What is the relationship between Mach number and compressibility in fluids?

[davon806]

Homework Statement

Hi,

The below website states the definition of Mach number, which is a quantity that expresses how compressible a fluid is.

https://physics.info/turbulence/

M = sqrt [ ( inertial resistance in the fluid ) / ( compressional resistance in the fluid ) ]

= v / c
If M is very large, then a fluid is traveling really fast. By the definition in the website, it is equivalent to saying that it requires a large amount of force to start the motion in fluid. By the definition of M, we can also say the compressional resistance is small, i.e. the fluid is compressible.

However, I don't see why the quantities are related: What does it have to do with an object that needs a huge amount of force to move it, to its compressibility ? It would be really helpful if someone can explain the physical picture of velocity ratio , in the role of determining the compressibility of a fluid.Thanks in advance

Homework Equations

The Attempt at a Solution

In corporated in (1)

 

[phinds]

The below website states the definition of Mach number, which is a quantity that expresses how compressible a fluid is.

No, it is not. You have completely mis-read the article.

What does it have to do with an object that needs a huge amount of force to move it, to its compressibility ?

It doesn't. Again, you have misread the article and you are mixing up the Reynolds number and the Mach number.

 

[davon806]

No, it is not. You have completely mis-read the article.

It doesn't. Again, you have misread the article and you are mixing up the Reynolds number and the Mach number.

So what does M mean?

BTW, Reynolds number measures how viscous the flow is ( from https://www.grc.nasa.gov/www/BGH/reynolds.html).

"The Mach number is the most important parameter in compressible flow analysis. " (from http://nptel.ac.in/courses/112104118/38).

I was just trying to understand the reason of why M is defined as inertia force/ compressibility force, I understand that if a fluid requires a huge force to compress it then M is small.

I am struggling to understand why inertia and compressible force is the quantity determining how compressible a fluid is. Why can't the numerator in M be other quantites like gravity or pressure?

(from P.250 in this book
https://books.google.co.uk/books?id=p7WsoU-CfPkC&pg=PA250&lpg=PA250&dq=mach+number+compressibility+inertia&source=bl&ots=7s1x8ExeAd&sig=lZDCOs5K2wGaCflWNlWManjLuR4&hl=en&sa=X&ved=0ahUKEwjZ1KHek6DZAhVC2aQKHRBTCD04ChDoAQhPMAY#v=onepage&q=mach number compressibility inertia&f=false )

And what is the physical picture that if a fluid is traveling fast, then we should not ignore the compressible effect on it ?