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I am trying to find simple ways to get rough answers to how much energy it would take for a unit volume of blood to move along a blood vessels. My main aim is to compare energies it would take for a unit volume of blood to move along different blood vessels.

I also have the length and diameters of the blood vessels too and know whether they are arteries or veins.

A very basic calculation would be that Energy required would be proportional to the length of the blood vessel where the energy would be purely lost to Frictional forces.

Are there any more accurate calculations of the Energy required to move a unit volume of blood through the blood vessel based on those parameters?

EDIT: The blood is not flowing up or down so gravity can be ignored.

EDIT2: The diameter of the vessel is fixed at a value d and a length L. The viscosity is constant throught the blood vessel at 0.00118 Pas and an initial flow speed of 650ml/minute and an initial pressure of 4000 Pa.

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  • $\begingroup$ Is the blood moving up or down the body? This matters because gravity makes one of the largest contributions to energy change in such a system. $\endgroup$
    – Jaywalker
    Commented Mar 9, 2016 at 11:46
  • $\begingroup$ @Jaywalker sorry its flat so it's not moving up or down. Thanks - I'll edit the OP. $\endgroup$
    – piccolo
    Commented Mar 9, 2016 at 11:51
  • $\begingroup$ See the Poiseuille equation $\endgroup$
    – lemon
    Commented Mar 9, 2016 at 11:52
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    $\begingroup$ When a blood vessel splits into two or more, the volume is the same, but the surface area increases, so you'd see an exponential increase in friction. Most of the blood pumping through your veins is passing through a very tiny blood vessel and not through the major veins and arteries since most of your blood system is composed of very small blood vessels. You'd need to find the exact statistics of that, because that's relevant to the amount of friction. $\endgroup$
    – Neil
    Commented Mar 9, 2016 at 12:06
  • $\begingroup$ @Neil I'm looking at the blood vessels (arteries and veins) on the chorionic plate of the human placenta which have a relatively lower blood pressure. I'm trying to get a decent estimate of the energy expended. $\endgroup$
    – piccolo
    Commented Mar 9, 2016 at 12:16

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You could approximate the cost with the viscous dissipation in a Poiseuille flow of a Newtonian liquid having the viscosity of blood in a tube of the given length and diameter. The relevant viscosity is an "effective" viscosity that can be measured in vitro by measuring the flow rate in a tube for a given pressure, the tube diameter should be similar to the vessel diameters you are interested in.

There will be several limitations:

  • if you have large blood vessels with high velocity, there will be turbulent flow and your calculation will fail.

  • It will also fail if you have very small blood vessels in which red blood cells deform a lot, although you may find "effective" viscosity measurements done in these conditions and use these.

  • Finally, the vessel walls are also deformable and part of the energy used in this deformation is lost.

To estimate the first two, you need numbers:

  • The Reynolds number will allow you to see whether turbulence is likely (see "Transition" in the wikipedia article). Use the viscosity of the plasma (close to the one of water).

  • The diameter of the vessel, to be compared to RBC size.

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  • $\begingroup$ Hi Joce. I've added an update on some parameters which I want to use to get a decent or rough estimate of the energy expended. $\endgroup$
    – piccolo
    Commented Mar 9, 2016 at 16:12
  • $\begingroup$ Hi--see my edit $\endgroup$
    – Joce
    Commented Mar 10, 2016 at 10:44

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