Pressure loss function

[Andybaz]

hi, been stuck on this question for a few hours and could not find the function online anywhere. would really appreciate some help cause i cant seem to make heads or tail from it.


As water flows through a pipe it loses pressure due to friction. The amount of pressure loss (P m) is related to the velocity of flow in the pipe (V m/s) and other constant factors such as diameter and pipe roughness. P and V are believed to be related by a function of the form P = kVn where k and n are constants

(V m/s) P metres
(0.73) 0.054
(0.85) 0.074
(0.91) 0.084
(0.98 ) 0.098
(1.06 ) 0.115
(1.11) 0.126
(1.34) 0.183
(1.46) 0.217

part one
Determine the values of the constants k and n

part two
State the function relating P and V


thanks for your time.

 

[tkhunny]

You've been stuck for hours? This must mean that you have written something. Will you share what it is you have been doing that constitutes "stuck"? More clues, please...

Do the parentheses mean a negative number?

Can you substitute known values enough times to get a good result for the constants?

Are ALL the known values consistent?

Is this a least-squares problem?

 

[Andybaz]

Do the parentheses mean a negative number?

no i put them there to split up the V m/s and the P meters as in the question they are in a table and i was unsure how to communicate this

Can you substitute known values enough times to get a good result for the constants?

as far as i know you can only use the values given in the table for V and P.

Are ALL the known values consistent?

not sure what you mean by this sorry.

Is this a least-squares problem?

no its meant to be algebra and functions.

all the information i have been given for the question i have put in the post I'm glad I'm not the only one struggling the only thing I've really managed to do is make a graph out of the table.

 

[tkhunny]

This: P = kVn

With this:

(V m/s) P metres
(0.73) 0.054

Means this: 0.54 m = k * (0.73 m/s) * n

Does that help us find k and n?

 

[Dr.Peterson]

P and V are believed to be related by a function of the form P = kVn where k and n are constants

I think you meant P = kV^n, i.e. P = kVⁿ. The data do (just about exactly) fit a formula of this type; I found that using Excel as a shortcut, but you can do it by taking any two rows in the table (I'd take the first and last for accuracy) as a system of two nonlinear equations in two unknowns.