Quesions Simple
 

Hello,

I have some quires, which appear to be simple, but yet unanswered.

1. If the fluid motion equations weren't based on the assumption that normal and shearing stresses are a linear function of rate of deformation, could one obtain a true description of the motion of a fluid by any other method, if any?

2. Even when we don't make any assumption on pressure drop, Reynolds number and viscosity, why is the solution obtained in Hagen – Poiseuille theory of pipe flow valid for only laminar flow?

3. Some authors say that there is conservation of momentum and some use the term momentum theorem to derive the NS equations based on Newton's Second Law of motion. Why is this confusion? Is the momentum really conserved? If not, what is the true fact?

4. When a fluid is at rest, does it develop a thermodynamic pressure or a hydrostatic pressure? If so, how?

regards

ram

Re: Quesions Simple
 

Hi Ram,

I can go into some of the questions you have raised, but I suggest you read GK Batchelors, Introduction to Fluid dynamics. It has discussions on almost all these questions (maybe not the H-P flow)

For the HP flow, we assume a single length scale and obtain a single Re! Which will probably give you the laminar solution. Turbulence has infinite length scales and is approached through growing disturbances and non-linear interactions between these disturbances. It is surely true that in the absence of any disturbances a parabolic profile is surely a solution to the NS equations even for arbitrarily large Reynolds numbers.

regards, chidu...

Re: Quesions Simple
 

H-P flow is only valid for laminar flow beacuse of the assumptions you have made about variation in shear stress in the y-direction. The only reason you can perform the integration necessary to obtain a solution is because you substitute d(tau)/dy with tau = miu*dv/dy. This substitution is only valid for laminar flow. In turbulent flow, extra terms are generated based on the variation of velocity rendering the integral unsolvable.

Thanks
 

Thank you

Re: Quesions Simple
 

When Linearity assumtions wrt to deformations are not valid, then the fluid is called Non-Newtonian and we need to have a different set of equations. Needless to say, they are even more sticky than the familier N-S equations. Modelling flow of Blood in arteries for example falls in this domain. There are researchers our there who work in this area, unfortunately I don't have any references at present. I will pass on any info I get in future