Paging all Physics experts: A good analogy for blood flow speed?

[Renmoo]

Dear all,
I am trying to come up with a good Physics analogy to describe the following Biology situation:

The speed of blood flow is influenced by the pressure on the source end as well as the radius of the vessel. The radius of the vessel is inversely proportional to the resistance.

Fact
1) As the pressure on the source end increases, the speed of blood flow increases as well.
2) As the resistance increases, the blood flow increases in speed (due to extra pressure prior to the constricted end) but the amount of flow decreases.

In terms of electricity, I would say pressure is liken to voltage (V). The speed of blood flow is current (I), while the amount of blood that flows is charge (Q).

Could you say that as the resistance increases (fact 2), the voltage increases proportionally (since V = IR), and therefore the blood flows faster? This does not seem possible to me since this means V, I, and R increase together.

On a second thought, perhaps since at the constricted region the amount of blood flow is less and the time it takes for that amount of blood to flow through the point is less, therefore the current is conserved?

Since Power = Voltage x Current, therefore what would be "power" within this context?

Cheers

[Terry Porritt]

You just can't. Fluid flow is fluid flow, and electron flow is electron flow.

There is just no point in trying to make analogies, because they can never be accurate, they lead to false conclusions, and the physics covering the two situations are different, so just stick with fluid dynamics theory to describe blood flow.

If blood had a 'Newtonian' viscosity then the flow rate is given by Poiseuille's equation:

http://en.wikipedia.org/wiki/Poiseuille's_law

But blood is non-Newtonian:
http://lhtc.epfl.ch/webdav/site/lhtc...0VISCOSITY.pdf

The other governing relation is flow Q=ρAv, ρ=density, A=area of flow, v=mean velocity across area of flow.

edit: something funny about the wiki link

[Renmoo]

-> http://en.wikipedia.org/wiki/Poiseuille's_law

At the end of the page...

[R2x1]

You . . .

But blood is non-Newtonian:

. . .

That is not what Sir Isaac's mum said.

[Terry Porritt]

-> http://en.wikipedia.org/wiki/Poiseuille's_law

At the end of the page...

Yes I know that is there, the concept of hydraulic resistance is useful, but analogies with electrical flow are limited.
Anyway, the average New Zealanders' knowledge of electricity is so poor, that trying to use it to explain hydraulics wont go far.............

Better to use hydraulics to give a simple understanding of electricity

[Terry Porritt]

Here's another link that could be useful:

http://www.physics.usyd.edu.au/teach.../viscosity.pdf

[SurferJoe46]

Dear all,
I am trying to come up with a good Physics analogy to describe the following Biology situation:

The speed of blood flow is influenced by the pressure on the source end as well as the radius of the vessel. The radius of the vessel is inversely proportional to the resistance.

Fact
1) As the pressure on the source end increases, the speed of blood flow increases as well.
2) As the resistance increases, the blood flow increases in speed (due to extra pressure prior to the constricted end) but the amount of flow decreases.

In terms of electricity, I would say pressure is liken to voltage (V). The speed of blood flow is current (I), while the amount of blood that flows is charge (Q).

Could you say that as the resistance increases (fact 2), the voltage increases proportionally (since V = IR), and therefore the blood flows faster? This does not seem possible to me since this means V, I, and R increase together.

On a second thought, perhaps since at the constricted region the amount of blood flow is less and the time it takes for that amount of blood to flow through the point is less, therefore the current is conserved?

Since Power = Voltage x Current, therefore what would be "power" within this context?

Cheers

I take exception with your "Fact #2": 2) As the resistance increases, the blood flow increases in speed (due to extra pressure prior to the constricted end) but the amount of flow decreases.

Any increase of velocity is NOT the effect of increased resistance.

Decrease the cross diameter area, and yes, there will be an increase in velocity IF all else remains the same. But you went and put an increase of resistance factor into the reason for increased flow.

Constriction at the discharge end of the vessel (like a hose nozzle) is not a reason for increased velocity in the vessel. It is a PERCEIVED increase in velocity that is really a decrease in the cross-sectional flow out of the decreased end of the vessel that does it.


In other words, the fluid volume and pressure create X amount of flow thru a vessel of a known diameter. If that diameter is decreased, then the flow will increase at that decreased cross sectional area if all other variables remain the same (pressure/volume/resistance).

That's how a garden hose nozzle works. We can discount the resistance in the nozzle in this instance as it's kinda hard to correlate to blood flow.

[Renmoo]

Constriction at the discharge end of the vessel (like a hose nozzle) is not a reason for increased velocity in the vessel. It is a PERCEIVED increase in velocity that is really a decrease in the cross-sectional flow out of the decreased end of the vessel that does it.

Continuing from the garden hose scenario:
Yes, I agree that the velocity increases at the constricted point, but how do we manage to perceive an increase in velocity of the water at the output end?

Terry: Yeap, I have taken a look at Poiseulle's law, but things got messier from that point onwards!

Cheers

[SurferJoe46]

Since the pressure remains a constant until the terminus or discharge of the flow, and the volume is still the same, the only available change is the velocity of discharge...we perceive it as increased pressure...but that's a misnomer.

It just flows or strikes harder than it would if the mean diameter of the discharge were to be the same as the delivery tube or vessel.....ergo the name "power nozzle".

Humans are easy to fool.

[Terry Porritt]

It's best just to stick to the simple maths, words and semantics just cause confusions

Forget talk about vessels, just consider a tube or blood capillary of constant radius 'a', length 'L', a constant Newtonian viscosity 'n', a fluid density 'p', having a static pressure (of which more later) differential P across the ends of the tube, and the flow through the tube is Q

Then from Poiseuille's formula

Q = P.pi.a^4/8nL

[electrical analogy is I = V/R, thus 8nL/pi.a^4 is an analogous flow resistance]

But as I said earlier the flow is also Q=pAv, where A = area of tube, v = mean velocity across the area of the tube. (The actual velocity distribution is parabolic across the tube diameter)

Combining the two equations gives for the mean flow velocity:

v = P.a²/8pnL

Thus you can see that the flow velocity is directly proportional to pressure difference across the ends of the tube times area of the tube.

So for constant applied pressure, if the tube is made larger (lower flow resistance) the flow speed will increase. If the pressure (voltage analogy) is increased the flow speed will increase.

This applies for smooth circular tubes sufficiently long that end effects can be ignored, for Newtonian fluids having a constant viscosity, and for flow velocities sufficiently low that the flow is laminar, ie Reynolds number is less than around 2000.

If electrical analogies are applied to derive an expression for an hydraulic resistance, then this would be ok for the conditions stated above, but once outside those conditions such as non-Newtonian fluids, turbulent flows, rough surfaces etc, the simple analogies fail and the equations become non-linear.


Talk of nozzles is misleading as different physics applies to flow through nozzles. But that as Kipling said is another story.

Now coming back to pressure, if there is fluid motion, then we have two pressures to consider, pressure due to static head measured at right angles to the flow, (static pressure), and pressure due to dynamic head measured pointing into the flow. The difference between the two is proportional to velocity squared. Hence this is how the pitot tube works to measure airspeed of a plane.

The physics of this is due to Bernoulli.
http://en.wikipedia.org/wiki/Bernoulli's_principle