- #1
Mangoes
- 96
- 1
Hi guys,
I've been working through some notes on Transport Phenomena by Bird and I've basically been just developing velocity and shear stress profiles for various (simple) models by a differential momentum balance and I'm trying to understand why a certain result happens.
When looking at (steady-state, laminar) flow in the z direction in an annular region between two coaxial pipes of radii kR and R respectively (k<1) you get the following results:
(1) a parabolic velocity profile occurs with maximum velocity occurring at a plane r = λR - this isn't surprising when looking at previous models
(2) a shear stress profile occurs with zero shear stress at the plane r = λR. However, the direction of the shear stress changes direction when crossing this plane.
I've gone through the derivation so I get that the math shows the results (1) and (2), but I'm just not understanding any intuition/reason why the shear stress would change directions at the plane of maximum velocity unlike, say, laminar flow in a pipe. I've noticed that this also happens when two immiscible fluids flow along each other in laminar flow... and again, not really able to figure out why this happens. Can anyone provide some insight here?
I've been working through some notes on Transport Phenomena by Bird and I've basically been just developing velocity and shear stress profiles for various (simple) models by a differential momentum balance and I'm trying to understand why a certain result happens.
When looking at (steady-state, laminar) flow in the z direction in an annular region between two coaxial pipes of radii kR and R respectively (k<1) you get the following results:
(1) a parabolic velocity profile occurs with maximum velocity occurring at a plane r = λR - this isn't surprising when looking at previous models
(2) a shear stress profile occurs with zero shear stress at the plane r = λR. However, the direction of the shear stress changes direction when crossing this plane.
I've gone through the derivation so I get that the math shows the results (1) and (2), but I'm just not understanding any intuition/reason why the shear stress would change directions at the plane of maximum velocity unlike, say, laminar flow in a pipe. I've noticed that this also happens when two immiscible fluids flow along each other in laminar flow... and again, not really able to figure out why this happens. Can anyone provide some insight here?