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