Fluid mechanicsMVP
Flow resistance
Hydraulic resistance of a channel — the microfluidic analogue of electrical resistance.
Inputs
Result
Enter values and calculate to see the result.
Interpretation
Hydraulic resistance behaves exactly like electrical resistance, which lets you analyse a whole chip as a circuit:
- ΔP ↔ Voltage
- Q ↔ Current
- R ↔ Resistance
Channels in series add (R = R₁ + R₂ + …); channels in parallel combine reciprocally (1/R = 1/R₁ + 1/R₂ + …) — just like resistors.
Formula
R ≈ 12 · μ · L / [ w · h³ · (1 − 0.63 · h/w) ]
First term of the exact series; assumes laminar, fully developed flow.
Variables
| Symbol | Variable | Unit |
|---|---|---|
| R | Hydraulic resistance | Pa·s/m³ |
| ΔP | Pressure drop | Pa |
| Q | Volumetric flow rate | m³/s |
| μ | Dynamic viscosity | Pa·s |
| L | Channel length | m |
| w | Channel width | m |
| h | Channel height | m |
Assumptions & validity
This tool assumes:
- R = ΔP/Q by definition (the 'from measurements' method makes no flow assumption).
- The rectangular formula R ≈ 12μL/(wh³(1−0.63 h/w)) is an APPROXIMATION (first term of the exact series); most accurate for h ≪ w.
- Rectangular method assumes fully developed, steady, laminar, Newtonian flow.
Worked example
A rectangular channel: μ = 1.0 mPa·s, L = 10 mm, w = 100 µm, h = 50 µm.
R ≈ 12 × 10⁻³ × 0.01 / [10⁻⁴ × (5×10⁻⁵)³ × (1 − 0.63 × 0.5)] ≈ 3.5×10¹³ Pa·s/m³