How does the pressure drop as a fluid flows through a pipe

In summary, assuming laminar viscous flow in an incompressible fluid, a pressure difference between the two ends of a pipe causes a net force to act on the fluid, resulting in it flowing from left to right. As the fluid travels along the pipe, it experiences a net force of 0 due to opposing forces from friction. The pressure gradually drops along the pipe due to viscous frictional forces and momentum transport in the transverse direction. This can be explained by a viscous shear stress that varies radially and a velocity profile that transitions from uniform to parabolic. The main pressure gradient is along the axis of the pipe, and the force acting on the fluid decreases as it flows from the higher pressure side to the lower pressure side
  • #71
seratia said:
Not about momentum. But about the description of the two plates. Here is what you said:

"To get an idea of viscous friction, think extreme cases like very viscous fluids like molasses, pancake syrup, and corn syrup. Imagine that you have the fluid contained between two horizontal parallel plates, and you are trying to slide the top plate to the right at constant speed. You need to exert a force on the upper plate to the right and a force on the lower plate to the left to hold it in place. OK so far?"

This is how I interpreted it:
View attachment 235821

It seems you are wanting to oppose the fluid moving with the plates - so "holding it in place" as you said ("it" being the fluid) while you move the plates, the upper plate to the right and the lower plate to the left.
No. The lower plate is not moving.
 
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  • #72
seratia said:
is to imply that the force is acting at the center of the fluid [edit, BvU:] only
No, it is not implied. Wherer do you get that idea ?
 
  • #73
seratia said:
it applies to this problem, the force pushing the fluid against friction (pushing the fluid from left to right) is getting reduced.

Why do you think the force is getting reduced? Across a small fluid element, the net forforce due to pressure is bases on the pressure difference from one side to the other, not simply the pressure on one side. This, taken to it's infinitesimal limit, implies that force is proportional to thrthe press gradient, not thethe press itself. So, a constant force requires qnconstsnt pressure gradient, not a constant pressure.
 
  • #74
seratia said:
To say that momentum is transported sideways is to imply that the force is acting at the center of the fluid, and the radial fluid is carried along by shear stress (thus momentum). When I asked before if the force is acting on the middle, I was told no, it acts against the cross sectional area all at once.

Is this what you mean:

View attachment 235817
This is close to what I'm saying, except that there should be an arrow on the left for each of the shells.
 

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