eku_girl83
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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!
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!