No credit will be give for wrong answers. Steam at 120 bar, 500 degree C, enters

Question

No credit will be give for wrong answers.

Steam at 120 bar, 500 degree C, enters a control volume with a volumetric flow rate of 460 m3/min. Twenty-two percent of the entering mass flow exits through duct "A" at 10 bar, 220 degree C, with a velocity of 20 m/s. The rest exits at another location through duct "B" with a pressure of 0.05 bar, a quality of 86.2%, and a velocity of 500 m/s. Determine the diameter of each exit duct, in meters, assuming that the control volume operates at steady state.

Explanation / Answer

Volumetric flow rate at feed- 460 m3/min @ 120 bar & 500 centigrade.

For mass flow rate, From steam tables, Specific volume V, 1 m3=0.0268 kg

So mass flow rate is 12.328 kg/min.

For Duct A, 22 % of total mass flow rate

In duct A the mass flow rate is (.22*12.328)=2.71216 kg/min.

@220 centigrade & 10 bar V is 1 m3=0.2167 kg

Hence Volumetric flow rate is 12.51 m3/min= 0.208 m3/sec

Hence A=F/velocity= 0.208/20=0.0104 m2

Hence For daimeter 0.785 D2= 0.0104 m2

D=0.11510 m , Daimeter of Duct A

For Duct B,

88% of mass flow rate

12.328*.88=10.84864 kg/min

From stem tables @ 0.05 bar , V is 1 kg=0.03415 m3

Hence volumetric flow rate is 0.37048 m3/min=6.174x10^-3 m3/sec

Area=6.174x10^-3/500=1.2349x10^-5 m2

Daimeter = 3.966x10^-3 m.

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