a$.$ Using dimensional analysis, determine whether the following equation satisfies the Principle of Homogeneity:

P$*$m$/$Q $+$ m$^2*$V$/($Volume$*$Area$)+$ Density$*$m$*$g$*$time$/$d$^2=$ constant

Where P $=$ pressure, m $=$ mass, V $=$ velocity, g $=$ gravity, d $=$ distance.

b$.$ Determine the dimensions of the constant, C$,$ in the following equation:

Q$*($m$^0\mathrm{.}5)=$ C$*$ density$*($time$*$m$*$@$/$A$)^2$

Where Q is a volume flowrate, m $=$ mass, A $=$ area.