KinexiaLEARN PHYSICS

Flow Rate — Aorta Blood Flow (Worked Example)

Medium
Problem

The aorta has diameter 2.5 cm and average blood speed 0.15 m/s. What is the volume flow rate (cardiac output)?

Given

  • d = 2.5 cm → r = 0.0125 m

  • v = 0.15 m/s

Find

The flow rate Q.

Principle

Blood is a fluid too: Q = Av gives the heart's output directly.

Formula

Solution

  1. Area: A=π(0.0125)2=4.909×10−4 m2A = \pi(0.0125)^2 = 4.909 \times 10^{-4}\ \mathrm{m^2}

  2. Substitute: Q=(4.909×10−4)(0.15)Q = (4.909 \times 10^{-4})(0.15)

  3. Multiply: Q=7.36×10−5 m3/sQ = 7.36 \times 10^{-5}\ \mathrm{m^3/s}

7.36 × 10⁻⁵ m³/s (73.6 mL/s ≈ 4.4 L/min)

Unit check

m² × m/s = m³/s. Area times speed is volume per time — the correct flow-rate units.

What this means physically

≈4.4 L/min — a normal resting cardiac output. During hard exercise this rises 4–5× as the heart beats faster and harder — same Q = Av physics, bigger v.

Common mistake

Forgetting unit conversion to familiar units. 7.36 × 10⁻⁵ m³/s means little; ×60,000 gives 4.4 L/min, which a doctor recognizes.