cross-sectional area
Summary
Cross-sectional area is the area of the face exposed when a pipe, vessel, or wire is cut perpendicular to the flow or current. For a steady incompressible fluid, Av is constant, so a smaller area means faster flow. In a wire of fixed length and material, a larger area means lower resistance.
Detail
Meaning: Cross-sectional area (A) is the area of the face exposed when a pipe, vessel, or wire is cut perpendicular to the flow or current. For a circle, A = πr². In steady incompressible flow, the same volume passes each point every second, so a narrower section means faster flow. In a wire of fixed length and material, larger A means lower resistance.
Equation: A₁v₁ = A₂v₂ = Q, where A is area (m²), v is flow speed (m/s), and Q is volume flow rate (m³/s). For a wire, R = ρL/A, where R is resistance (Ω), ρ is resistivity (Ω·m), and L is length (m).
On the MCAT: A passage describes a constriction; find the new speed, then apply Bernoulli (horizontal ideal fluid: faster flow, lower pressure). Or a wire's diameter doubles, so A quadruples and R falls to one fourth. In circulation, capillaries have the greatest total area, so blood flows slowest there.
Common confusion: Students compare radii and forget the square. They assume the tiny capillaries have the smallest total area and so the fastest blood flow. Each capillary is narrower than the aorta, but their combined area is far larger, so speed is lower.
Sources
- Physics (Giancoli)
- Physics (Cutnell and Johnson)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.