How Is the Force Distributed in an Evacuated Chamber with a Panel Cover?

[Arctangent]

Fluids -- evacuated chambers

I've worked on this problem in a few different ways. Maybe I'm having trouble with the direction of my forces:

We have a
an evacuated chamber
the pressure inside of the chamber is 23.0 kPa
a 5cm diameter hole covered by a
0.225m diameter circular panel (mass is negligable)

And the question asks for the force required to pull off the panel.

My first thinking was that because the "vacuum" is being caused by the pressure of the atmosphere,
I'm calling it Fair,
is the force pointing down on the panel
The force of the air inside the chamber is pushing up through the 5cm diameter hole on a small section of panel
Fc,
and the pulling force required to take off the panel is upwards,
Fp.


So,
Fnet = Fp + Fc - Fair = 0
Fp = Fair - Fc

Fc = PA = 23000*pi*r^2 = 45.16 N
where r is the radius of the hole in the chamber

Fair = 101300*pi*R^2 = 4028 N
where R is the radius of the panel

And then I'd solve for Fp. But my answer -- 3982.61 N -- was incorrect.

I'm obviously missing something critical. Would you have any ideas of what I'm doing wrong, and maybe point me in the right direction?

Thanks!

 

[Andrew Mason]

Your approach is correct. I get 4026 N for $F_{air}$ which gives 3981 N.

AM

 

[Gamma]

"a 5cm diameter hole covered by a
0.225m diameter circular panel (mass is negligable"

I am trying to visualize this. A 5 cm hole covered by a 2.25 cm panel? What am I missing?

 

[Arctangent]

"a 5cm diameter hole covered by a
0.225m diameter circular panel (mass is negligable"

I am trying to visualize this. A 5 cm hole covered by a 2.25 cm panel? What am I missing?

.225m = 22.5 cm

.05m = 5.0 cm

just mixed up the conversion a little, that's all.

 

[Arctangent]

Your approach is correct. I get 4026 N for $F_{air}$ which gives 3981 N.

AM

Are you sure? I think I have something wrong here. My final answer is supposed to be in 3 significant digits.

Would the air from the chamber only be pushing up to that 5 cm diameter area or would it be pushing up on the whole panel?