Air enters an electrical furnace at 20oC, 100 kPa, with a volumetric flow rate o

Question

Air enters an electrical furnace at 20oC, 100 kPa, with a volumetric flow rate of 30 m3/min. The furnace delivers air at 40oC to a duct system with three branches consisting of two 15-cm-diameter ducts and a 30-cm-diameter duct. The air behaves as an ideal gas, and the pressure in the exit ducts is 100kPa. If the velocity in each 15-cm duct is 4 m/s, determine, for steady operation: a) The mass flow of air entering the furnace, in kg/s. b) The volumetric flow rate in each 15-cm duct, in m3/min. c) The velocity in the 30-cm duct, in m/s.

Explanation / Answer

a>.the volume of air entering the furnance per min is =30m^3

thus mass =mole= P*V/RT=1*30*1000/293*0.0821=1247.12

thus mass=mol. wt.*mole

=3.6kg/m =0.6Kg/s

b>. velocity in each 7.5cm duct=4m/s.

so volume of gas enterd in 1 sec= 4*3.14*(0.075)^2

=706.5*10^-4m^3s.

=70.6L/s

thus moles= 1*70.6/313*0.0821

=2.75mol/min

thus mass =mole *mol. wt. =79.7gm/s

=7.97*10^-2 kg/s

b>.aplying conservation of moles we get

30000*1/293=2*A1*V1/313+A2V2/313

we get v2= 44.36m/mi

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