Hello Kyle,
Subscripts can be a pain, but if you start thinking in TeX's box language, I find that things get a bit easier.
Plot[{\[CapitalDelta]pfu[x]/psi, \[CapitalDelta]pfd[x]/psi}, {x, 0 ft,
120 ft}, AxesLabel -> {
DisplayForm@
StyleBox[
RowBox[{SubscriptBox["\[CapitalDelta]h", "u d"], "[ft]"}]],
DisplayForm@
StyleBox[
RowBox[{SubscriptBox["\[CapitalDelta]p", "f"], "[psi]"}]]
}, GridLines -> Automatic]
WCC
