Archived Filling an Empty Tank: Calculating Pressure & Temp

  • Thread starter Thread starter chellam2206
  • Start date Start date
  • Tags Tags
    Empty Tank
AI Thread Summary
A cylindrical object reentering at Mach 25 from 80 km altitude faces a normal shock, leading to pressure and temperature calculations inside the cylinder. The process involves modeling the cylinder as a convergent-divergent nozzle, where air enters through a 20 cm orifice until internal pressure matches external pressure. The calculations account for the density and isentropic relations, with a focus on the transition of Mach number from supersonic to subsonic as pressure equalizes. Concerns are raised about the density of air at 80 km, suggesting that while it is low, it remains sufficient for continuum mechanics. The discussion also questions the specifics of the cylinder's design and the orifice's placement, which could impact the flow dynamics.
chellam2206
Messages
1
Reaction score
0
Hi,

A cylindrical object is reentering at a Mach number of say 25 at an altitude of 80 km. I like to calculate static pressure and static temperature inside the cylinder.

Yes Obvious, normal shock will form. But the problem is a small orifice (say 20 cm ) is available in the cylinder, the air starts entering the cylinder through this orifice until the total pressure outside is equal to inside pressure.

I have solved/attempted this problem in the following way

Step1: I assumed cylinder as a CD nozzle having convergent portion ,orifice (as throat) and divergent portion as my cylindrical volume and also assumed sonic flow in throat. Since I know the critical mass flow rate, I calculated the density inside the cylinder and using the isentropic relation I calculated the Mach number (Initially flow reaches supersonic speed in the cylinder) inside the cylinder and subsequently pressure and temperature also calculated. This process exist until static pressure inside reaches the pressure at throat.
.
Step2: Reduction in Mach number from 1 to 0 until it reaches the outside pressure.

Is this process is correct? Static temperature inside the cylinder also will reach the temperature behind the shock?
 
Physics news on Phys.org
At 80km, is the air dense enough to use continuum mechanics? Otherwise you might have to employ more interesting formulas.
 
We loose about half the atmosphere every 5.5Km of altitude. So by my calculations, at 80km we would be down to 0.03Torr - or about 1/24000 what we have at the surface. That's still plenty dense.

But getting back to the OP. Is this a closed cylinder? Where is the orifice? If it's on the backside of a closed cylinder, it will draw a vacuum. And if 20cm is a "small orifice", how big is this cylinder?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top