Question regarding ideal fluids vs. non-ideal fluids

  • Thread starter Makarov
  • Start date
  • Tags
    Fluids
In summary, in an ideal fluid, increasing the cross-sectional area of a pipe results in an increase in pressure exerted on the walls of the pipe. In a non-ideal fluid, such as blood, this relationship may not hold due to factors like the volume of the blood cells and their collisions. In order to decrease pressure drop and maintain flow rate, the length of the pipe must be decreased or the diameter must be increased. This explains why the body dilates blood vessels when blood pressure rises. Factors like gravity and friction also play a role in these relationships.
  • #1
Makarov
1
0
I understand that in an ideal fluid, when the cross-sectional area of the pipe is increased, the pressure that the fluid exerts on the walls of the pipe also increases. Also, when the cross-sectional area of the pipe is decreased, the pressure that the fluid exerts on the walls of the pipe decreases.

However, I am a little confused as the how a non-ideal fluid works. Is it the other way around? When the radius of the pipe is decreased, the total peripheral resistance increases, and the pressure on the walls of the pipe rises?

The reason I am asking this question is because I am studying about the blood vessels of the body. Whenever the blood pressure rises, the body causes the vessels to dialate in order to counteract the increase in pressure and keep it constant. This seems to be contrary to what I want to think (increase in radius = increase in pressure). Is my conclusion about non-ideal fluids correct?

Thanks
 
Physics news on Phys.org
  • #2
We assume that the particles within the ideal fluid do not interact and that their volume is negligible. It's not the same in reality, but there is not much deviation (of course, there are some limits). So, many non-ideal fluids act almost the same as the ideal model. So, your conclusion is not quite correct.

You have completely different example with the blood vessels. We cannot ignore the volume of the blood cells and their collisions, so it can't be considered as an ideal fluid. Therefore, some fluid mechanics laws cannot be applied here.

That's my assumption. I'm not sure if it's correct.
 
Last edited:
  • #3
I'm not sure what you mean. In Poiseuille flow, there's several parameters- the pressure drop along the pipe, the diameter of the pipe, viscosity of the fluid, etc. I would expect that keeping the volume flow constant, increasing the pipe diameter will decrease the pressure exerted against the wall because the fluid velocity goes down.

Blood is a shear-thinning fluid; the larger the shear rate, the less viscous the fluid. Also, blood pressure can change due to changes in blood volume in addition to vasoconstriction/vasodilation.
 
  • #4
Consider a flow through a pipe having a diameter D.
For a given mass flux, a bigger passage area means smaller velocity.
Let me call G the mass flux (dm/dt), and V the velocity.
So:

G = [tex]\rho[/tex] V S --> V = G / ([tex]\rho[/tex] S)

The pressure drop due to the friction against the pipe walls is given by:

[tex]\Delta[/tex]p = 1/2 f (L/D) (V^2)/g

Now, let me simplify both equations (because I understand that you're more interested in qualitative explanation) by saying that:

V [tex]\propto[/tex] (G / S)

[tex]\Delta[/tex]p [tex]\propto[/tex] (L/D) V^2

S [tex]\propto[/tex] D^2

Combine these and you obtain that ("[tex]\propto[/tex]" means "proportional to"):

[tex]\Delta[/tex]p [tex]\propto[/tex] L (G^2) / (D^5)

or, for a fixed G:

[tex]\Delta[/tex]p [tex]\propto[/tex] L/(D^5)

So, if you want to decrease the pressure drop and mantain the flow rate of the fluid, you have to either decrease the length of the pipe or to increase it's diameter. That's why our body behaves in a way you have described.

Somewhere in the middle of it there are coefficients and constants like gravity "g", friction factor "f" and some other stuff, but the qualitative explanation is just like that.
 

What is the difference between ideal fluids and non-ideal fluids?

Ideal fluids are theoretical fluids that have no viscosity, or resistance to flow, and no internal friction. Non-ideal fluids, on the other hand, have some level of viscosity and internal friction.

What are some examples of ideal fluids?

Some examples of ideal fluids include air, water (under certain conditions), and other gases that can be approximated as having no viscosity or internal friction.

How do ideal fluids behave differently from non-ideal fluids?

Ideal fluids follow the laws of fluid dynamics perfectly, meaning they have no resistance to flow and can be modeled as if they were flowing without any friction. Non-ideal fluids, on the other hand, have varying levels of resistance to flow and do not always follow the laws of fluid dynamics.

Why are ideal fluids used in many fluid dynamics calculations?

Ideal fluids are used in calculations because they simplify the equations and make it easier to understand the basic principles of fluid dynamics. They also provide a good baseline for comparison with real-world non-ideal fluids.

In what situations would non-ideal fluids be more appropriate to use?

Non-ideal fluids are more appropriate to use in situations where the level of viscosity and internal friction play a significant role in the behavior of the fluid. This could include high-pressure or high-temperature environments, or when studying specific types of fluids such as non-Newtonian fluids.

Similar threads

  • Biology and Medical
Replies
10
Views
2K
Replies
18
Views
937
  • Classical Physics
2
Replies
35
Views
2K
  • General Engineering
Replies
11
Views
2K
Replies
2
Views
1K
Replies
3
Views
3K
  • Classical Physics
2
Replies
48
Views
2K
  • Materials and Chemical Engineering
Replies
16
Views
2K
Replies
4
Views
2K
Replies
4
Views
2K
Back
Top