An offshore oil platform is venting natural gas $($assume it is all $C{H}_4)$ at a rate of $150$ liter$/sec$ through a stack with diameter $15cm$ at a height $45m$ above the sea. The wind is blowing at $4\frac{m}{sec}.$ Because the ocean is relatively cool, the atmosphere can be regarded as having neutral stability despite the strong sunlight.

c$.$ Estimate the $C{H}_4$ plume rise $100m$ downwind. In the case of $C{H}_4,$ the density difference driving plume rise is due to molecular weight, not temperature. Note that in Eq$.(4\mathrm{.}19),$ the factor $(\frac{T_s-T_a}{T_s})$ can be thought of as a measure of plume density relative to air. Given the ideal gas law, this factor could be rewritten as $(\frac{\frac{1}{{}_{\text{g}\text{a}\text{s}}}-\frac{1}{{}_{\text{a}\text{i}\text{r}}}}{\frac{1}{{}_{\text{g}\text{a}\text{s}}}}).$

In practice there are also other concerns, such as the fact that $H_{2}S,$ often associated with venting natural gas, is highly toxic. As a result, there are specific regulations that must be followed for landing helicopters on oil platforms.