Safety Valve/Pressure System question

• atay5510
In summary, the valve for the pressure system has a discharge hole with a 50mm diameter. The spring used has a free length of 250mm and a coiled length of 207mm, with a spring constant of 120kN/m. Using the Hook's Law equation, the force exerted by the spring to keep the hole closed is calculated to be 24.84kN. The valve will open at a pressure of 12.65 kPa. The given diagram includes additional information such as the 400mm diameter of the tank and the 25mm thickness of the walls, but these are not necessary for the solution.
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!

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• Assign1.jpg
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atay5510 said:

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?

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 :)

atay5510 said:
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

Your attempt at a solution looks correct. However, there are a few things to consider when determining the pressure at which the valve will open:

1. Make sure to convert all units to SI units (meters and newtons) before plugging into the equations. This will ensure the correct answer in pascals (Pa).

2. The valve will open when the force exerted by the spring is greater than the force of the pressure acting on the valve. So, the correct equation to use would be F = kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the spring. In this case, x would be the difference between the free length and the coiled length of the spring.

3. The diagram and other information attached may be relevant in determining the correct pressure at which the valve will open, so make sure to consider all given information carefully.

Overall, your approach seems correct and your answer looks reasonable. Just make sure to double check your units and equations to ensure the correct solution.

1. What is a safety valve and how does it work?

A safety valve is a mechanical device used to control or release pressure in a system to prevent damage or dangerous situations. It works by opening when the pressure in the system reaches a predetermined level, allowing excess pressure to be released and maintaining a safe pressure level.

2. Why is a safety valve important in a pressure system?

A safety valve is crucial in a pressure system to prevent overpressure, which can cause explosions, ruptures, or other hazards. It serves as a last line of defense to protect the system and its components from damage or potential harm.

3. How do I know if a safety valve is working properly?

To ensure a safety valve is functioning correctly, it should be regularly inspected and tested according to industry standards. Visual inspections can also be performed to check for any physical damage or signs of wear. If there are any doubts about its functionality, a qualified professional should be consulted.

4. Can a safety valve be adjusted or tampered with?

No, a safety valve should never be adjusted or tampered with unless done by a qualified professional. Altering the valve's settings or components can compromise its ability to function properly and put the system at risk.

5. Are there different types of safety valves for different applications?

Yes, there are various types of safety valves designed for specific pressure systems and applications. Some common types include spring-loaded, pilot-operated, and thermal safety valves. It is essential to use the correct type of valve for a specific system to ensure proper functioning.

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