colebrook–White for turbulent flow), pressure drop and head loss for a straight pipe plus fittings.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Flow | L/min | Volume flow through the pipe. |
| Pipe inside diameter | mm | Inside diameter (not nominal size). |
| Pipe length | m | Length of straight pipe. |
| Kinematic viscosity | cSt | Kinematic viscosity at the operating temperature (1 cSt = 1 mm²/s; ISO VG 32 oil is 32 cSt at 40 °C, water about 1 cSt). |
| Density | kg/m³ | Density of the fluid at the working temperature (mineral hydraulic oil about 870 kg/m³, water about 998 kg/m³). |
| Pipe roughness | mm | Absolute roughness: about 0.0015 mm for drawn tube, 0.045 mm for commercial steel. |
| Sum of fitting loss coefficients | Sum of loss coefficients for bends, tees and valves from fittings data. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Flow
- What it is
- The volume of fluid flowing through the pipe each minute at the operating condition you want to check.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0.000001 L/min to 10000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pressure drop rises roughly with the square of flow in turbulent flow, and in proportion in laminar flow.
- Get it right
- Use the maximum flow the line carries; pressure drop rises steeply with flow.
What this means: Pipe inside diameter
- What it is
- The actual inside diameter of the pipe, tube or hose bore that the fluid flows through.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pressure drop falls very steeply as bore increases.
- Get it right
- Use the true bore, not the nominal pipe size or the outside diameter of tube.
What this means: Pipe length
- What it is
- The total length of straight pipe between the two points, with bends and fittings counted separately in the fittings coefficient.
- Units and format
- Enter a number in m: metres. The form accepts 0 m to 1000000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The straight-pipe part of the pressure drop rises in direct proportion.
- Get it right
- Enter metres; count fittings in the loss coefficient, not as extra length.
What this means: Kinematic viscosity
- What it is
- How easily the fluid flows, as dynamic viscosity divided by density, at the actual operating temperature, from the fluid data sheet.
- Units and format
- Enter a number in cSt: centistokes (kinematic viscosity, 1 cSt = 1 mm²/s). The form accepts 0.000001 cSt to 1000000 cSt. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 cSt as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher viscosity lowers the Reynolds number and raises the friction factor.
- Get it right
- One centistoke is one square millimetre per second. Oil viscosity changes strongly with temperature.
What this means: Density
- What it is
- The mass per unit volume of the fluid at its working temperature, from the fluid supplier’s data sheet.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 870 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pressure drop rises in direct proportion; head loss does not change.
- Get it right
- Use density at operating temperature, not at the reference temperature.
What this means: Pipe roughness
- What it is
- The average height of the bumps on the inside wall of the pipe, a property of the pipe material and its condition, from pipe or fluid-mechanics data.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.045 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only matters in turbulent flow, where rougher pipe raises the friction factor.
- Get it right
- Enter millimetres; old corroded pipe is rougher than new.
What this means: Sum of fitting loss coefficients
- What it is
- The total of the loss coefficients of all bends, tees, valves and other fittings in the line, each taken from fittings data and added together.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 10000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Adds a pressure drop proportional to the square of velocity.
- Get it right
- Add up one coefficient per fitting; leave it at 0 for straight pipe only.
Method and formulas
- v = Q ÷ A; Re = v d ÷ ν.
- Laminar (Re < 2300): f = 64 ÷ Re. Turbulent: 1/√f = −2 log₁₀(ε/3.7d + 2.51/(Re√f)) solved iteratively.
- Δp = (f L ÷ d + ΣK) × ρ v² ÷ 2.
- Example: 100 L/min of 15 cSt oil in a 25 mm pipe gives Re = 5,658.8, f = 0.03816 and 1.6814 bar.
Limitations
- Fully developed, incompressible flow; the transition region (Re about 2300–4000) is uncertain.
- Viscosity of oil changes strongly with temperature; use the operating value.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size hydraulic, coolant and water lines
- Find the pressure drop to a remote user
- Compare pipe sizes and materials
Who it is for
- Hydraulic and process engineers
- Maintenance engineers
- Design engineers
What you get
- Velocity and Reynolds number
- Flow regime and friction factor
- Pressure drop and head loss
Interpreting the result
- If the drop is too high, a larger diameter is far more effective than any other change (Δp ∝ 1/d⁵ in turbulent flow).
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3024–3027. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Regimes, crossovers and the danger of extrapolating
In Scale Models by the Numbers
What it covers: Recognise when a flow changes regime, read a crossover from the local slope of test data, carry pipe losses to full size through the friction factor, and avoid extrapolating across a crossover.
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