So neat explanation I am amazed to see your lectures Sir...... Everything in fluid mechanics is now so relatable to me.... I am thermal engineering PhD scholar at IITD.... I have watched your 15 lectures in a single day... It's like tv series.... Fluid was going over my head during my course work but now it seems so easy and interesting.... I understand your quote from 1st lecture now that No subject is difficult, it is the teacher who made it easy or difficult......
Here we students should be very careful about shear stress (tau). Like, when we are trying to mention shear stress in free body diagram of fluid element in z direction (channel/pipe length direction) with outer surface at r= r, not R then it is shear force on the fluid element surface exerted by adjacent/outer fluid layer. And when we are trying to define Shear stress at wall then it is the shear stress at wall (r=R) surface exerted by adjacent fluid layer. At r=R, the magnitude of shear stress/force on fluid by wall surface or on wall surface by adjacent fluid is same but opposite in direction (by Newton's 3rd law). By taking care of the respective shear stresses related to fluid and wall it will be easier to avoid confusion.
When the acceleration of fluid is zero, forces are balanced. Acceleration can be zero if velocity gradient is zero. Velocity gradient is zero if velocity is constant. Constant can either be zero or a non zero numeric value
Your confusion is very much valid. The net zero force can have different effects in different situations. When fluid/particle is at rest then it will remain in rest and there won't be any flow/motion at all because of net zero force and hence zero acceleration. This is the case when the fluid is simply lying stagnant/in rest inside the channel/pipe with no motion at all (a trivial case, situation of no interest for us). But if there is some flow/motion taking place (with changing velocity because of whatsoever cause of motion) and then when zero net force condition is achieved then the flow velocity will stop changing which is the case here. In a single statement a fully developed flow is the case of net zero force with constant nonzero velocity. To understand how this constant nonzero velocity flow is achieved you may refer the points below. Actually here we are talking about the situation (and a specific region along pipe/channel length) after the time when flow has reached steady state and become fully developed. Let's talk about situation which could have been associated with the flow before the above conditions were reached. Initially inside the entry region (entry region is the length along the channel/pipe after which steady fully developed conditions are reached) there is net force on fluid element which might be giving some acceleration and hence some velocity. Inside the entry region flow situation remain like this (not fully developed flow). But after the entry region due to growth of boundary layer fully developed conditions are achieved and net force and hence acceleration of fluid element becomes zero and the velocities reach at certain value and stops changing. Now this is the condition we study in the steady fully developed flow (which occurs after the entry region). There could still be net force in the entry region while we are analysing the fully developed flow in the region after entry length.
So neat explanation I am amazed to see your lectures Sir...... Everything in fluid mechanics is now so relatable to me.... I am thermal engineering PhD scholar at IITD.... I have watched your 15 lectures in a single day... It's like tv series.... Fluid was going over my head during my course work but now it seems so easy and interesting.... I understand your quote from 1st lecture now that No subject is difficult, it is the teacher who made it easy or difficult......
What about the normal components of the stress tensor? I.e. The normal tau's in the balance?
thank you so much for share your knowledge... thanks thanks!!!!!!!
8:35 it's not clear to me how y is opposite to r for which you took minus sign ?
Here we students should be very careful about shear stress (tau). Like, when we are trying to mention shear stress in free body diagram of fluid element in z direction (channel/pipe length direction) with outer surface at r= r, not R then it is shear force on the fluid element surface exerted by adjacent/outer fluid layer. And when we are trying to define Shear stress at wall then it is the shear stress at wall (r=R) surface exerted by adjacent fluid layer.
At r=R, the magnitude of shear stress/force on fluid by wall surface or on wall surface by adjacent fluid is same but opposite in direction (by Newton's 3rd law).
By taking care of the respective shear stresses related to fluid and wall it will be easier to avoid confusion.
Why all forces are balance d???? Fluid is flowing na??
because fluid flows at constant velocity in fully developed region.
When the acceleration of fluid is zero, forces are balanced. Acceleration can be zero if velocity gradient is zero. Velocity gradient is zero if velocity is constant. Constant can either be zero or a non zero numeric value
Your confusion is very much valid.
The net zero force can have different effects in different situations.
When fluid/particle is at rest then it will remain in rest and there won't be any flow/motion at all because of net zero force and hence zero acceleration. This is the case when the fluid is simply lying stagnant/in rest inside the channel/pipe with no motion at all (a trivial case, situation of no interest for us).
But if there is some flow/motion taking place (with changing velocity because of whatsoever cause of motion) and then when zero net force condition is achieved then the flow velocity will stop changing which is the case here.
In a single statement a fully developed flow is the case of net zero force with constant nonzero velocity.
To understand how this constant nonzero velocity flow is achieved you may refer the points below.
Actually here we are talking about the situation (and a specific region along pipe/channel length) after the time when flow has reached steady state and become fully developed.
Let's talk about situation which could have been associated with the flow before the above conditions were reached.
Initially inside the entry region (entry region is the length along the channel/pipe after which steady fully developed conditions are reached) there is net force on fluid element which might be giving some acceleration and hence some velocity. Inside the entry region flow situation remain like this (not fully developed flow). But after the entry region due to growth of boundary layer fully developed conditions are achieved and net force and hence acceleration of fluid element becomes zero and the velocities reach at certain value and stops changing. Now this is the condition we study in the steady fully developed flow (which occurs after the entry region). There could still be net force in the entry region while we are analysing the fully developed flow in the region after entry length.