KinexiaLEARN PHYSICS

Flow Rate — Garden Hose (Worked Example)

Easy
Problem

Water flows through a garden hose of diameter 2.0 cm at 3.0 m/s. What is the volume flow rate?

Given

  • d = 2.0 cm → r = 0.010 m

  • v = 3.0 m/s

Find

The volume flow rate Q.

Principle

Q = Av: area times speed is the volume passing per second — the continuity equation's core.

Formula

Solution

  1. Area: A=πr2=π(0.010)2=3.142×10−4 m2A = \pi r^2 = \pi(0.010)^2 = 3.142 \times 10^{-4}\ \mathrm{m^2}

  2. Substitute: Q=(3.142×10−4)(3.0)Q = (3.142 \times 10^{-4})(3.0)

  3. Multiply: Q=9.42×10−4 m3/sQ = 9.42 \times 10^{-4}\ \mathrm{m^3/s}

9.42 × 10⁻⁴ m³/s (0.942 L/s)

Unit check

m² × m/s = m³/s — correct.

What this means physically

0.942 L/s — nearly a litre every second, filling a 10 L bucket in ~11 s. Squeeze the nozzle (smaller A) and v rises to keep Q steady — continuity in your hand.

Common mistake

Using diameter as radius. A = πr² needs r = d/2 — the diameter-squared error quadruples the area.