# Permissible error

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1. Jun 14, 2015

### Malu666

How to calculate the permissible error?
A force F is applied on a square plate of size L . If the percentage error in determination of L is 2% and that in F is 4% . What will be the permissible error in pressure?

2. Jun 14, 2015

### rude man

EDITed:
Depends on how you define "permissible".
First, you say a "square" sheet. Is it really square? You have to assume "I don't know" so the area could be that of a general quadrilateral. That requires the measurement of 4 sides plus two opposite angles: http://keisan.casio.com/exec/system/1322718508
Plus a 7th independent measurement is for the force F.
So, assume the error in measuring each side's length and that of each of the two angles is 2%,
if the errors are random in all 7 cases, error propagation theory says to take the square root of the sum of the squares:
error = √(6(.022) + .042) = 0.063 = 6.3%.

But there is also the "worst-case" error which you would get if all your measurements are at their respective extremes, in which case the error would be (1.02)6(1.04) - 1 = 17.1%.

Last edited: Jun 14, 2015
3. Jun 14, 2015

### Malu666

Thanks for the reply. Maybe you went for a higher level of explanation. I think that the question interconnects between force , area and pressure. As pressure = force/ area , can you precisely explain about the permissible error in pressure ?

4. Jun 14, 2015

### rude man

If the error in force is 4.0% and the error in area is 2.0%, the error in pressure is √(.0402 + .0202) = 4.4%.

But L is likely to mean length, not area, so then it'd be √(.0402 + .0202 + .0202) = 4.9%.

5. Jun 14, 2015

### haruspex

We are told it is square. The two length errors are correlated?

6. Jun 14, 2015

### rude man

Good point. So it's just √(.022 + .042).

7. Jun 14, 2015

### Staff: Mentor

Just a friendly reminder, if the template isn't used or the information required in the template isn't used, such as what the member has tried themselves to solve the problem, please do not reply, please send a report.

8. Jun 14, 2015

### rude man

OK. Sorry. I thought after I wrote that it was probably excessive. Will be more on guard henceforth.
r m

9. Jun 14, 2015

### Staff: Mentor

You're cool, we're just trying to get things more even in responses, some members get turned back while some get answered.

10. Jun 15, 2015

### haruspex

No, the answer should get bigger, not smaller.