Linearizing Data


The table below represents water velocity vs. water depth, as inferred from stream range vs. depth by one student:

depth velocity

0.16 m

1.4 m/s

0.12

1.3

0.08

1

0.04

0.64

0

0.04

To linearize this data we can take different powers of the velocity column and graph them vs. depth.

One power that does not work is the -1 power (the reciprocal).  Taking the reciprocals of the v column we get

depth velocity^-1

0.16 m

.7

0.12

.77

0.08

1

0.04

1.53

0

250

This transformation doesn't linearize very well at all, as can be easily seen by graphing y = velocity^-1 vs. depth.

Using a more appropriate power function (which you should find for yourself) the above data gives us the linearized graph below.  The y axis isn't labeled, so you will have to find your own linearization.

 We can use this linearization to get velocity v as a function of depth h:

You should now linearize the given data (or the data you have obtained for the experiment) using an appropriate power of v and using the appropriate units on your graph.