Conditions in one zone of a dualduct conditioning system are

Conditions in one zone of a dual-duct conditioning system are to be maintained at 75 degree F and 50% relative humidity (RH). The cold deck air is at 52 degree F and 90% RH, while the hot deck air (outdoor air) is at 90 degree F and 20% RH. The sensible heat factor for the/one is 0.65. Assume sea level pressure. In what proportion must the warm and cold air be mixed to satisfy the space condition? If the total zone load is 50 tons, what is the total volume flow rate of air supplied to the zone? Sketch the states and processes on a psychrometric chart.

Solution

Given inputs

TR = 75 F

RH=50 %

Thot =90 F

RH_hot =20 %

Tcold = 52 F

RH_cold =90 %

Ts = 14.2^o C = 57.56 F

Patm = 101.325

Ws = 0.007

Sensible Heat factor = 0.65

Total zone load = 50 tons

Solution :

hR = enthalpy (airH2O, T = TR, R=RR,P = Patm)

Hhot = enthalpy (airH2O, T = Tcold,R= Rcold, P = Patm)

Hcold = enthalpy (airH2O, T = Tcold,R= Rcold, P = Patm)

hs = enthalpy (airH2O, T = Ts, w = ws, P = Patm)

vs = volume (airH2O, T = Ts, w = ws, P = Patm)

50*200/.9478 = ms*(hR-hs)

Hs = (mhot/ms)*hhot+(1-(mhot/ms))*hcold

Volsupply = ms*vs

HotColdRatio = mhot/(ms-mhot)

SOLUTION :

Hcold =29.57 C         Hhot = 47.31        HotcoldRatio = 0.1573   hR = 47.83

Hs = 31.98                mhot = 90.49        ms = 665.9                       Patm = 101.325

Rcold =0.9                 Rhot = 0.2            RR = 0.5                             Tcold = 11 C

Thot = 32 C                TR = 24 C             Ts = 14.2                           VolSupply = 548.1

Vs =0.8232                ws = 0.007

Supply Volume = 548.1 m³ /min

Hot to Cold ratio = 0.1573

pyschometric chart http://www.uigi.com/UIGI_SI.PDF