Physics of Blood Pressure and Blood Energy

[Superlieutenant1]

TL;DR

How are energy, velocity and gravity connected in real fluids like blood with changing vessel diameters and total cross sectional areas.

Hello I am a physiology student who is curious about the physics underyling blood flow and pressure. I have taken physics classes however at the elementary level the focus is on ideal fluids in systems with no friction. I would appreciate any answers or if you could point me in the right direction.

Upon trying to search for a physics based explanation, one point I saw was that in blood we can consider three energies.
The energy associated with the fluid hitting the walls of the vessel (Pressure/ Ep), the kinetic energy of fluid moving linearly (Ek) and the potential energy associated with gravity (Eg).

The left ventricle imparts most of the pressure and kinetic energy to blood and the walls of the vessels remove energy through friction.

1. Is pressure a property only associated with the outer layers of fluid which contact with the walls of the vessel? Likewise is linear kinetic energy associated only with the inner layers?

2. In a horizontal blood vessel why is it only the pressure that decreases and not the velocity? The continuity equation is for frictionless systems, so I would expect both velocity and wall pressure to decrease as the fluid encounters friction. Is it only the outer layer of fluids that are affected by friction and hence only the pressure decreases.

3. In a vertical blood vessel, gravity gives energy. Why is gravitational potenital energy converted into pressure but not into velocity?

4. If a large vessel breaks into smaller vessels, that have the same TOTAL cross sectional area, is there an increase in resistance and large drop in pressure? How would this change if the total cross sectional area of the branching fluids is less than the single vessle? What about if larger?

I greatly appreciate any help!

 

[Godot_]

Many of your problems become irrelevant, as the circulatory system is ... "circular".

Communicating vessels, hydrostatic principles void all those gravity effects. (my nomenclature might seem a wee odd - not an English native speaker, and this topic is a wee off my home turf, I learned that in my native German)

Also, the flow is absolutely not frictionless. The Hagen-Poiseulle-equation is the law of the land in circulation. Which also will answer your cross section question...

I suggest you go to the library, book store or look online for a medical physiology textbook. Reading the circulatory system chapter should answer your questions more thoroughly than we can do in the space here.

 

[pinball1970]

Summary: How are energy, velocity and gravity connected in real fluids like blood with changing vessel diameters and total cross sectional areas.

Hello I am a physiology student who is curious about the physics underyling blood flow and pressure. I have taken physics classes however at the elementary level the focus is on ideal fluids in systems with no friction. I would appreciate any answers or if you could point me in the right direction.

Upon trying to search for a physics based explanation, one point I saw was that in blood we can consider three energies.
The energy associated with the fluid hitting the walls of the vessel (Pressure/ Ep), the kinetic energy of fluid moving linearly (Ek) and the potential energy associated with gravity (Eg).

The left ventricle imparts most of the pressure and kinetic energy to blood and the walls of the vessels remove energy through friction.

1. Is pressure a property only associated with the outer layers of fluid which contact with the walls of the vessel? Likewise is linear kinetic energy associated only with the inner layers?

2. In a horizontal blood vessel why is it only the pressure that decreases and not the velocity? The continuity equation is for frictionless systems, so I would expect both velocity and wall pressure to decrease as the fluid encounters friction. Is it only the outer layer of fluids that are affected by friction and hence only the pressure decreases.

3. In a vertical blood vessel, gravity gives energy. Why is gravitational potenital energy converted into pressure but not into velocity?

4. If a large vessel breaks into smaller vessels, that have the same TOTAL cross sectional area, is there an increase in resistance and large drop in pressure? How would this change if the total cross sectional area of the branching fluids is less than the single vessle? What about if larger?

I greatly appreciate any help!

As Godot suggests this is a complex system, a dynamical system. I wrote a much longer answer than this initially but I do not want to muddy your waters. Are you UG? First year? I have a decent book ref but I am traveling right now. @BillTre @jim mcnamara I would learn all the systems anatomy and pathology first before reducing to physics but that is me. I do not want to mislead him.

 

[256bits]

Summary: How are energy, velocity and gravity connected in real fluids like blood with changing vessel diameters and total cross sectional areas.

Summary: How are energy, velocity and gravity connected in real fluids like blood with changing vessel diameters and total cross sectional areas.

In a vertical blood vessel, gravity gives energy.

The continuity equation is for frictionless systems,

Continuity is for all systems - what goes in must come out, otherwise there is not conservation of mass.
For an incompressible flow, one would also have volumetric continuity - volume in == volume out.
One can treat blood flow as incompressible.

Summary: How are energy, velocity and gravity connected in real fluids like blood with changing vessel diameters and total cross sectional areas.

3. In a vertical blood vessel, gravity gives energy. Why is gravitational potenital energy converted into pressure but not into velocity?

Again, continuity for a constrained system, - the circulatory system is confined within the walls of the blood vessels

 

[Lnewqban]

Welcome @Superlieutenant1 !

You could see certain similitude with hydronic systems for highriser buildings.
Please, see:
https://en.m.wikipedia.org/wiki/Hydronics

https://en.m.wikipedia.org/wiki/Hydronic_balancing

https://en.m.wikipedia.org/wiki/Diaphragm_pump

In your case, the pump is one that cyclically varies its internal volume, transferring mechanical energy into the blood: flow rate, pressure, height.

The pulsing unidirectional flow is achieved with internal check (non-return) valves, and the ones located inside veins and arteries along the closed system.

For any distribution pipeline or duct, keeping flow velocity as constant as possible through the mains and branches saves energy.
That is so because any unitary mass doesn’t need to accelerated back and forth, being the reason for the relation between cross-section and volumetric flow at each point of the system.

As it happens in modern hydronic systems with variable velocity pumps, when more flow is demanded by muscle exercise or anxiety, the pumping rate, heart rate or volume rate is increased.
The pump works faster, pushing and sucking a higher volume per unit of time, which requires more energy (oxygen and sugar) or blood flowing into the heart muscle.

Because the veins and arteries are elastic, more volume can be forced to go into the lowest or highest portions of your body when subject to g-forces in an airplane; therefore, less volume flows to the opposite end, causing problems in extreme cases.

Please, see:
https://en.m.wikipedia.org/wiki/G-LOC

 

[hutchphd]

and the ones located inside veins and arteries along the closed system.

I was taught that the check valves were only in the veins. Just a detail.

 

[BillTre]

I agree with @Godot_, you should get a physiology book at a graduate or med school level.
Many of these issues are dealt with there.

 

[pinball1970]

TL;DR Summary: How are energy, velocity and gravity connected in real fluids like blood with changing vessel diameters and total cross sectional areas.

Hello I am a physiology student who is curious about the physics underyling blood flow and pressure. I have taken physics classes however at the elementary level the focus is on ideal fluids in systems with no friction. I would appreciate any answers or if you could point me in the right direction.

Upon trying to search for a physics based explanation, one point I saw was that in blood we can consider three energies.
The energy associated with the fluid hitting the walls of the vessel (Pressure/ Ep), the kinetic energy of fluid moving linearly (Ek) and the potential energy associated with gravity (Eg).

The left ventricle imparts most of the pressure and kinetic energy to blood and the walls of the vessels remove energy through friction.

1. Is pressure a property only associated with the outer layers of fluid which contact with the walls of the vessel? Likewise is linear kinetic energy associated only with the inner layers?

2. In a horizontal blood vessel why is it only the pressure that decreases and not the velocity? The continuity equation is for frictionless systems, so I would expect both velocity and wall pressure to decrease as the fluid encounters friction. Is it only the outer layer of fluids that are affected by friction and hence only the pressure decreases.

3. In a vertical blood vessel, gravity gives energy. Why is gravitational potenital energy converted into pressure but not into velocity?

4. If a large vessel breaks into smaller vessels, that have the same TOTAL cross sectional area, is there an increase in resistance and large drop in pressure? How would this change if the total cross sectional area of the branching fluids is less than the single vessle? What about if larger?

I greatly appreciate any help!

Did you get sorted? "An introduction to cardiovascular physiology" J.R. Levick is a good one. I picked up 4th Edition for a £1.
Second hand book shops if the library copies are on loan or you are on a budget.
Chapter 8 covers a lot of your points.

 

[hutchphd]

Good Questions. Here are (not complete) answers. Remember that blood is ~incompressible and so influx=efflux for any given volume you look at
1 Pressure is everywhere, but is most interesting at the interface. In any pipe the flow is preferentially at the center...just like in a river ...because the walls are stationary.
2 incompressible in=out
3 incompressible (like a stack of bricks). But the pressure can induce velocity if given the chance
4 in practice this is complicated and depends upon turbulence in the flow and other stuff. I'm only a philosophical Doctor (and I don't know!)

 

[Godot_]

[...] Remember that blood is ~incompressible and so influx=efflux for any given volume you look at [...]

But the blood vessels are elastic... ...and do change their diameter passively as well as actively (that's what the lamina muscularis of the vessel wall does...) for regulation purposes.

Hence I repeat as recommended above: Grab a textbook...

 

[hutchphd]

OOPs. I was answering your answer. Got confused!