Question

Please help Idk how to start . Thanks in advance

Answer 1

The percent error for the viscosity is 25.5%

Step-by-step explanation:

Recall that the percent uncertainty is in fact the so called "relative error" of each measurable quantity in percent form.

So let's write the "relative error" associated with each of the measured variables;

`(\delta\,p)/(p) =0.02` since its percent error is 2%

`(\delta\,r)/(r) =0.05` since its percent error is 5%

`(\delta\,l)/(l) =0.005` since its percent error is 0.5%

`(\delta\,V/t)/(V/t) =0.03` since its percent error is 3%

Recall as well, that the error analysis treatment with relative errors is quite simple, since it considers just the power at which the measured variable appears in the rational expression that relates them.

Let's start then solving for the derived quantity "viscosity" in the given rational expression:

`(V)/(t) =(\pi\.p\,r^4)/(8\,l\,\eta) \\\eta=(\pi)/(8) \,(p\,r^4)/(l\,(V/t))`

Then, given this expression, the relative error in the viscosity
`\eta`, is derived from the following propagation of errors:

`(\delta\,\eta)/(\eta) =(\delta\,p)/(p) +\,4\,(\delta\,r)/(r)+(\delta\,l)/(l)+(\delta\,V/t)/(V/t)\\(\delta\,\eta)/(\eta) =0.02+4\,*\,0.05+0.005+0.03\\(\delta\,\eta)/(\eta) =0.255`

Therefore, the percent error for the viscosity is 25.5%