A fluid moves through a tube of length 1 meter and radius r=0.006±0.00025 meters under a pressure p=4⋅105±2000 pascals, at a rate v=0.375⋅10−9 m3 per unit time. Use differentials to estimate the maximum error in the viscosity η given by
To find maximum error in viscosity we have to use differentials because when the error is small it can be approximated by a derivative. First we find relative error in each of the variables that viscosity depends on. These are radius and pressure. After that, we find partial derivatives of viscosity with respect to radius and pressure, divide them by viscosity and sum. That will give us maximum error.
Relative error in the radius is: