Worked Exercise — The Leaking Tap

Problem

A tap drips $30\;\text{cL}$ of water every $4\;\text{s}$. How many litres fill up in 3 days?

Solution

Step 1 — Conversion to consistent units. First we convert the time to seconds and the volume to litres, so we can combine the data without ambiguity.

$3\;\text{days} = 3\cdot 24\cdot 60\cdot 60\;\text{s} = 259\,200\;\text{s}$

$30\;\text{cL} = 0{,}3\;\text{L}$

Step 2 — Flow rate of the tap. The flow rate is the volume lost per unit time:

$Q = \frac{0{,}3\;\text{L}}{4\;\text{s}} = 0{,}075\;\text{L/s}$

Step 3 — Total volume over 3 days. Multiplying the flow rate by the total time:

$\ev{V = Q\cdot t = 0{,}075\cdot 259\,200 = 19\,440\;\text{L} \approx 19\;\text{m}^3}$

That is the equivalent of a $3\times 3\times 2$ metre box room filled completely with water!

Links

Topics: Grandezze fisiche e misura Skills: Conversione di unità Methods: Metodo dei fattori di conversione