When a gas flows through a pipe filled with a porous solid matrix, the pressure of the gas drops due to resistance when the gas passes by the cavities, over a length $N,$ the decrease in pressure is given by:

$P=3\mathrm{.}61\frac{{}^{0\mathrm{.}15}N{}^{0\mathrm{.}85}{v}^{1\mathrm{.}85}}{D^{1\mathrm{.}15}}$

Where:

$P=$ pressure drop,$\frac{N}{m^2}$

$=$ fluid viscosity $K\frac{g}{m}.s$

$N=$ length $of$ pipe $,m$

$=$ fluid density $,K\frac{g}{m^3}$

$u=$ fluid velocity $,\frac{m}{s}$

$D=$ pipe diameter, $m$

$($a$)$ What are the units of $3\mathrm{.}61?$

$($b$)$ Suppose you are given data for $,N,,v,$ and $D$ in American Engineering units $($mass in $l{b}_m,$ length in $ft),$ which you prefer to use directly rather than converting them to SI units for substitution in the formula. Modify the formula so that the pressure drop will still be calculated in N$/$m$2$ but the other terms would be in American Engineering units.