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You are correct up to a point. The water coil model does result in a design capacity very near your calculations. However, that capacity is only used to calculate a coil UA value.

Hair,in = 70561.3
Qcoil,des = 259107.0
UAdesign = 21109.9

Other coil parameters are also calculated during this sizing effort, such as bypass factor, SHR, etc. The model then changes the inlet conditions to nominal values to determine what physical coil would be used for these application input parameters (i.e., the user entered coil conditions shown above).

Tcoil,inlet,air,db = 26.67
Tcoil,inlet,air,wb = 19.44
Tcoil,inlet,water = 6.67
Qcoil,actual = 186127.2

These calculations result in the following:

Tcoil,outlet,air = 11.96
Wcoil,outlet,air = 0.0084
Tcoil,outlet,water = 10.32

Realize now that your coil inlet air temperature was 32 C. This physical water coil would have a much higher capacity if the inlet air temperature was increased from 26.7 C to 32 C. The result is the actual physical coil you would specify for your application (i.e., coil area, etc.)