Fitting data - Your turn

Fitting data - Your turn#

The same students have repeated their experiments at Reynolds numbers between \(10^4\) and \(10^5\) and have found a constant drag coefficient of \(C_{\mathrm{D}} = 0.4775\). Assume the density of air \(\rho\) is \(1.25\) kg/m\(^3\). The following table gives the drag force on the sphere as a function of the air speed.

\(F_{\mathrm{D}}\) (N)

\(V\) (m/s)

0.036

4

0.09298

6

0.10682

7

0.1568

8

0.193

9

Find the radius of the sphere used in the experiments by following these steps.

Part (a)#

In the definition of the drag force:

\[ F_{\mathrm{D}} = \dfrac{1}{2} C_{\mathrm{D}} \rho V^2 \pi r^2, \]

the group \(\dfrac{1}{2} C_{\mathrm{D}} \rho \pi r^2\) is now a constant, since the drag coefficient is assumed to be constant. That means that the plot of \(F_{\mathrm{D}}\) vs. \(V^2\) should be close to a straight line. Using polyfit(), find an equation of a line that best fits the data given in the table.

# TODO: Write your solution below

Part (b)#

Using the results in part (a) extract the value of \(\dfrac{1}{2} C_{\mathrm{D}} \rho \pi r^2\).

# TODO: Write your solution below

Part (c)#

Using the numerical values provided, estimate the radius of the sphere.

# TODO: Write your solution below

Exporting your work#

When you’re ready, the easiest way to export the notebook is to File > Print it and save it as a PDF. Remove any excessively long, unrelated outputs first by clicking the arrow → next to the output box and then Show/hide output. Obviously don’t obscure any necessary output or graphs!

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