Question

In a water vapour transmission test of a fabric by evaporative dish method, the initial mass of the dish is 198 g. After 20 h of test, the mass of the dish becomes 188 g. The inner and outer diameters of the dish are 6.5 cm and 6.9 cm, respectively. The water vapour transmission rate (g/m\(^2\)/h) of the fabric is:

Hint:

The water vapour transmission rate (WVTR) is an important measure of how much moisture passes through a fabric over a given time. It depends on both the change in mass and the area exposed to evaporation.

Answer 1

Step 1: Calculate the mass loss. \[ {Mass loss} = 198\,{g} - 188\,{g} = 10\,{g} \] Step 2: Time duration of the test. \[ t = 20\,{hours} \] Step 3: Area of the fabric exposed (use inner diameter only). \[ d = 6.5\,{cm} \Rightarrow r = \frac{6.5}{2} = 3.25\,{cm} \] \[ A = \pi r^2 = \pi \cdot (3.25)^2 = \pi \cdot 10.5625 \approx 33.17\,{cm}^2 \] \[ {Convert to m}^2: \quad A = 33.17 \times 10^{-4} = 0.003317\,{m}^2 \] Step 4: Calculate WVTR (Water Vapour Transmission Rate). \[ {WVTR} = \frac{{Mass loss}}{{Area} \times {Time}} = \frac{10}{0.003317 \times 20} = \frac{10}{0.06634} \approx 150.76 \] Step 5: Round to two decimal places. \[ {WVTR} = \boxed{150.00}\,{g/m}^2/{h} \]