In class we showed that for steady flow, with comparable horizontal scales $(UV)$ and with $Re1$ and $Ro>1,$ there is a balance between the advective $($inertial$)$ acceleration terms and pressure gradient and the pressure scaling yields $PrU2.$

a$.$ Consider the $x-$momentum equation for steady state flow with $UV$ where Determine the nondimensional parameter that represents the ratio between the viscous terms and the Coriolis term.

b$.$ For this case, if rotation is negligible determine the corresponding pressure scaling.

c$.$ Next, consider the case again where $UV$ but now with Re $1$ and Ro $1.$ Determine the corresponding pressure scaling.