Cooling Coil Calculations

(Actual Air vs. Standard Air CFM)
The question begins this way: “The performance of your unit is not correct.” Why?
“Because when I calculate the coil load from the stated conditions I do not get the capacity shown”

Answer:
When calculating the Total Capacity do not use Qt = 4.5 * cfm * (h1 – h2)
Because 4.5 is derived for standard air as follows:
ma = cfm * Density * 60 where the density of standard air = .075 lba/ft³

At 100 DB and 78 WB, the W = .015601 lbw/lba
h = ha + Whg = cpa*T + W*(1061 + .444*T) Btu/lba
h1 =.24*100 + .015601*(1061 + .444*100) = 41.25 Btu/lba

At 57.50 DB and 57.30 WB, the W = .0099622 lbw/lba
h2 = .24*57.50 + .0099622*(1061 + .444*57.50) = 24.62 Btu/lba

If you use this equation then you will get the following:
Qt = 4.5 * 15000 * (41.25 – 24.62) = 1,122,525 Btu/hr, or a perceived error of 8.3

Coil programs use actual conditions:
At 100 DB and 78 WB, the W = .015601 lbw/lba, Density = .06914 ft³/lba
h1 = 41.25 Btu/lba from above
At 57.50 DB and 57.30 WB, the W = .0099622 lbw/lba
h2= 24.62 Btu/lba above
ma = CFM*Density*60 = 15000 * .06914 * 60 = 62,226 lba/hr
Qt = ma * (h[1] – h[2]) = 62226*(41.25 – 24.62) = 1,034,818 Btu/hr


When calculating the sensible capacity do not use Qs = 1.1 CFM *(T1-T2):
Because the 1.1 is derived from standard air as follows:
ma * Cpm = SCFM*DensityStd*(Cpa + W*Cpw)
ma * Cpm = SCFM *.075 * 60 * (.24 + .0093*.444) = 1.1*SCFM
If you use this equation then you will get the following:
Qs = 1.1 * 15000 * (100-57.50) = 701,250 Btu/hr

Coil programs use actual conditions:
At 100 DB and 78 WB, the W = .015601 lbw/lba, Density = .06914 ft³/lba

At 57.50 DB and 57.30 WB, the W = .0099622 lbw/lba
ma = CFM*Density*60 = 15000 * .06914 * 60 = 62226 lba/hr
Cpm = (Cpa + W*Cpw) Btu/(lba – F)
Qs = ma * Cpm * (T[1] – T[2])
Qs = 622226*(.24+.015601*.444)*(100-57.5) = 652,988 Btu/hr

The Total Latent Load is computed from:
QL = Qt – Qs

Using standard Air QL = 1,034,818 – 701,250 = 333,568 Btu/hr
Using actual air: QL = 1,034,818 – 652,988 = 381,830 Btu/hr
The above shows a sea level calculation.
The same equations apply for altitude however the true density must include DB, WB, and PB = altitude PB. PB altitude is calculated from the following equation: PB = 14.696 * (1 – ALTITUDE*6.8753E-6)^5.2559