Ah, better.

Ok, a few things. Mathematica is absolutely fanatic about use of {} versus () versus [] and those all mean completely different things to it. Use one where it expects another and you won't get what you need. So I changed a couple of [] into () which is what I'm guessing you wanted. And for the moment I'm going to avoid Mathematica's handling of units and just changed all your inputs to inches and pounds. We can go back and try to fix that later.

Here is what I have now.

In[1]:= h = 75 *12*inch;

\[Sigma] = 7100 (lb/inch^2);

\[Sigma]u = 7700 (lb/inch^2);

\[Sigma]d = 8100 (lb/inch^2);

KIC = 1000 (lb/inch^2)/Sqrt[inch];

\[Rho] = rhowat;

C1 = .163;

C2 = 3.91;

C3 = .0069;

\[CapitalDelta]pfu[hu_] := (C1/Sqrt[hu]) (KIC (1 - Sqrt[hu/h]) + C2 (\[Sigma]u - \[Sigma]) Sqrt[hu] ArcCos[h/hu]) +

C3 \[Rho] (hu - 0.5 h)

\[CapitalDelta]pfd[hd_] := (C1/Sqrt[hd]) (KIC (1 - Sqrt[hd/h]) + C2 (\[Sigma]d - \[Sigma]) Sqrt[hd] ArcCos[h/hd]) +

C3 \[Rho] (hd - 0.5 h)

\[CapitalDelta]pfu[175 *12*inch]/(lb/inch^2)

Out[12]= (1/lb)inch^2 ((0.00355695 ((1000 (1 - Sqrt[7/3]) lb)/inch^(5/2) + (121256. lb)/

inch^(3/2)))/Sqrt[inch] + 11.385 inch rhowat)

In[13]:= Expand[%]

Out[13]= 431.301 - 1.87638/inch + (11.385 inch^3 rhowat)/lb

That is a little closer to where I think you are trying to go.

Now we have to deal with ArcCos and whether it is expecting something with or without units as an argument and what you are expecting Sqrt to do. Since at this point Mathematica has no idea what "inch" really is I think it is trying to resist simplifying that because it doesn't know whether that might be a negative number or even complex.

Is this getting a little closer to your goal? Can you see the next thing that needs to be corrected?