Thread: Flow rate

sdf

Originally Posted by angelica2007

How do you find the best fit line and describe the features of the original data and the rate of change of the data considering the rate of flow between 00:00 on Oct 27 and 00:00 on Nov 2 for the following:
Time: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144
Flow: 440, 450, 480, 570, 680, 800, 980, 1090, 1520, 1920, 1670, 1440, 1380, 1300, 1150, 1060, 970, 900, 850, 800, 780, 740, 710, 680, 660

Looking at this data a best fit line will not be a usefull way to describe the
data. I suspect that the best you can do with this data is to just plot it
unless you know something about the underlying process which produced it.

RonL

Well

Originally Posted by angelica2007

Well I'm supposed to find whether a linear, quadratic, cubic, etc line best describes the data.

You had better decide that yourself. My professional opinion is that
there is insufficient data to warrant any such fitting process.

How would I find the rate of change for it?

Calculate the difference quotients.

So at time t=time(i)+time(i+1), the rate of change is:

~= (flow(i+1)-flow(i))/(time(i+1)-time(i)).

The attachment shows a plot of this.

RonL

Well I
I don't understand how to find the rate of change. Can you please ellaborate.

how about seperating the data/bestfit to before t<=54 and after t>=54

so

Originally Posted by angelica2007

Well I'm supposed to find whether a linear, quadratic, cubic, etc line best describes the data. How would I find the rate of change for it?

You need to investigate the use of a rational function to represent the data,
something like a Pade approximation.

RonL

I'm

Originally Posted by angelica2007

I'm confused on finding the rate of change using rational functions..I have learned Pade approximation...

If you have an approximating/interpolating function f(t) for your data, then
estimate the rate of change at t by the derivative f'(x) of f(x) with respect
to x.

RonL

Once I find the derivative do evaluate it at 0 to find the slope?

Originally Posted by angelica2007

Once I find the derivative do evaluate it at 0 to find the slope?

The derivative is the slope or rate of change of flow at every point at which
it is defined. You could evaluate it at all the times you have flow data for, which
will illustrate how the rate of change of flow varies with time.

RonL

I understand it now. So when it said to consider the time between 00:00 on Oct 27 and 00:00 on Nov 2, does that have an effect?

Originally Posted by angelica2007

I understand it now. So when it said to consider the time between 00:00 on Oct 27 and 00:00 on Nov 2, does that have an effect?

That is what the time data are, hours from 00:00 Oct 27.

RonL

So would the best fit line be the one that crosses the most points?