# 7.1.2 Leakage rate

Let us consider a bicycle tube having a volume of 4 liters. It has been inflated to a pressure of three bar (3,000 hPa), and without any additional inflation should have a maximum pressure loss of 1 bar (1,000 hPa) after a period of 30 days.

The leakage rate has already been defined in 1.3.3: (Formula 1-35).

$Q_L=\frac{\Delta p \cdot V}{\Delta t}$

 $Q_L$ Leakage rate [Pa m3 s-1] $\Delta p$ Pressure change during measurement period [Pa] $V$ Volume [m3] $\Delta t$ Measurement period [s]

Or to illustrate: The leakage rate of a vessel having a volume of 1 cubic meter is 1 Pa m3 s-1, if the interior pressure increases or decreases by 1 Pa within 1 second. Please refer to Table 1-8 or to our app for conversion to other customary units.

Inserting the values for our bicycle tube then yields the permissible leakage rate

$Q_L = \frac{1 \cdot 10^5 \mathrm{\ Pa} \cdot 4 \cdot 10^{-3} \mathrm{m}^3}{30 \cdot 24 \cdot 3,600 \mbox{s}} = 1.5 \cdot 10^{-4} \mathrm{\ Pa\ m}^3 \mathrm{s}^{-1}$

and we find that the bicycle tube with this leakage rate is sufficiently tight. These kinds of leakage rates can be found by means of the well-known bubble test method (Figure 7.1).

Figure 7.1: Bubble leak test on a bicycle tube

Now let us consider a refrigerator in which a loss of 10 g of refrigerant is allowable over a ten-year period. The refrigerant we use is R134a (1,1,1,2-Tetrafluoroethane) with a molecular weight of 102 g mol-1. The permissible loss is therefore about 224 Pa m3. This results in a permissible leakage rate of

$Q_L = \frac{224\mathrm{\ Pa\ m}^3}{10 \cdot 365 \cdot 24 \cdot 3,600 \mathrm{\ s}} = 7.1 \cdot 10^{-7} \mathrm{\ Pa\ m}^3 \mathrm{s}^{-1}$

These kinds of leakage rates can only be localized and quantified by means of extremely sensitive measuring methods, for example with mass spectrometry and test gases that are not present in the atmosphere.