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How are ideal and nonideal fluids not opposite (radius change)?

hellocubed

Full Member
Jul 9, 2011
313
1
0
  1. Medical Student
Ek states that ideal fluids an nonideal fluids react the same way to a change in radius/velocity/pressure, but the viscosity in the nonideal fluid causes a slight deviation from expected behavior.
They greatly stress that they are NOT opposite.


Im wonder how exactly this is possible.
With radius held constant:

Bernoullis equation (ideal fluids) says an increase in fluid velocity results in decreased pressure.
In Poiseuille (nonideal fluida) shows that an increase in fluid velocity causes increase in pressure.

Radius change also results in opposite results.


So....... Im not exactly sure what EK is saying. It seems pretty obviously clear that they are opposite....
 
Last edited:

milski

1K member
5+ Year Member
Dec 30, 2009
2,641
527
141
Where the rain grows
  1. Pre-Medical
Poiseuille's law is volume flow rate, which is different than flow velocity

No.

It is flow velocity if you eliminate r^2 from both sides.
I specificaly noted that radius was held equal

Bernoulli's law gives you the pressure on the walls of the pipe as it goes up/down, changes radius, etc.

Poiseuille's law give you the pressure difference/loss after the fluid has flown over certain length of that pipe with certain properties.

The former tells you that if you increase the velocity of the same flow (by reducing the cross-section) the pressure will drop. It does not tell you what will happen if you change the flow through the pipe - the constant on the right side of the Bernoulli's equation is constant only for that specific flow, it will change if you change the flow rate.

The latter tells you how much pressure is lost for that velocity - if you start moving the fluid faster (which would normally imply higher pressure at the source end), you'll have a larger drop of pressure over the same pipe.
 
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