How can uncertainties be calculated for equations and variables?

[dagg3r]

Hi guys, i am trying to work out the uncertainty of this equation

Y = (AC-CX)/(B+X)
and i am needed to work out the uncertainty in Y.

values for these are:
Y=2.18 UNCERTAINTY UNKNOWN
A=29m Uncertainty in A denoted (Sa)=3mm
B=710mm Uncertainty in B denoted(Sb)=3mm
C=5.85mm Uncertainty in C denoted(Sc)=0.2mm
D=0.150mm Uncertainty in D denoted (Sd)=0.005mm
X=18.68m Uncertainty in X denoted (Sx)=0.005mm

using these values i used the formula:

Sy/Y = (Sc/C)+ S[(A-x)(B+x)]/[(A-x)(B+x)]
Sy/Y = (0.2/5.85) + (0.1099555934/0.3723445134)
Sy= 0.7182971382

i obtained an uncertainty of 0.7 it is very large hence i think i may have done something wrong in my calculations.

to obtain S[(A-x)(B+x)]
i did
[S(A-x)/(a-x)] + [S(B+x)/(B+x)]
=[(3mm+.005)/(29-18.68)] + [(3mm+.005)/(710+18.68)]
=0.1099555934

so can anyone please check this thanks!

also another simple question
Y= (AC-CX)/(B+X)
how do i derive for B, keeping everything else constant?
eg if i were to derive with respect to C, whilst keeping everything else constant i would get
: [A-X/(B+X)] ... so how do i derive with respect to B while keeping everything else constant since it is in the denomitor...

THANKS ALL

 

[HallsofIvy]

First question: Looks to me like your arithmetic is just wrong!
0.2/5.85= 0.034188... and 0.1099555934/0.3723445134= 0.29530606591642170268376325203836. Their sum is about 0.329, not 0.7.


As for the derivative of Y= (AC-CX)/(B+X) with respect to B, use the quotient formula:
\frac{\partial Y}{\partial B}= \frac{(0)(B+X)- (AC-CX)(1)}{(B+X)^2}= \frac{CX- AC}{(B+X)^2}.

 

[dagg3r]

Sy/Y = (0.2/5.85) + (0.1099555934/0.3723445134)
yes you are correct the sum is 0.329
but i had
Sy= 0.7182971382

which is the sum multiplyed by Y
so
0.329*2.18=0.7182971382
which is the uncertainty in Y... but i don't know if its right or not the way i went about it all.

so is their another way of working out uncertainty?

 

[HallsofIvy]

Well, one thing you could do is this: calculate each of the given number plus[\b] their "uncertainty" and minus. Use those to see what is the largest and smallest values Y could have.