Problem 2

        We wish to measure the dimensionless drag on a sphere settling
through a viscous fluid at low Reynolds numbers.  We have conducted an 
experiment with a particular sphere and have obtained the following 
results (with one sigma error limits):

        U = 0.679 cm/s +- 0.012 cm/s
        visc = 1.22p +- 0.03p (note: poise is the cgs unit of measurement 
                                of viscosity)
        a = 0.051cm +- 0.004cm (the sphere radius)
        density(sphere) = 2.40 g/cm3 +- 0.05 g/cm3
        density(fluid) = 1.215 g/cm3 +- 0.005 g/cm3
        g = 980.0 cm/s2 (no error in this value)

a.  Using this data, calculate the dimensionless drag defined by:

Drag = U / [(density(sphere)-density(fluid))*g*a^2/visc] 

and determine the 95% confidence limits.  Is this value within 2 sigma of 
the theoretical value of 2/9 found for zero Reynolds number?  

b.  If you could improve only one of the above measurements to 
increase the accuracy of the final result, which one would it be?  
(e.g., which measurement has the largest contribution to the final error?)  

While the derivatives of the above expression can be taken analytically, it is
actually alot simpler to write a function which takes in the measured values
as a 5x1 array (or 6x1 including gravity), and then returns the dimensionless
drag.  You can then use a finite difference algorithm to calculate all the relevant
derivatives numerically, and do the whole problem in matrix form.  Remember
that if the measurements are all taken to be independent, then their matrix
of covariance is purely diagonal.