Problem $7\mathrm{.}9\mathrm{.}6$

As winds blow past buildings, complex flow patterns can develop due to various factors such as flow separation and interactions between adjacent buildings. Assume that the local gage pressure, p$,$ at a particular location on a building is a function of the air density, $$; the wind speed, V; some characteristic length, $l,$ and all other pertinent lengths, $l_i,$ needed to characterize the geometry of the building or building complex. $($a$)$ Determine a suitable set of dimensionless parameters that can be used to study the pressure distribution. $($b$)$ An eight$-$story building that is $100$ ft tall is to be modeled in a wind tunnel. If a length scale of $1$:$300$ is to be used, how tall should the model building be$?($c$)$ How will a measured pressure in the model be related to the corresponding prototype pressure? Assume the same air density in model and prototype.