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System To vacuum pump V = 1 m³ Q = pv Air Leak Po= 1 bar (a) (10 pts) Set up the transient mass balance equation and show that dp_cp-(c+v)p dt V Integrating this equation and show that V t= In Pov C+V (c+v)p-cpo

System To vacuum pump V = 1 m³ Q = pv Air Leak Po= 1 bar (a) (10 pts) Set up the transient mass balance equation and show that dp_cp-(c+v)p dt V Integrating this equation and show that V t= In Pov C+V (c+v)p-cpo

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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This problem concerns the tank shown in the following figure the gas flow rate out of the tank depends on the
density of the air inside the tank. The mass flow rate of the leak equals c(ρ0 − ρ), where c =10−5 m3
/s is a constant, ρ0 is the density of the ambient air, and ρ is the density of the air inside the tank. The mass flow rate of the air out of the tank equals to ρv, where v = 10-3 m3/s.
The initial density of air inside the tank is also ρ0.
(a) Set up the transient mass balance equation and show that it equals the equation shown in the picture. 

(b) What is the lowest attainable pressure P∗ inside the tank? 
(c) How long will the pressure fall halfway from its initial value to P∗?

System To vacuum pump V = 1 m³ Q = pv Air Leak Po= 1 bar (a) (10 pts) Set up the transient mass balance equation and show that dp_cp-(c+v)p dt V Integrating this equation and show that V t= In Pov C+V (c+v)p-cpo
Transcribed Image Text:System To vacuum pump V = 1 m³ Q = pv Air Leak Po= 1 bar (a) (10 pts) Set up the transient mass balance equation and show that dp_cp-(c+v)p dt V Integrating this equation and show that V t= In Pov C+V (c+v)p-cpo
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