Homework Help: Error Calculation in Multiplication of two measurement points

1. Apr 23, 2012

1. The problem statement, all variables and given/known data
Hi All, I have a problem in calculating the thickness of a coating material inside a tube. The tubes inside diameter is measured before and after coating. The coating thickness is calculated by substracting the diameters and dividing by two to get the thickness of the coated material. The before coat diameter is 0.3949". The after coat diameter is 0.3893". The measurement error's standard deviation is 0.00017". I need to calculate the coating thickness value and its associated error.

2. Relevant equations
Coating Thickness = (Before Coat Dia. - After Coat Dia.)/2

3. The attempt at a solution
I am thinking the thickness without error = (0.3949 - 0.3893)/2 = 0.0028"

My error for each measurement would be measured value +/- 3 x the Standard Deviation Error.
For uncoated = 0.3949" +/- 0.00051"
For Coated = 0.3893" +/- 0.00051

The minimum thickness = (0.3949 - .00051) - (0.3893 + 0.00051) = 0.00458"

The maximum thickness = (0.3949 + 0.00051) - (0.3893 - .00051) = 0.00662"

Error Thickness = (.00662 - 0.00458)/2 = 0.00102"

Coating Thickness = 0.0028" +/- 0.00102"?

2. Apr 23, 2012

tms

There are standard formulas for doing this. Look up 'propagation of errors' in Bevington or some similar book.