Aerodynamics - Standard Atmosphere problem

[eku_girl83]

Here's the problem:
We are ascending in an elevator at sea level. Our eardrums feel a 1 percent decrease in pressure per minute. Calculate the upward speed of the elevator.
My solution:
*I am using the equation p1/p0 = (T1/T0)^(-g/aR), where p1 and p0 are pressure at point 1 and point 0, respectively.
*T1 and T0 are temperatures at point 1 and 0, g is acceleration due to gravity, a is the slope of the first gradient layer (Temperature/Altitude), and R is the specific gas constant for air.
*In the context of the problem, we know that p1 = .9 p0, T0 = 288.16K (temperature at sea level), g= 9.8 m/s^2, a = -.0065 K/m (from temperature distribution graph in textbook), and R = 287 J/kg K.
*Plugging these values into my equation and solving for T1, I get T1 = 282.4382 K.
*Since the temp./altitude distribution is a straight line for this region, I know T1 = T0 + a(h-h0).
*h0 is zero, so plugging in and solving for h I obtain h = 880 m.
*Since this took place in the course of a minute (which is the time for a 10% pressure decrease to occur, according to the problem), the velocity is 880m/min upward.

This seems a little fast? Did I do things right?

I would appreciate any input!
Thanks!

 

[zigga15]

I would assign a random value for displacement - say 100m, you can use resources to find the values for temp and pressure etc at that height and then sub that into your formula for point 2, to either check or to help solve...

 

[piercas]

Your calculations and approach seem correct. However, it is important to note that the 1% decrease in pressure per minute may not be a linear decrease. It could also be a logarithmic decrease or follow some other function. This would affect the accuracy of your calculation for the velocity. Additionally, the temperature distribution in the atmosphere is not a perfect straight line, so there may be some error in your calculation for the altitude. Overall, your approach is sound but it is important to consider any potential factors that may affect the accuracy of your solution.