Which equation best represents Poiseuille's law for pressure drop in a vessel in terms of pressure P, flow Q, and resistance R?

• A. P = Q x R
• B. ΔP = Q x R
• C. P = Q / R
• D. ΔP = R / Q

Answer: (A)

The driving idea is that, for a vessel segment with a fixed hydraulic resistance, the pressure difference across it is directly proportional to the flow through it. This is the vascular form of Ohm’s law: the pressure drop (P) equals the flow (Q) times the resistance (R). Because the question uses P for pressure, the correct expression is P = Q × R.

The other forms are not aligned with this naming: using ΔP is just another way to denote pressure drop, so ΔP = Q × R is equivalent if you interpret P as ΔP. But with the variables given, the direct relation P = Q × R is the proper representation. Integer inverse forms like P = Q / R or ΔP = R / Q imply an inverse relationship, which does not describe how pressure drives flow through a fixed resistance.