Free · Physics models
Laminar Pipe Flow and Hydraulic Resistance
Relate pressure drop, flow, viscosity, radius and length for a fully developed laminar Newtonian pipe flow.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
For a 1 mm radius pipe, 1 m length, 1 mPa·s viscosity and 1,000 Pa drop, the ideal flow is about 3.927 × 10⁻⁷ m³/s.
Q = π Δp r⁴/(8 μ L); R = Δp/Q = 8 μ L/(π r⁴).
Worked example
Enter these known values and leave the other values blank.
- Dynamic viscosity (μ)
- .001 Pa⋅s
- Radius of the pipe (r)
- .001 m
- Length of the pipe (l)
- 1 m
- Initial pressure
- 2000 Pa
- End pressure
- 1000 Pa
- Pressure change (Δp)
- 1000 Pa
- Volumetric flow rate
- 3.927e-7 m³ / sec
- Hydraulic resistance Δp/Q
- 2546479089 Pa⋅s / m³
Assumptions and limitations
- Assume steady incompressible Newtonian flow in a rigid circular tube with no slip, fully developed laminar velocity profile and constant viscosity. Entrance losses and turbulent flow are omitted.
- This equation alone does not establish laminar conditions. Check Reynolds number separately using density and resulting mean velocity.
- The pressure drop is inlet minus outlet. The retained branch requires positive pressures, positive pressure drop, geometry, viscosity and flow.
- The two flow selectors form volume per selected time; resistance selectors form viscosity units per selected volume, equivalent to Pa·s/m³.
- Enter known quantities and leave the unknown blank. Editable quantities support inverse solutions and locks; inconsistent locked quantities are reported. Unit selectors convert the quantity independently of its display.
Common questions
What happens if radius doubles?
With other inputs fixed, predicted flow increases sixteenfold because it scales with radius to the fourth power.
Can this calculate turbulent flow?
No. It assumes fully developed laminar Newtonian flow; Reynolds number and entry conditions must be checked separately.
How do I use the inverse calculation?
Clear the quantity you want to find and enter the remaining known values in their selected units. The model can only solve branches with enough independent information.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.