volumetric flow rate
Summary
Volumetric flow rate (Q) is the volume of fluid passing a cross-section per unit time, Q = Av, in m³/s. For an incompressible fluid with no leaks, Q is the same at every point along the pipe, so the fluid speeds up where the area narrows.
Detail
Meaning: Volumetric flow rate is the volume of fluid crossing a cross-section of a pipe or vessel per unit time. For an incompressible fluid with no leaks, the same volume passes every point each second, so a narrower section has faster flow (continuity). Viscous flow rises with pressure difference and falls with resistance.
Equation: Q = Av = ΔV/Δt, where Q is volumetric flow rate (m³/s), A is cross-sectional area (m²), v is average speed (m/s), ΔV is volume (m³), and Δt is time (s). Continuity: A₁v₁ = A₂v₂. Driven flow: Q = ΔP/R, with ΔP in Pa and R in Pa·s/m³.
On the MCAT: Passages use blood in the aorta, arteries and capillaries, or a pipe that narrows. Area scales with r², so halving the radius quadruples the speed at constant Q. Total capillary area far exceeds the aorta's, so blood speed is lowest in capillaries even though Q through the whole circuit is the same.
Common confusion: Flow rate is not flow speed: Q is volume per time, v is distance per time. In a narrowing pipe Q stays constant while v changes. For branching vessels, compare the combined area of all branches, not one vessel.
Sources
- Physics (Cutnell and Johnson)
- College Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick and Walker)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.