resistance to flow
Summary
Resistance to flow is how strongly a tube opposes the movement of a viscous fluid, so a pressure drop is needed to keep the fluid moving. For steady laminar flow it scales as 1/r⁴, so halving a tube's radius raises its resistance 16-fold.
Detail
Meaning: Resistance to flow is how strongly a tube opposes the movement of a real fluid, so a pressure difference is needed to keep it moving. It arises from viscosity (internal friction between fluid layers) and drag at the walls. For steady laminar flow it rises with viscosity and tube length and falls steeply as radius grows. It is analogous to electrical resistance, with pressure difference like voltage and flow rate like current.
Equation: R = 8ηL/(πr⁴), with ΔP = QR. R is resistance (Pa·s/m³), η is viscosity (Pa·s), L is tube length (m), r is inner radius (m), ΔP is the pressure drop along the tube (Pa), and Q is volume flow rate (m³/s).
On the MCAT: Expect scaling questions: halving r raises R 16-fold, and doubling L doubles R. Resistances add in series; in parallel 1/Rtotal = 1/R₁ + 1/R₂ + …, so the total is below that of any single branch. Passages on vasoconstriction or narrowed vessels ask how ΔP or Q changes when R changes.
Common confusion: Students use r² because the continuity equation involves area, but resistance depends on r⁴. Also, Bernoulli's equation assumes an ideal, zero-viscosity fluid, so it has no resistance term; the resistance relation above applies to viscous, laminar flow.
Sources
- Physics (Cutnell and Johnson)
- Physics: Principles with Applications (Giancoli)
- College Physics (Serway and Vuille)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.