Irrigation water is to be provided to a crop in a field to bring the moisture content of the soil from the existing $18 \%$ to the field capacity of the soil at $28 \%$. The effective root zone of the crop is $70$ cm. If the densities of the soil and water are $1.3 \: g/cm^3$ and $1.0 \: gm/cm^3$ respectively, the depth of irrigation water (in mm) required for irrigating the crop is ________