In an experiment on near surface winds, the average wind speed (y, in m/s) is measured at various distances above the ground (x, in m). The winds speeds are measured with an accuracy of 0.05 m/s.

According to von Kármán's law of the wall, for a turbulently flowing fluid near a wall (e.g., stream bottom, duct or pipe wall, or in this case the ground) the average fluid velocity depends logarithmically on the distance from the wall:

v = (u_*/k) log(x/d)

where u_* is the friction velocity (related to the fluid viscosity and overall stream flow), k is the von Kármán constant (k=.41 unitless), and d is the roughness length.

1. Fit this data with a natural log relationship. [Note: here log = log_e = ln ]
2. Consider von Kármán's scientific claim of a natural log relationship. Does this evidence (data) confirm or contradict this claim? Support your answer quantitatively.
3. Properly report (sigfigs, error, units) the A and B parameters of the best-fit relationship.
4. Use a spreadsheet to calculate the friction velocity, u_*; Use the spreadsheet to also calculate the uncertainty in u_*.
5. Properly report (sigfigs, error, units) the values for u_*.
6. Self-document the spreadsheet and turn in a hardcopy of the page.
7. Make a hardcopy plot of the data with best-fit curve. Make an additional hardcopy plot with scales chosen so as to linearize the curve.

X (m)	Y (m/s)
0.75	2.46
0.96	2.68
0.98	2.68
1.69	3.14
5.1	4.02
6.3	4.16
6.4	4.09
7.1	4.20
7.8	4.40
15	4.90