Answer
The constant with it's units, is $0.027 in^{1.22}$
Work Step by Step
Using the English System of Units:
$Δp=in$
$d= in$
$L=ft=12 in$
$V=ft/min$
$Vo= ft/min$
$Δp = 0.027 ( \frac{L}{d^{1.22}}) (\frac{V}{Vo})^{1.82}$
$(in)=0.027 ( \frac{ft}{in^{1.22}}) (\frac{ft/min}{ft/min})^{1.82}$
$(in)=0.027 ( \frac{in}{in^{1.22}})\frac{(ft/min)^{1.82}}{(ft/min)^{1.82}}$
$\frac{(in)(in^{1.22})}{(in)}=0.027$
$0.027=in^{1.22}$
