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Basic hydraulic pump work-energy relationship

  1. Feb 9, 2016 #1
    I have a very simple question that's been driving me nuts. It's biology context, but probably all the physics equates to normal positive displacement pumps.

    The pressure in and volume of the left ventricle of the heart can be measured experimentally. (For example, https://en.wikipedia.org/wiki/Pressure-volume_loop_analysis_in_cardiology). During a typical contraction, blood stored in the atrium first fills the ventricle while the muscular wall is relaxed. When the ventricle is full enough, the ventricle wall begins to contract. The rising pressure in the ventricle pushes the mitral valve that leads to the atrium closed, meaning there's no backflow out from then on. When the pressure gets high enough, it pushes the aortic valve open, and the ventricle ejects the blood into the aorta.

    The phase of contraction after the mitral valve closes but before the aortic valve opens is called isovolumetric contraction. When I first heard this, I assumed that "isovolumetric" has to be a simplification like "infinite conducting wire". I can imagine, from a biological perspective, that the ventricle wall could get stiffer without the ventricle changing its volume. But I have no idea how this increasing stiffness could be translated into rising pressure in the blood inside the ventricle. If the wall does not move, how can it do work on the blood to raise the pressure? How does the blood know how stiff the ventricle wall is if nothing is moving in the system? My guess was, the ventricle is actually shrinking a tiny amount (and blood is not actually perfectly incompressible), which allows for energy transfer to the blood to account for the pressure rise.

    My professor swears that I'm confused, and the contraction is truly isovolumetric - not just unmeasurably small. But I still couldn't follow him. Basically, what I'm stuck on is if you block up the outlet of a pump, how does the pressure go up inside?

  2. jcsd
  3. Feb 9, 2016 #2

    jack action

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    If nothing goes in and nothing goes out (i.e. mass is constant), then if the density varies, the volume must also vary.

    For example, this is the pressure-temperature-density relationship for water (source: http://www.engineeringtoolbox.com/fluid-density-temperature-pressure-d_309.html):


    According to the equation found in the previous link, increasing the pressure of water by 12 000 Pa (90 mmHg) would result in a density increase (or volume decrease) of only 0.00048 %.

    I would argue the infinitesimal volume change.
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