Psych Solutions

7/29/2019 Psych Solutions

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File:Psych1HeatCoil.EES 10/21/2003 3:41:38 PM Page 1

EES Ver. 6.867: #317: CEAE University of Colorado, Boulder

"AREN 3010

In-Class Psychrometric Problem #1"

"

Moist air enters a heating coil at 40F dry-bulb temperature

and 36F wet-bulb temperature at a rate of 2000 cfm.

Barometric pressure is 14.696 psia. The air leaves the

coil at a dry-bulb temperature of 140F. "

"Given information"

P_atm = 14.696

T_sa = 140

T_ma = 40

TWB_ma = 36CFM_ma = 2000

TW_ent = 180

TW_lvg = 160

T_steam = 250

"Calculate properties of mixed air"

W_ma = HUMRAT(AIRH2O,t=T_ma, b=TWB_ma,p=P_atm)

h_ma = ENTHALPY(AIRH2O,t=T_ma, w=W_ma,p=P_atm)

v_ma = VOLUME(AIRH2O,t=T_ma, w=W_ma,p=P_atm)

c_p = SPECHEAT(AIRH2O,t=T_ma,w=W_ma,p=P_atm)

"a) How much heat is added to the air?"

m_sa = CFM_ma/v_ma*CONVERT(hr,min)

h_sa = ENTHALPY(AIRH2O,t=T_sa, w=W_ma,p=P_atm)

Q_air = m_sa*(h_sa-h_ma)

Q_airT = m_sa*c_p*(T_sa-T_ma)

"b) If the heat is provided by hot water that enters the coil at 180F

and leaves at 160F, what is the water flow rate?"

c_WATER = SPECHEAT(WATER,t=TW_ent,p=P_atm)

m_w = Q_air/(c_WATER*(TW_ent-TW_lvg))

"c) If the heat is provided by a steam coil with saturated steam at 250F,

what steam flow rate is required?


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Assume that the steam leaves the coil as a saturated liquid?"

hfg_steam = ENTHALPY(STEAM,t=T_steam,x=1)-ENTHALPY(STEAM,t=T_steam,x=0)

m_steam = Q_air/hfg_steam

AREN 3010

In-Class Psychrometric Problem #1

Moist air enters a heating coil at 40F dry-bulb temperature

and 36F wet-bulb temperature at a rate of 2000 cfm.

Barometric pressure is 14.696 psia. The air leaves the

coil at a dry-bulb temperature of 140F.

Given information

Patm = 14.696

Tsa = 140

Tma = 40

TWBma = 36

CFMma = 2000

TWent = 180

TW lvg = 160

Tsteam = 250

Calculate properties of mixed air

Wma = 'AirH2O' , T = Tma , B = TWBma , P = Patm

hma = h 'AirH2O' , T = Tma , w = W ma , P = Patm

vma = v 'AirH2O' , T = Tma , w = W ma , P = Patm

cp = Cp 'AirH2O' , T = Tma , w = Wma , P = Patm

a) How much heat is added to the air?

msa =CFMma

vma 60

min

hr

hsa = h 'AirH2O' , T = Tsa , w = W ma , P = Patm

Qair = msa hsa hma

QairT = msa cp Tsa Tma

b) If the heat is provided by hot water that enters the coil at 180F

and leaves at 160F, what is the water flow rate?

cWATER = Cp 'Water' , T = TWent , P = Patm


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mw =Qair

cWATER TW ent TW lvg

c) If the heat is provided by a steam coil with saturated steam at 250F,

what steam flow rate is required?

Assume that the steam leaves the coil as a saturated liquid?

hfgsteam = h 'Steam' , T = Tsteam , x = 1 h 'Steam' , T = Tsteam , x = 0

msteam =Qair

hfgsteam

Unit Settings: [F]/[psia]/[lbm]/[degrees]

CFMma = 2000 [cfm] cp = 0.2419 [Btu/lbm-R] cWATER = 1.002 [Btu/lbm-R]

hfgsteam = 945.5 [Btu/lbm] hma = 13.42 [Btu/lbm] hsa = 37.62 [Btu/lbm]

msa = 9473 [lbm

/hr] msteam = 242.4 [lbm

/hr] mw = 11435 [lbm

/hr]

Patm = 14.7 [psia] Qair = 229218 [Btu/hr] QairT = 229162 [Btu/hr]

TWBma = 36 [F] TWent = 180 [F] TWlvg = 160 [F]

Tma = 40 [F] Tsa = 140 [F] Tsteam = 250 [F]

vma = 12.67 [ft3/lbm] Wma = 0.003532

No unit consistency or conversion problems were detected.


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File:Psych2ZoneHeat.EES 10/21/2003 3:50:04 PM Page 1


"AREN 3010


"A building space is to be maintained at 70F dry-bulb and 30% RH

when the barometric pressure is 14.696 psia. The total heating load

on the space has been calculated to be 60,000 Btu/hr.

Supply air is delivered to the space at a temperature of 120F "

"Given information"

P_atm = 14.696

T_sa = 120T_ra = 70

RH_ra = .3

Q_heat = 60000

Q_fan = 400*CONVERT(W,Btu/hr)

"Calculate properties of outdoor and return air"

W_ra = HUMRAT(AIRH2O,t=T_ra, r=RH_ra,p=P_atm)

v_ra = VOLUME(AIRH2O,t=T_ra, w=W_ra,p=P_atm)

v_sa = VOLUME(AIRH2O,t=T_sa, w=W_ra,p=P_atm)

c_p = SPECHEAT(AIRH2O,t=T_ra,w=W_ra,p=P_atm)

"a) What is the volumetric airf low required for the space?"

m_sa=Q_heat /(c_p*(T_sa-T_ra))

CFM_sa = m_sa*v_sa/CONVERT(hr,min)

CFM_ra = m_sa*v_ra/CONVERT(hr,min)

"b) What is the discharge air temperature?"

T_da = T_sa-Q_fan/(m_sa*c_p)

AREN 3010


A building space is to be maintained at 70F dry-bulb and 30% RH

when the barometric pressure is 14.696 psia. The total heating load

on the space has been calculated to be 60,000 Btu/hr.Supply air is delivered to the space at a temperature of 120F


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File:Psych2ZoneHeat.EES 10/21/2003 3:50:05 PM Page 2


Given information

Patm = 14.696

Tsa = 120

Tra = 70

RH ra = 0.3

Qheat = 60000

Q fan = 400 3.41214 Btu/hr

W

Calculate properties of outdoor and return air

W ra = 'AirH2O' , T = Tra , R =RH ra , P = Patm

v ra = v 'AirH2O' , T = Tra , w = W ra , P = Patm

vsa = v 'AirH2O' , T = Tsa , w = W ra , P = Patm

cp = Cp 'AirH2O' , T = Tra , w = W ra , P = Patm

a) What is the volumetric airflow required for the space?

msa =Qheat

cp Tsa Tra

CFMsa = msa vsa

60 min

hr

CFMra = msa v ra

60 min

hr

b) What is the discharge air temperature?

Tda = Tsa Q fan

msa cp


CFMra = 1110 [cfm] CFMsa = 1214 [cfm] cp = 0.2425 [Btu/lbm-R]

msa = 4949 [lbm/hr] Patm = 14.7 [psia] Qfan = 1365 [Btu/hr]

Qheat = 60000 [Btu/hr] RHra = 0.3 Tda = 118.9 [F]

Tra = 70 [F] Tsa = 120 [F] vra = 13.45 [ft3/lbm]

vsa = 14.72 [ft3/lbm] Wra = 0.004648



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File:Psych3CoolCoil.EES 10/21/2003 12:01:00 PM Page 1


"AREN 3010


"

Moist air enters a cooling coil at 78F dry-bulb temperature and

50% RH at a rate of 2400 cfm. Barometric pressure is 14.696 psia.

The air leaves the coil at a dry-bulb temperature of 55F and a

dew-point temperature of 53F. The condensate leaves at a

temperature of 52F. "

"Given information"

P_atm = 14.696

T_da = 55

TDP_da = 53

T_ma = 78

RH_ma = .5

CFM_ma = 2400T_cond = 52

"Calculate properties of mixed and supply air"

W_ma = HUMRAT(AIRH2O,t=T_ma, r=RH_ma,p=P_atm)

h_ma = ENTHALPY(AIRH2O,t=T_ma, w=W_ma,p=P_atm)

v_ma = VOLUME(AIRH2O,t=T_ma, w=W_ma,p=P_atm)

W_da = HUMRAT(AIRH2O,t=T_da, d=TDP_da,p=P_atm)

h_da = ENTHALPY(AIRH2O,t=T_da, w=W_da,p=P_atm)

c_p = SPECHEAT(AIRH2O,t=T_ma,w=W_ma,p=P_atm)

"a) What is the total load on the coil?"

m_sa = CFM_ma/v_ma*CONVERT(hr,min)

h_cond = ENTHALPY(WATER,t=T_cond,p=P_atm)

m_cond = m_sa*(W_ma-W_da)

Q_totExact = m_sa*(h_ma-h_da)-m_cond*h_cond

Q_tot=m_sa*(h_ma-h_da)

Error_Q = (Q_tot-Q_totExact)/Q_totExact

"b) What is the sensible heat ratio?"

Q_sen = m_sa*c_p*(T_ma-T_da)

SHR = Q_sen/Q_tot

"c) What are the supply air conditions?"

Q_fan = 1200*CONVERT(W,Btu/hr)


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T_sa = T_da+Q_fan/(m_sa*c_p)

W_sa = W_da

AREN 3010


Moist air enters a cooling coil at 78F dry-bulb temperature and

50% RH at a rate of 2400 cfm. Barometric pressure is 14.696 psia.

The air leaves the coil at a dry-bulb temperature of 55F and a

dew-point temperature of 53F. The condensate leaves at a

temperature of 52F.

Given information

Patm = 14.696

Tda = 55

TDPda = 53

Tma = 78

RHma = 0.5

CFMma = 2400

Tcond = 52

Calculate properties of mixed and supply air

Wma = 'AirH2O' , T = Tma , R = RHma , P = Patm

hma = h 'AirH2O' , T = Tma , w = W ma , P = Patm


W da = 'AirH2O' , T = Tda , D =TDPda , P = Patm

hda = h 'AirH2O' , T = Tda , w = W da , P = Patm

cp = Cp 'AirH2O' , T = Tma , w = Wma , P = Patm

a) What is the total load on the coil?

msa =CFMma

vma 60

min

hr

hcond = h 'Water' , T = Tcond , P = Patm

mcond = msa W ma W da

Q totExact = msa hma hda mcond hcond

Q tot = msa hma hda


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ErrorQ =Q tot Q totExact

Q totExact

b) What is the sensible heat ratio?

Qsen = msa cp Tma Tda

SHR =Qsen

Q tot

c) What are the supply air conditions?

Q fan = 1200 3.41214 Btu/hr

W

Tsa = Tda +Q fan

msa cp

W sa = W da


CFMma = 2400 [cfm] cp = 0.2449 [Btu/lbm-R] Error Q = 0.004553

hcond = 20.09 [Btu/lbm] hda = 22.48 [Btu/lbm] hma = 29.94 [Btu/lbm]

mcond = 17.58 [lbm/hr] msa = 10452 [lbm/hr] Patm = 14.7 [psia]

Qfan = 4095 [Btu/hr] Qsen = 58866 [Btu/hr] Qtot = 77949 [Btu/hr]

QtotExact = 77596 [Btu/hr] RHma = 0.5 SHR = 0.7552

TDPda = 53 [F] Tcond = 52 Tda = 55 [F]

Tma = 78 [F] Tsa = 56.6 [F] vma = 13.78 [ft3/lbm]

Wda = 0.008539 Wma = 0.01022 Wsa = 0.008539



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File:Psych4Mix.EES 10/21/2003 9:26:57 AM Page 1


"AREN 3010


"

Outdoor air is mixed with building return air in a mixing chamber

prior to conditioning. The outdoor air is at 90F and 40% RH with

an airflow of 1000 cfm. The return air is 80F and 67F wet-bulb with

an airflow rate of 3000 cfm. "

"Given information"

P_atm = 14.696

T_ra = 80

TWB_ra = 65

cfm_ra = 3000T_oa = 90

RH_oa = .4

cfm_oa = 1000


h_ra = ENTHALPY(AIRH2O,t=T_ra, b=TWB_ra,p=P_atm)

W_ra = HUMRAT(AIRH2O,t=T_ra, b=TWB_ra,p=P_atm)

v_ra = VOLUME(AIRH2O,t=T_ra, b=TWB_ra,p=P_atm)

h_oa = ENTHALPY(AIRH2O,t=T_oa, r=RH_oa,p=P_atm)

W_oa = HUMRAT(AIRH2O,t=T_oa, r=RH_oa,p=P_atm)

v_oa = VOLUME(AIRH2O,t=T_oa, r=RH_oa,p=P_atm)

"What is the mixed air condition?"

m_oa = cfm_oa/v_oa*CONVERT(hr,min)

m_ra = cfm_ra/v_ra*CONVERT(hr,min)

m_ma = m_oa+m_ra

OA_frac = m_oa/m_ma

h_ma = OA_frac*h_oa + (1-OA_frac)*h_ra

W_ma = OA_frac*W_oa + (1-OA_frac)*W_ra

T_ma = TEMPERATURE(AIRH2O,h=h_ma,w=W_ma,p=P_atm)

v_ma = VOLUME(AIRH2O,T=T_ma,w=W_ma,p=P_atm)

cfm_ma = m_ma*v_ma/CONVERT(hr,min)

AREN 3010



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Outdoor air is mixed with building return air in a mixing chamber

prior to conditioning. The outdoor air is at 90F and 40% RH with

an airflow of 1000 cfm. The return air is 80F and 67F wet-bulb with

an airflow rate of 3000 cfm.

Given information

Patm = 14.696

Tra = 80

TWB ra = 65

cfmra = 3000

Toa = 90

RHoa = 0.4

cfmoa = 1000


h ra = h 'AirH2O' , T = Tra , B = TWBra , P = Patm

W ra = 'AirH2O' , T = Tra , B =TWBra , P = Patm

v ra = v 'AirH2O' , T = Tra , B = TWBra , P = Patm

hoa = h 'AirH2O' , T = Toa , R =RHoa , P = Patm

W oa = 'AirH2O' , T = Toa , R =RHoa , P = Patm

voa = v 'AirH2O' , T = Toa , R = RHoa , P = Patm

What is the mixed air condition?

moa =cfmoa

voa 60

min

hr

m ra =

cfmra

v ra 60

min

hr

mma = moa + m ra

OA frac =moa

mma

hma = OA frac hoa + 1 OA frac h ra

Wma = OA frac W oa + 1 OA frac W ra

Tma = T 'AirH2O' , h = hma , w = W ma , P = Patm


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cfmma = mma vma

60 min

hr


cfmma = 4000.005 [cfm] cfmoa = 1000 [cfm] cfmra = 3000 [cfm]

hma = 31.14 [Btu/lbm] hoa = 34.91 [Btu/lbm] hra = 29.91 [Btu/lbm]

mma = 17274 [lbm/hr] moa = 4248 [lbm/hr] mra = 13027 [lbm/hr]

OAfrac = 0.2459 Patm = 14.7 [psia] RHoa = 0.4

TWBra = 65 [F] Tma = 82.47 [F] Toa = 90 [F]

Tra = 80 [F] vma = 13.89 [ft3/lbm] voa = 14.13 [ft

3/lbm]

vra = 13.82 [ft3/lbm] Wma = 0.01031 Woa = 0.01206

Wra = 0.009743



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15/22

File:Psych5OneZone.EES 10/21/2003 9:28:52 AM Page 1


"AREN 3010


"

A building space is to be maintained at 78F dry-bulb and 65F wet-bulb.

The total cooling load on the space has been calculated to be 60,000 Btu/hr

of which 42,000 Btu/hr is sensible heat gain. Supply air is delivered to the

space at a temperature of 58F. For acceptable air quality, 500 cfm of

outside air is required. Outdoor conditions are 90F and 50% RH. "

"Given information"P_atm = 14.696

T_sa = 58

T_ra = 78

TWB_ra = 65

T_oa = 90

RH_oa = .5

cfm_oa = 500

Q_sen = 42000

Q_tot = 60000


h_ra = ENTHALPY(AIRH2O,t=T_ra, b=TWB_ra,p=P_atm)

W_ra = HUMRAT(AIRH2O,t=T_ra, b=TWB_ra,p=P_atm)




c_p = SPECHEAT(AIRH2O,t=T_ra,b=TWB_ra,p=P_atm)

"a) What is the airflow required for the space?"

m_sa=Q_sen /(c_p*(T_ra-T_sa))

"b)What is the supply air humidity ratio?"

h_sa = h_ra - Q_tot / m_sa

W_sa = HUMRAT(AIRH2O,t=T_sa, h=h_sa,p=P_atm)


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"c) What is the capacity of the cooling coil?"

m_oa = cfm_oa/v_oa*CONVERT(hr,min)

OA_frac = m_oa/m_sa



Q_coil = m_sa*(h_ma - h_sa)

"d) What is the sensible heat ratio of the cooling coil?"


Q_scoil = m_sa*c_p*(T_ma - T_sa)

SHR_coil = Q_scoil/Q_coil

AREN 3010


A building space is to be maintained at 78F dry-bulb and 65F wet-bulb.



space at a temperature of 58F. For acceptable air quality, 500 cfm of

outside air is required. Outdoor conditions are 90F and 50% RH.

Given information

Patm = 14.696

Tsa = 58

Tra = 78

TWB ra = 65

Toa = 90

RHoa = 0.5

cfmoa = 500

Qsen = 42000

Q tot = 60000


h ra = h 'AirH2O' , T = Tra , B = TWBra , P = Patm

W ra = 'AirH2O' , T = Tra , B =TWBra , P = Patm




cp = Cp 'AirH2O' , T = Tra , B = TWBra , P = Patm


17/22



a) What is the airflow required for the space?

msa =Qsen

cp Tra Tsa

b)What is the supply air humidity ratio?

hsa = h ra Q tot

msa

W sa = 'AirH2O' , T = Tsa , h = hsa , P = Patm

c) What is the capacity of the cooling coil?

moa =cfmoa

voa 60

min

hr

OA frac =moa

msa



Qcoil = msa hma hsa

d) What is the sensible heat ratio of the cooling coil?


Qscoil = msa cp Tma Tsa

SHRcoil =Qscoil

Qcoil


cfmoa = 500 [cfm] cp = 0.2449 [Btu/lbm-R] hma = 31.99 [Btu/lbm]

hoa = 38.31 [Btu/lbm] hra = 29.92 [Btu/lbm] hsa = 22.93 [Btu/lbm]

moa = 2114 [lbm/hr] msa = 8576 [lbm/hr] OAfrac = 0.2464

Patm = 14.7 [psia] Qcoil = 77720 [Btu/hr] Qscoil = 48251 [Btu/hr]

Qsen

= 42000 [Btu/hr] Qtot

= 60000 [Btu/hr] RHoa

= 0.5

SHRcoil = 0.6208 TWBra = 65 [F] Tma = 80.98 [F]

Toa = 90 [F] Tra = 78 [F] Tsa = 58 [F]

voa = 14.19 [ft3/lbm] Wma = 0.01142 Woa = 0.01515

Wra = 0.0102 Wsa = 0.008272



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19/22

File:Psych6OneZoneOffDesign.EES 10/21/2003 9:29:37 AM Page 1


"AREN 3010


"

A building space is to be maintained at 78F dry-bulb temperature.



space at 58F and 90% RH. The outdoor air mass flow rate is 25% of the total

supply mass flow rate. Outdoor conditions are 80F and 55% RH. "

"Given information"P_atm = 14.696

T_sa = 58

RH_sa = .90

T_ra = 78

T_oa = 80

RH_oa = .55

OA_frac = .25

Q_sen = 27000

Q_tot = 30000


W_sa = HUMRAT(AIRH2O,t=T_sa, r=RH_sa,p=P_atm)

h_sa = ENTHALPY(AIRH2O,t=T_sa, w=W_sa,p=P_atm)




c_p = SPECHEAT(AIRH2O,t=T_ra,r=.5,p=P_atm)

"a) What is the airflow required for the space?"

m_sa=Q_sen /(c_p*(T_ra-T_sa))

"b)What is the zone air humidity ratio?"

h_sa = h_ra - Q_tot / m_sa

W_ra = HUMRAT(AIRH2O,t=T_ra, h=h_ra,p=P_atm)


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"c) What is the capacity of the cooling coil?"

OA_frac = m_oa/m_sa



Q_coil = m_sa*(h_ma - h_sa)

"d) What is the sensible heat ratio of the cooling coil?"


Q_scoil = m_sa*c_p*(T_ma - T_sa)

SHR_coil = Q_scoil/Q_coil

AREN 3010


A building space is to be maintained at 78F dry-bulb temperature.



space at 58F and 90% RH. The outdoor air mass flow rate is 25% of the total

supply mass flow rate. Outdoor conditions are 80F and 55% RH.

Given information

Patm = 14.696

Tsa = 58

RHsa = 0.9

Tra = 78

Toa = 80

RHoa = 0.55

OA frac = 0.25

Qsen = 27000

Q tot = 30000


W sa = 'AirH2O' , T = Tsa , R =RHsa , P = Patm

hsa = h 'AirH2O' , T = Tsa , w = W sa , P = Patm




cp = Cp 'AirH2O' , T = Tra , R = 0.5 , P = Patm

a) What is the airflow required for the space?


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msa =Qsen

cp Tra Tsa

b)What is the zone air humidity ratio?

hsa = h ra Q tot

msa

W ra = 'AirH2O' , T = Tra , h = h ra , P = Patm

c) What is the capacity of the cooling coil?

OA frac =moa

msa



Qcoil = msa hma hsa

d) What is the sensible heat ratio of the cooling coil?


Qscoil = msa cp Tma Tsa

SHRcoil =Qscoil

Qcoil


cp = 0.2449 [Btu/lbm-R] hma = 30.16 [Btu/lbm] hoa = 32.42 [Btu/lbm]

hra = 29.4 [Btu/lbm] hsa = 23.96 [Btu/lbm] moa = 1378 [lbm/hr]

msa = 5513 [lbm/hr] OAfrac = 0.25 Patm = 14.7 [psia]

Qcoil = 34165 [Btu/hr] Qscoil = 27677 [Btu/hr] Qsen = 27000 [Btu/hr]

Qtot = 30000 [Btu/hr] RHoa = 0.55 RHsa = 0.9

SHRcoil = 0.8101 Tma = 78.5 [F] Toa = 80 [F]

Tra = 78 [F] Tsa = 58 [F] voa = 13.87 [ft3/lbm]

Wma = 0.01031 Woa = 0.01204 Wra = 0.009731

Wsa

= 0.009226



22/22

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