Physics Foundations · Topic 3 of 6
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Flow, pressure and resistance
Pressure drives flow through resistance — the hydraulic–electrical analogy that turns a chip into a circuit.
What you’ll learn
- How pressure, flow rate, and resistance relate
- The hydraulic–electrical analogy and how to use it
- How channel resistances combine in series and parallel
The concept
Driving fluid through a channel requires a pressure difference ΔP. The resulting flow rate Q depends on the channel’s hydraulic resistance R through ΔP = Q·R — Ohm’s law for fluids.
For laminar flow the analogy is exact: pressure ↔ voltage, flow rate ↔ current, resistance ↔ resistance. A whole chip becomes an electrical circuit you can analyse with the same rules.
Resistances in series add (R = R₁ + R₂ + …); in parallel they combine reciprocally (1/R = 1/R₁ + 1/R₂ + …). For a circular channel R = 128μL/(πD⁴); a rectangular channel has a close approximation. The fourth-power dependence on diameter makes resistance extremely sensitive to channel size.
Why it matters
You can predict and balance the flow split across a network, size a channel for a target flow rate, and see where most of your pressure is being spent.
The equation
Ohm’s law for fluids, with the circular-channel resistance.
Variables
| Symbol | Variable | Unit |
|---|---|---|
| ΔP | Pressure drop | Pa |
| Q | Volumetric flow rate | m³/s |
| R | Hydraulic resistance | Pa·s/m³ |
| μ | Dynamic viscosity | Pa·s |
| L | Channel length | m |
| D | Channel diameter | m |
Worked example
How sensitive is resistance to size? Halve a circular channel’s diameter and see what happens to R (which scales as 1/D⁴):
R ∝ 1/D⁴ → halving D multiplies R by 2⁴ = 16
The same pump pressure now delivers only 1/16 of the flow. Small dimensions dominate the hydraulics.
Try it yourself
Put these numbers into the flow resistance calculator and see the result for your own channel.
Open the Flow resistance calculator →Common mistakes
Watch out for:
- Forgetting the strong D⁴ (or w·h³) dependence, so small dimension changes are underestimated.
- Adding parallel resistances directly instead of combining them reciprocally.
Keep going
Further reading
- Theoretical Microfluidics — Henrik BruusChapters on hydraulic resistance and networks. Verify the current edition.
Continue learning
Flow, pressure and resistance
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Surface tension, wetting & capillarity
Physics Foundations
Why liquids pull themselves into narrow channels — the interfacial physics that lets a microfluidic device move fluid with no pump at all.
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