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# Bernoulli's equation of total energy

Learn how total energy of a fluid helps explain why fluids can move from low pressure to high pressure! Rishi is a pediatric infectious disease physician and works at Khan Academy. Created by Rishi Desai.

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• I remembered you did a video said that the smaller the diameter of the artery or tube is the higher the pressure . Why in this video is the opposite ?
• The smaller the diameter of the artery or tube is the higher the pressure CHANGE, or pressure DROP, that is, the pressure difference measured from before entering the stricture and after will be greater if a tube has small diameter.
• I don't get why the pressure is lower in and area where there is littler amount of space to get thought
• I think you are confusing with concept related to static fluid where pressure is related inversely to volume that it occupies. This is a moving fluid where bernouli sheds light on relation between pressure and area or velocity
• Why does 'little p' stand for density? Shouldn't it be a little D?
• Generally, the Greek letter rho is used to represent density. It looks a lot like a lower-case p.

http://en.wikipedia.org/wiki/Rho
• I have a similar question as others have in this forum, which I don't think has been adequately answered; in this video pressure is lower in the part of the tube (artery) with a lower diameter. This directly seems to contradict earlier videos about resistance in tubes (in the blood pressure series). In those videos, as diameter of the tube decreases, resistance increases, which causes pressure (specifically change in pressure) to increase, via the equation: deltaP = Q * R. In this equation, R = resistance, which is inversely related to the diameter of the tube. For example, vasoconstriction decreases an artery's diameter, which increases blood pressure. Please help clarify this for me and others.
• I did not see this video but can answer your question. If there was only a single continuous tube then yes as the radius decreases the pressure would increase (due to increased resistance). However, the key is that the big vessels split into many smaller tubes so there are parallel pathways that the blood can flow. When you add parallel pathways you decrease the overall resistance of the system. 1/R(total) = 1/R1 + 1/R2 + 1/R3 .... and so on. You can look up the formula if you have any questions. This is why in capillaries which are very small diameter vessels - the pressure is very low. Also this is why when you remove an organ you increase the resistance of the whole system which is sometimes a question on tests.

I'm an MD- learned it in med school.
• I know this question may sound silly, but I am having a hard time reconciling the Venturi Effect as described by Bernoulli's principle and Vasoconstriction/Vasodilation. So according to Bernoulli, in constant fluid flow, as fluid moves from a broader tube to a narrower tube, there is a pressure decrease and subsequent increase in fluid velocity in order to conserve the principle of continuity. So basically, we see a drop in pressure with a narrower tube. However, in blood fluid dynamics, we see an increase in blood pressure in vasoconstriction where the blood vessels become narrower, which appears to contradict Bernoulli's principle in the Venturi effect. I know I am probably applying something incorrectly but I was wondering if anyone could clarify this for me.
• Wow.. I absolutely can't understand this video.. hahahaha
As someone already asked below, smaller diameter of artery has higher pressure in the previous video. Someone answered that high pressure exists before entering the tube and after.. right? So.. this means that pressure in the middle of artery is low? And why pressure increases after if blood came out from small diameter to wider side? I really cannot undersatnd what is going on here. Somebody help me!!
• I have asked and pondered this many times and my only answer was compliance and elastance. I'm very sorry for the confusion. I'm with you. Even an engineer friend of mine was scratching his head for weeks trying to figure it out.
• What kind of experiments did Bernoulli do to discover this equation?