Square root units question

[gshockxcc]

I have to identical equations using a square root (flow calculation).  If I use the "psf" units for lbm/ft^2, the radical doesn't evaluate the squared units correctly.  But if I force the units to be lbm/ft^2 under the radical, then the expression evaluates correctly to lb/s; mass flow.  

I don't understand why this doesn't evaluate correctly.  Is there a way to make this more robust?

See attached.

[Werner_E · Accepted solution]

Why do you think that psf = lbm*ft^-2 ??

There is a gravity factor missing:

So you possibly are looking for

[gshockxcc]

Yes, you're correct.  Oversight on my part.  Thanks for catching that mistake.

[Fred_Kohlhepp]

In your second line you change psf into lbm/ft^2.  This introduces a (happy in this case) unit balance error.

Mathcad recognizes pounds force (lbf), pounds mass (lb or lbm).  When you edited the units you (happily) removed an extraneous gravity acceleration from your first line.  Since Mathcad recognizes and converts units, There's  a better way:

Note that you have squared the 0.915 as well as the unit ft  when specifying area.

File attached Prime 8

[gshockxcc]

Yes, thank you.  I left off the other constants for the area, so I was only squaring diameter, but I take your point.