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A 60 liter vacuum tank with an initial vacuum of 509 mmHg (251 mmHg absolute) is opened up to the outside air and flows through a 6.5 mm hole.
What is the equation that represents the pressure in terms of time?
What is the equation that represents volumetric flowrate into the tank in terms of time?
I have a vacuum tank at work that I am trying to determine the flow rate and pressure curve of when I open up the tank and I just cannot figure these equations out.
Environment: average office space
Atmospheric pressure: 29.92 inHg (per weather information)
Temperature: 72°F
Tank info:
Material: Stainless steel
Tank capacity: 60L (I measured it to be 59.5 liters)
Initial vacuum: 509 mmHg (251 mmHg absolute)
Entrance hole diameter: 6.5 mm
Thermodynamics isn't my strong suit (vibrations and dynamics are). After going back through my thermodynamics and fluid dynamics I'm still having problems. So I ran a test on it to see what the real world values were. I used my iPhone and filmed the pressure gauge in slow motion as I opened the tank up. I found that the pressure rose in a very linear manner (R^2=0.995) in the first 4.5 seconds with a slope of 10165 pascals/second. If I take the partial derivative of PV=mRT I get, dm/dt = dp/dt * V/(RT). Plugging in the values above I get the experimental mass flow rate of 10165*0.059528/(287*294.261) = 0.0072 kg/second. That's the mass flow rate but how do I get the volumetric flowrate? I'm making the assumption that the air is compressing and then expanding which changes the density of the air. So I don't know what the density of the air is entering the tank otherwise I would just divide the mass flow rate by the density to get the volumetric flow rate.
I was also making the assumption that the process was isothermal but then I stumbled upon this:
http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node17.html#fig0:TankFilling
which says that the air would have an increase in temperature of at least 200°F... that sounds pretty insane which means that I also have to factor in heat transfer?
I need help of understanding the physics at play here.
Environment: average office space
Atmospheric pressure: 29.92 inHg (per weather information)
Temperature: 72°F
Tank info:
Material: Stainless steel
Tank capacity: 60L (I measured it to be 59.5 liters)
Initial vacuum: 509 mmHg (251 mmHg absolute)
Entrance hole diameter: 6.5 mm
Thermodynamics isn't my strong suit (vibrations and dynamics are). After going back through my thermodynamics and fluid dynamics I'm still having problems. So I ran a test on it to see what the real world values were. I used my iPhone and filmed the pressure gauge in slow motion as I opened the tank up. I found that the pressure rose in a very linear manner (R^2=0.995) in the first 4.5 seconds with a slope of 10165 pascals/second. If I take the partial derivative of PV=mRT I get, dm/dt = dp/dt * V/(RT). Plugging in the values above I get the experimental mass flow rate of 10165*0.059528/(287*294.261) = 0.0072 kg/second. That's the mass flow rate but how do I get the volumetric flowrate? I'm making the assumption that the air is compressing and then expanding which changes the density of the air. So I don't know what the density of the air is entering the tank otherwise I would just divide the mass flow rate by the density to get the volumetric flow rate.
I was also making the assumption that the process was isothermal but then I stumbled upon this:
http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node17.html#fig0:TankFilling
which says that the air would have an increase in temperature of at least 200°F... that sounds pretty insane which means that I also have to factor in heat transfer?
I need help of understanding the physics at play here.