Safety Valve/Pressure System question

[atay5510]

Homework Statement

A valve for a pressure system has a discharge hole whose diameter is 50mm. The spring has a free length of 250mm (if you stretched the spring out), a coiled length (measured top to bottom while spring is coiled) of 207mm and a spring constant of 120kN/m. At what pressure will the valve open?

Homework Equations

Not 100% but I think
a) p = F/A
b) F = kx

The Attempt at a Solution

Area of discharge hole = ∏r² = 1.963x10^-3m²
Force exerted by spring to keep hole closed = length of spring x spring constant = .207m x 120kN/m = 24.84kN
Therefore valve open pressure = 24.84kN/1.963x10^-3m² = 12.65 kPa.

How does that look? There is a diagram with some other info attached but I'm not sure it's relevant.

Thanks!

 

[gneill]

Homework Statement

A valve for a pressure system has a discharge hole whose diameter is 50mm. The spring has a free length of 250mm (if you stretched the spring out), a coiled length (measured top to bottom while spring is coiled) of 207mm and a spring constant of 120kN/m. At what pressure will the valve open?

Homework Equations

Not 100% but I think
a) p = F/A
b) F = kx

The Attempt at a Solution

Area of discharge hole = ∏r² = 1.963x10^-3m²
Force exerted by spring to keep hole closed = length of spring x spring constant = .207m x 120kN/m = 24.84kN
Therefore valve open pressure = 24.84kN/1.963x10^-3m² = 12.65 kPa.

How does that look? There is a diagram with some other info attached but I'm not sure it's relevant.

Thanks!

Hook's Law requires the change in length of the spring from its equilibrium point (relaxed condition). You've used the compressed length only. What if the spring were compressed to nearly zero length? Would the force then be nearly zero?

 

[atay5510]

Aha! So the resistance force due to the spring is F = -kx where x = 250mm - 207mm and k is as given.
I feel like they are giving me a little more info in the picture than is necessary. Specifically the 400mm diameter of the tank (not the discharge hole) and the 25mm thickness of the walls. My solution doesn't involve these numbers. Is that correct?
Thanks for the help :)

 

[gneill]

Aha! So the resistance force due to the spring is F = -kx where x = 250mm - 207mm and k is as given.
I feel like they are giving me a little more info in the picture than is necessary. Specifically the 400mm diameter of the tank (not the discharge hole) and the 25mm thickness of the walls. My solution doesn't involve these numbers. Is that correct?
Thanks for the help :)

Yes, sometimes you'll find extraneous information given, particularly on diagrams. This may be because: It's placed there to confuse you; To get you used to picking the required data out of actual engineering diagrams; Simply because the diagram originally came from some other question entirely. Pick one or more