5 replies to this topic

[dianzz]

guys im bit confused about viscosity equation..

in Warren.L McCabe book Unit Operation:
shear stress = viscosity*shear rate

shear stress=F/A . shear rate=du/dy
du/dy means = velocity gradien,
more close to the surface tube the the velocity gradient increase, so the shear stress.

but in J. Patrick Abulencia book, FLUID FLOW FOR THE
PRACTICING CHEMICAL ENGINEER

i found this equation is a bit different with an addition for negative value in viscosity, without further explanation ..

shear stress = - viscosity*shear rate

can someone explain me. where this negative came from??

thank you

Edited by dianzz, 03 June 2012 - 09:02 AM.

[smrtchemengg]

Dear dianzz

The answer to the above question can be understood if you read the section more than once. It is purely common sense. It would be good if you get it yourself as it helps you in understanding the concept. if the problem/doubt remains i would give you a helping hand.

smrtchemengg

[Shivshankar]

Dianzz,

The negative sign shows that the viscous force is directed in a direction opposite to the direction of the motion of the liquid.

Means viscosity will be obstacle to velocity of liquid, hence reducing it.


Regards
Shivshankar

[dianzz]

well thanx for the replay. but i find the explanation
"negative sign was introduced since momentum is transferred in the
negative z-direction due to a positive velocity gradient"

i dont fully grasp this concept. but its different from what @Shivshankar mention right?

[latexman]

It is clearer to me when I think of it as follows using the classical model of a Newtonian fluid between two parallel plates, one plate stationary and the other moving in the x direction, v_x. In this model at steady-state, momentum is transferred from the moving plate to the adjacent layer of fluid. That layer of fluid transfers momentum to the next adjacent layer of fluid. And on, and on, and on until the stationary plate is contacted. Momentum is transferred from the moving plate in the y direction, perpendicular to v_x. Shear stress can be thought of as the viscous momentum flux. This viscous momentum flux is in the direction of the negative velocity gradient, i.e. momentum goes in the direction of decreasing velocity.

Since there is no such thing as a negative viscosity, a negative sign is required to show the force exerted on the moving plate is in the same direction as v_x.

I refer you to Bird, Stewart, and Lightfoot's "Transport Phenomena" 1st Ed, 1960, pages 3-5.

[dianzz]

It is clearer to me when I think of it as follows using the classical model of a Newtonian fluid between two parallel plates, one plate stationary and the other moving in the x direction, v_x. In this model at steady-state, momentum is transferred from the moving plate to the adjacent layer of fluid. That layer of fluid transfers momentum to the next adjacent layer of fluid. And on, and on, and on until the stationary plate is contacted. Momentum is transferred from the moving plate in the y direction, perpendicular to v_x. Shear stress can be thought of as the viscous momentum flux. This viscous momentum flux is in the direction of the negative velocity gradient, i.e. momentum goes in the direction of decreasing velocity.

Since there is no such thing as a negative viscosity, a negative sign is required to show the force exerted on the moving plate is in the same direction as v_x.

I refer you to Bird, Stewart, and Lightfoot's "Transport Phenomena" 1st Ed, 1960, pages 3-5.

yap. this clear explanation..
understood . thanks