Explanation about thrust blocks Eq. A.6.6.1d NFPA 13, ed. 2019 (A.10.6.2.1d ed. 2016)

[UFT12]

I had this question for some good time now and always forgot to ask. Now it s the time.

The equation per the thread title is for calculating thrust blocks for vertical movement. However looking closely, it seems that the product of Vg x Wm gives mass while the product of P x A gives force (of course we ignore Sf & sinθ as unitless). Shouldn't the gravitational acceleration g be right next to Wm as part of the denominator? This is going on for many editions. Do I miss something here?

 

[chicopee]

Here is the problem. When I was in high school (H.S.), the equation F= Ma had for units the following F(lb)= M (slugs) G(ft/sec^2). After H.S., in college taking ME courses, the English units used in physics were the same as those used in high school, but I also remember using the metric system. Now moving to junior and senior years in college, the units used in thermo, heat transfer and mechanical courses, the units reverted back to modified English units as follows F(lbf)= M(lbm) G(ft/sec^2)/ Gc(=32.2 lbm-ft/lbf-sec^2).

So what does that mean with the NFPA eq A.6.6.1 d NFPA13 ed2019 Vc= (Sf P(lbf/in^2) x A(in^2) x sin(theta))/ Wm(lbm/ft^3). When you simplify all the units, then the units for Vc
has that form (Lbf-Ft^3/Lbm). The definition of density is mass/ volume therefore units for Vc are(lbm/ft^3). Now back to Newton classical equation W=MxG whose units are the same as used in H.S but if using the modified English units that same equation is W(lbf)= M(lbm) G(ft/sec^2)/Gc(=32.2lbm-ft/lbf-sec^2); On earth G=32.2 ft/sec^2) therefore Wf lbf for unit.
The thing to be aware is that the density value is not in slugs as it was back in the early 60's. If the density is stated as lbm/ft^3 or as lbf/ft^3or as lb/ft^3 no correction in needed. If in slugs then multiply by Gc= 32.2 and not by G=32.2(earth value) because if you were anywhere else in the universe G would be totally different as in the moon where Gmoon=(1/6) G earth. In essence, on earth lbf=lbm=lb.

 

[UFT12]

Thanks for the taking the time. Ok so in short I understand that the Wm is the specific weight in kN/m3 or lbf/ft3. I just got confused because the standard denotes that as "density" of block material (lb/ft3). I got to say this lb or lbf or lbm unit is confusing.