# Fluid Dynamics and Blood Pressure Question

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#### betterfuture

##### Full Member
7+ Year Member
When you suddenly stand up after lying down for a while, your body may not compensate quickly enough for the pressure changes and you might feel dizzy for a moment..

If the gauge pressure of the blood at your heart is 13.3 kPa and your body doesn’t compensate,
(b) What would it be at your feet, 1.30*10^2 cm below your heart?
Hint: The density of blood is 1060 kg/m3.

Use Pressure=(fluid density)(gravity)(height) to calculate the relative change in pressure depending on the height difference. Pressure should increase as you go down the body.

The equation seems straightforward but how do I take into account the height differences? What is the zero level? Head is above heart, and the feet are below the heart so seems like a negative height would be the case but that makes pressure negative and that can't be true.

Well the gauge pressure acts as a standard. So for the pressure close to your head you would do 13.3kpa-(1060)(9.8)(.5) since there is less fluid pressing down. For the pressure below the heart, you'd add it to the gauge pressure

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I know fluid pressure changes with height but I can never grasp the 'height'. Do they refer to height against a zero level? Like in the case for the heart. If a person was lying down, the pressure everywhere would be the same because the level is the same. Once you stand up, pressure changes because heart has to pump against the force of gravity to push blood towards the head. Can you clue me in on what the height is in the equation and how to use it? Thanks!

I know fluid pressure changes with height but I can never grasp the 'height'. Do they refer to height against a zero level? Like in the case for the heart. If a person was lying down, the pressure everywhere would be the same because the level is the same. Once you stand up, pressure changes because heart has to pump against the force of gravity to push blood towards the head. Can you clue me in on what the height is in the equation and how to use it? Thanks!

The height is not always the zero level as you suggest, in this case it is because they tell you the gauge pressure at the heart. The question stem provides you with gauge pressure which functions as the zero reference point. From physics, you should remember that the pressure a fluid exerts= pressure fluid (pgh) + atmospheric pressure. In this case, we don't have to worry about atmospheric pressure and you just have to know that the pressure increases with increasing height of water on top. In other words, if you have a barrel of water, the water will exert double the pressure at 20m beneath surface of water compared to 10m below.
Therefore, in A you are above the heart and there's less fluid so a smaller pressure will be exerted. In B you will be lower than the heart and will have more fluid pressing on top, so a higher pressure.

a) gauge pressure- pgh = gauge - (1060)(9.8)(.5)
b) gauge pressure + pgh = gauge + (1060)(9.8)(1.3)

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Awesome explanation. I just got confused at what the surface of the blood would be since the blood is not open to atmospheric pressure or anything. In your case, you explained it well. The lower you go down into a fluid, the greater the pressure exerted. The head would exert lower pressure than down below at the feet. Thanks! I am beginning to appreciate and like physics!

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