Question

Air enters the duct of an air-conditioning system at 15 psia and 50°F at a volume flow rate of 450 ft3/min. The diameter ofthe duct is 10inches and heat is transferred to the air in the duct from the surroundings at a rate of 2 Btu/s. Determine [a]the velocity of the air at the duct inlet and (b) the temperature of the air at the exit. Answers (a) 825 ft/min. (b) 64=F

Answer 1

a) v = 825 ft^3/min

b) T = 64.005 F

Step-by-step explanation:

given data:

pressure ar airc conditioning system is 15 psia

volume flow rate is \dot V = 450 ft^3/min

duct diameter is D 10 inch

Q_{in} = 2 Btu /s

Inlet temp =50 F = 50 +460 = 510 R

From air table

gas constant of air R = 0.3704 psia ft^3/lbm R

specific heat constant
`c_p = 0.24 Btu/ lbm R`

velocity at inlet is
`= (\dot V)/(A)`

`V_1 = (\dot V)/(\pi r^2)`

`V_1 = (450)/([\pi [(5)/(12)]^2) = 825 ft^3/min`

b) by ideal gas equation

`PV =\dot RT`

`15* 450 = \dot m 0.3704 * 510`

`dot m = 35.73 lbm/min`

from energy equation we have

`\dot m h_1  + Q =\dot m h_2`

`h_2 = h_1 +(Q)/(\dot m)`

`Cp T_2 = Cp T_1 +(Q)/(\dot m)`

`T_2 =T_1 + (Q)/(\dot m Cp)`

`= 510 + (2)/(0.595 * 0.24)`

`T_2 = 524.005 R = 64.005 F`