Question

Air at 104°F with a relative humidity of 30% enters a heater and leaves at 77°F with a relative humidity of 20%. The volumetric flow rate leaving the system is 1,000 in3 per second. Using the psychrometric chart determine the flow rate of dry air (lb/min) through the dryer, whether water is evaporated or condensed, and the rate at which the condensation or evaporation occurs (lb/min)

Answer 1

Volumetric flowrate of leaving air = 1000 in³/s

1 inch = 0.0254 m

= (0.0254) ³ ×1000= 0.016387 m³/s

T (out) = 77°F = 25°C = 298.15 K

P = 1 atm= 1.013×10⁵ Pa

n = PV/(RT)

n = (1.013×10⁵× 0.016387) /(8.314×298.15)

n = 0.66967 mol/s = 40.1804 mol/min

Outlet R H = 20%

At T = 77°F and R. H = 20%

From psychometric chart

Y'(outlet humidity ratio) = 0.0039 Kg water/kg air

Outlet mole ratio =

(0.003909) (M.W of air/M.W of water) = 0.003909(29/18) = 0.0062978

Total moles of outlet gas = 40.1804 mol/min

Dry air flowrate through dryer = 40.1804/(1+0.062978) = 39.9289 mol/min

M. W of dry air = 29 g/mol = 0.029 Kg/mol

Mass rate of dry air = 39.9289(0.029) =

1.1579 Kg/min

1 Kg = 2.205 lb

Mass rate of dry air (Gs) = 1.1579(2.205) =

2.5532 lb/min

Inlet air conditions

T = 104°F , R. H = 30%

From psychometric chart

Y(inlet humidity ratio) = 0.013877

Inlet humidity ratio is greater than outlet humidity ratio, hence condensation of water occurs

Doing material balance

Water condensed = Gs (Y - Y')

Gs - dry air flowrate

Water condensed = 2.5532(0.013877- 0.003909)

= 0.02545 lb/min

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