ratio problem: If a valve with a 4.3% preload opens at 3.5 PSI, and a valve with...

[dave8441]

If a valve with a 4.3% preload opens at 3.5 PSI, and a valve with a 1.6% preload opens at 1.75 PSI, at what PSI will a valve with a 3% preload open?
I believe this is a ratio problem, but I do not know how to solve it. Thanks in advance for your help.

 

[Deleted member 4993]

If a valve with a 4.3% preload opens at 3.5 PSI, and a valve with a 1.6% preload opens at 1.75 PSI, at what PSI will a valve with a 3% preload open?
I believe this is a ratio problem, but I do not know how to solve it. Thanks in advance for your help.

To the solve the problem, we need to assume that %-preload and the pressure (psi) are linearly co-related.

Is that a reasonable assumption under this situation?

 

[dave8441]

To the solve the problem, we need to assume that %-preload and the pressure (psi) are linearly co-related.

Is that a reasonable assumption under this situation?

I would say yes.

 

[soroban]

If a valve with a 4.3% preload opens at 3.5 PSI,
and a valve with a 1.6% preload opens at 1.75 PSI,
at what PSI will a valve with a 3% preload open?

\(\displaystyle \text{We have: }\;\begin{array}{ccc}4.3\% & \to & 3.5 \\
1.6\% & \to & 1.75 \\
3.0\% & \to & ? \end{array}\)

This is NOT a linear function.

 

[stapel]

I would say yes.

On what basis? What other information or equation did your class give you, related to this homework problem, which led you to this conclusion?

Note: It looks like, in real life, linearity should probably not be assumed! (here or here)

 

[Deleted member 4993]

\(\displaystyle \text{We have: }\;\begin{array}{ccc}4.3\% & \to & 3.5 \\
1.6\% & \to & 1.75 \\
3.0\% & \to & ? \end{array}\)

This is NOT a linear function.

Why not?

L = percent of pre-load

P = pressure (in psi)

(P - 1.75)/( 0.03 - 0.016) = (3.5 - 1.75)/(0.043 - 0.016) → P = ??

 

[dave8441]

Why not?

L = percent of pre-load

P = pressure (in psi)

(P - 1.75)/( 0.03 - 0.016) = (3.5 - 1.75)/(0.043 - 0.016) → P = ??

This answer agrees with another one that I received. So (3.5 - 1.75)/(0.043 - 0.016) = 64.8148. Then (64.8148*3%Preload) = (64.8148*.03) = 1.94 PSI. Thank you very much.