If you're seeing this message, it means we're having trouble loading external resources on our website.

Hvis du sidder bag et internet-filter, skal du sikre, at domænerne *. kastatic.org og *.kasandbox.org ikke er blokeret.

Hovedindhold
Aktuel tid:0:00Samlet varighed:6:58

Bernoullis ligning for det samlede energi

Video udskrift

let's say you're looking at this blood vessel the first thing you obviously notice is that it's full of after ominous plaque right that's what all this yellow and white stuff is this is at the Romanist plaque and your thought other than wow that's a lot of fatty meals someone's been having is how does blood move through this narrow little space right you can add a little channel that the blood is supposed to be moving through how does it get through there so you do a little experiment you take a few pressure readings you say okay let's figure out what the pressure is right here and it's about ninety and you say what is it right here and it's 70 in the middle of the channel and you say what is it on the other side and over here it's about 80 so you're looking here and you're saying okay now I need a 70 that makes sense that blood is moving from high to low pressure but then what's going on between 70 and 80 that seems kind of strange right because we usually think of pressure is going from our blood moving from high to low pressure and here blood is moving from 70 and then going to 80 now this seems a little counterintuitive because this is going against the pressure gradient so how is that possible or or have we made a mistake so to answer that question we turn to a Swiss mathematician this guy came up with a set of formulas that helps us kind of frame how we think about this issue and his name is Bernoulli so you might have heard of Bernoulli's equation so Bernoulli's equation basically looks like this he says total fluid energy equals a few things not just pressure but it's pressure plus let's say kinetic energy and I'll explain all the the symbols me too just a second and it's there we go so he said the big P is pressure energy okay well that part we understood we were already looking at pressure and thinking about why it is that it's going from low pressure too high pressure but he said you also have to look at movement energy this is movement energy and another word for that would be kinetic energy but here the little P right here is density the density of whatever fluid it is here we'd be talking about blood and V is the interesting one this is velocity how fast the blood is moving so now we have to actually consider how quick the blood is moving and then he also talked about a third term this is here a third term which is potential energy potential energy and here he's talking about the potential energy as it pertains to gravity so G is gravity the little P again is density then we've got gravity and we've got height how high something is off the ground so here he's saying if you have some blood in your head obviously that's going to be higher off the ground than blood in your toe and there's some potential energy that comes with being in your head versus being in your toe and so that's that's what that potential energy part is talking about now for our example I'm going to go ahead and erase that and you'll see why because really the height of all three I'm assuming is at the same level so there should be really no difference between the potential energy from a height stand point for the points that I have shown in my picture so really I'm left with just that so if I'm going to try to figure out the answer to my problem I think it would be helpful to use this equation and let's see how we can use it so to figure this out let's call this a and let's call this B this point now what Bernoulli wanted to say is that pressure and movement energy in this case combine to stay the same over time so a and B have the same total energy so total energy remains the same between the two points so total energy at a equals total energy at B and if we think about it that way then you actually can easily figure out what is going on I'll show you what I need so total energy at a is going to be the 70 pressure plus 1/2 the density of blood times the velocity at a squared that's got to equal 80 plus 1/2 density of blood the velocity of B squared so if this number right here is smaller and it is than 80 and that's where the whole problem started with right and we know that overall this has got to be the same as this well then the only explanation would be that this term right here has got to be bigger right and then there's no other way to explain this and Bernoulli was right that if you actually look and and check the velocity of blood how fast it's moving when it goes through little tiny channels like let's say you have a little skinny little gap between this point over here right here and this point right here when it's trying to get through a little gap it doesn't have much space to move through right and so when blood is moving through tiny spaces it has to speed up and that makes complete sense because we have a large amount of blood we need to move from here all the way over here and the only way to get all that blood through is that when we have less space to do it with to move it even quicker to make it go even faster and so as it's going through this skinny little channel the velocity goes way up so that's where this starts to really fit together right so this is going way up and in that makes sense because the density stays the same so the only difference is that the velocity at a goes way way up and that explains why you have less pressure at point a versus point B but overall total energy at point A and point B are the same