Velocity Profile Analysis for Force Balance Equation in Fluid Dynamics

[haruspex]

ok , back to the topic . by taking the example aforementioned as anology , which is box ? which is object ? which is carpet? r ? r+ del (r) ?

The box is the annulus between r and r+Δr. The carpet is the next smaller annulus (faster moving) and the object is the next larger (slower moving).

 

[hotjohn]

The box is the annulus between r and r+Δr. The carpet is the next smaller annulus (faster moving) and the object is the next larger (slower moving).

all the box , object and carpet are subjected to the same velocity , right ? this is not same as the situation in the water , which at different point , the partcile would have different velocity ?

 

[haruspex]

all the box , object and carpet are subjected to the same velocity , right ? this is not same as the situation in the water , which at different point , the partcile would have different velocity ?

As I framed it, the object slides on the box and the box slides on the carpet, so the three are at different velocities.

 

[Chestermiller]

can someone try to explain why the shear stress force at down and above in diagram 8-11 is opposite in direction ? why in diagram 8-12 , they are in the same direction ?

Drawing it this way really stems from the Cauchy Stress Relationship. This relationship has nothing to do with the type of material that is being deformed. Hot John, unfortunately, until you are taught in your courses the details of how to work with 2nd order tensors like the stress tensor, I'm afraid you're just going to have to accept the fact that you need to draw the specific stress components acting on opposite sides of a body with opposite directions. You had no trouble doing this with the pressure stresses on the ends of the body (which are just normal components of the stress tensor). Mathematically, the normal pressure force is done this way for the same basic reason that the shear stresses are drawn with opposite directions on the other faces of the fluid.