Bernoulli Principle - blood flow

[jsmith613]

I have been reading about Bernouli's principle and would like to clarify something

I have read that the total energy of blood in vessels (assuming a vertical position) is given by the sum of pressure energy, GPE and KE.

I have seen two different equations:
1) P + pgh + KE = constant
2) P - pgh + KE = constant

I am wondering why the sign associated with pgh changes as I cannot find this out. Thank you

[studiot]

I don't know where you read either of those equations but I would suggest looking for some better books that explain themselves properly.

 

Bernoulli's equation does not apply directly to blood vessels since there is significant resistance to flow (an energy dissipative process) and Bernoulli is a conservation equation.

 

In some instances a modification to Bernoulli is possible where an extra term is introduced to model this dissipative loss.

This may be the reason for the negative in your second equation.

 

A second process is also present in blood circulation. The pumping process.

Pumps, like resistance, are modelled in Bernoulli by introducing extra terms.

The circulation pressure component of Bernoulli is not constant, but varies during the pumping cycle.

So it depends what is meant by the 'pressure'.

A mean pressure,as a function of the systolic and diastolic pressures is defined.

 

https://en.wikipedia.org/wiki/Blood_pressure

[jsmith613]

I don't know where you read either of those equations but I would suggest looking for some better books that explain themselves properly.

 

Bernoulli's equation does not apply directly to blood vessels since there is significant resistance to flow (an energy dissipative process) and Bernoulli is a conservation equation.

 

In some instances a modification to Bernoulli is possible where an extra term is introduced to model this dissipative loss.

This may be the reason for the negative in your second equation.

 

A second process is also present in blood circulation. The pumping process.

Pumps, like resistance, are modelled in Bernoulli by introducing extra terms.

The circulation pressure component of Bernoulli is not constant, but varies during the pumping cycle.

So it depends what is meant by the 'pressure'.

A mean pressure,as a function of the systolic and diastolic pressures is defined.

 

https://en.wikipedia.org/wiki/Blood_pressure

Thanks

I read about my original question in my Physiology textbook (and my lecturer mentioned it).

She said that Bernoulli Principle was IDEAL but was not, in fact, reality because of resistance, as you said

[studiot]

The best way to look at it mechanically is the statement

 

Fluid tries to flow from high pressure to low pressure.

 

But pressure in Pascals is not a useful measure, since not all processes can be measured in Pascals.

 

Bernoulli offers a way to overcome this by using a term known as 'head' or pressure head.

 

All the processes, standing pressure of the fluid, the kinetic energy of the fluid, the resistance to flow of the pipework, the energy injected by pumps can be expressed in terms of pressure head (measured as a length or distance) and thus compared and accoutned for.

 

I do not think the gravitational variation is significant or even measurable (although it too can be expressed as a head) in human circulatory systems.

[imatfaal]

also a considerable amount (although I have no idea of whether the proportion is large or small) would be held as elastic potential energy manifest in the stretching of the large arteries. The blood flows because the heart in systole pushes some of it around AND because the large proximal arteries (most notably the aorta) are stretched and will revert to normal shape and size during diastole causing blood to continue to flow. You can think about this by looking at the increase in pulse pressure from the young and fit to the old and not so fit - this increase is due (in part) to lowering of aortic compliance and thus need for heart to work differently

 

The formula for linear springs is Elastic Potential Energy = 1/2 kx^2 where k is the spring constant and x is the displacement - I am sure there will be a 2d and 3d equivalent (I would think you would need the 2d) but I really do not ever recall seeing them

[studiot]

also a considerable amount (although I have no idea of whether the proportion is large or small) would be held as elastic potential energy manifest in the stretching of the large arteries. The blood flows because the heart in systole pushes some of it around AND because the large proximal arteries (most notably the aorta) are stretched and will revert to normal shape and size during diastole causing blood to continue to flow. You can think about this by looking at the increase in pulse pressure from the young and fit to the old and not so fit - this increase is due (in part) to lowering of aortic compliance and thus need for heart to work differently

 

The formula for linear springs is Elastic Potential Energy = 1/2 kx^2 where k is the spring constant and x is the displacement - I am sure there will be a 2d and 3d equivalent (I would think you would need the 2d) but I really do not ever recall seeing them

 

Interesting, I didn't know that the blood vessels changed diameter appreciably during the pumping cycle.

By comparison, canvas hozes do not stretch appreciably even under fire hose pressures.

 

What happens to the surrounding tissue when they expand or contract?

[John Cuthber]

I have been reading about Bernouli's principle and would like to clarify something

 

I have read that the total energy of blood in vessels (assuming a vertical position) is given by the sum of pressure energy, GPE and KE.

 

I have seen two different equations:

1) P + pgh + KE = constant

2) P - pgh + KE = constant

 

I am wondering why the sign associated with pgh changes as I cannot find this out. Thank you

Both equations are plainly wrong anyway; check the units..

However, since height is measured from an arbitrary starting point, you can choose whichever sign you like for the height.

Do you measure down from the head, or up from the feet.

You can't use Bernoulli's equations reliably for calculating blood flow because the muscles in the blood vessels do work on the system.