so we're going to continue with the circulatory system in this lecture but we're going to step outside of the heart and consider what happens to blood as it flows through the whole body and so here we have a schematic of the circulatory system and just think about the speed of blood flow for a second in the large vessels you want the blood to flow quickly because we know that all the cells of the body are metabolically active they are dependent on nutrients and dissolve gases oxygen in order to maintain that high metabolism so speed matters if the blood flows too slowly then there'll be insufficient delivery of what's necessary for metabolism on the other hand when the blood arrives at the cells that need those nutrients and gases then you want the blood to flow really slowly to allow time for chemical diffusion to work so we have different needs for the speed of blood flow in different regions of the body and so the question for this lecture is what determines that speed of blood flow in the different regions of the body here we have a highly schematized version of the circulatory system just to remind us of the major parts of this system so the blood of course flows from the the lungs fully oxygenated then they enter into the left heart the left atrium left ventricle the blood emerges from there passes into the aorta and passes through the major arteries or the systemic arteries eventually they branch off into small branches so let's see here we've got some major arteries in red through the arms here we've got a major artery to the kidneys down the body then eventually you have these smaller branches and finally they branch into the capillaries after exchange has occurred the blood is gathered up into larger vessels in the veins it then moves into the right heart and then finally onto the lungs where eventually we have a branching network again that ends with the capillaries okay so let's follow a parcel of blood as it passes through the circulatory system in these different regions so we're going to put those regions in order starting from the left heart and ending in the capillaries for the lungs and we've got that parcel of blood moving through like that oxygenated oxygenating the cells and then deoxygenated it back to the lungs now speed changes and if you were to measure the flow speed in these different regions then your measurements would look like this okay so here we have those different positions and our graph of flow speed in the different regions so as you might expect the flow speed is quite high in the left heart and the major arteries it then decreases through the capillaries increases in the veins the right heart and then finally it will decrease again in the capillaries for the lungs where exchange occurs so the fast flow this is exactly what you would hope for if you've got fast flow in those large vessels to quickly transport the blood and all that it carries and then there are there's slow flow at the exchange surfaces both uh the systemic capillaries that's the cells of the body and in the lung capillaries where the blood picks up oxygen and drops off co2 so our question relates to what governs this pattern okay now that we see the pattern that doesn't really explain how or or what it is that determines this particular pattern so in order to understand what's governing this pattern let's consider a simple case so we've got a blood vessel that's just a cylinder that's full of some fluid and we're gonna push a particular volume of fluid into this system at one end okay so that's our v for volume v n and if this is full of blood then as we push that volume in one end then we would expect a comparable volume exactly equal in fact volume to come out the other end so the volume in equals the volume out for a closed system that is we're not adding any liquid as it passes through this vessel we're not subtracting anything and if those two volumes are equal and we're pushing the input volume in over some change in time then it follows that the volume per unit time on the input end is equal to that on the output end and so we get this relationship here which is essentially just restating conservation of mass it's known as the law of continuity and you can extend this or generalize this beyond just the input and output ends but the law of continuity suggests that the volume flow rate or often just referred to as the flow rate in physiology textbooks flow rate refers to volume per unit time the flow rate is constant everywhere so if you were to monitor the flow rate in the middle of this vessel it would be the same be the same here everywhere it should be the same if it's a closed system now we can restate the law of continuity in a way that takes into account the geometry of the vessel in particular the cross-sectional area so we've got the area on the input end there and then the dimension the linear dimension along the length of the vessel so we're going to call that x and so as we push this volume into the system it moves through a change in x a delta x so the input volume we can restate as the cross sectional area times that change in x and if we plug that relationship into our equation for the law of continuity we end up with the product of the input cross sectional area times delta x over delta t we get the same for the output end of things of course delta x over delta t is the flow speed and so we can restate the law of continuity as the product of cross-sectional area and flow speed both for the input and output ends again this product should hold for anywhere in a closed system and it follows that if the product of speed and cross-sectional area has to stay the same everywhere then if you have a change in one of those variables you must have a change in the other so you could imagine if the cross-sectional area changed for example if you had an increase in cross-sectional area then you must have a proportionate decrease in speed so that their product remains constant and so we can see that right here we're going to input our volume but in this case our pipe system expands in its diameter we have a bottleneck here so we have an output area that's bigger than the input area and if this volume that emerges is supposed to be equal to that volume if the area is bigger then the x dimension has to be less and if we push the this in for some delta t then that means the speed at which the front edge of this volume moves at is going to be slower on the output end than on the input end now if we were to take this large cross-sectional area and partition it just imagine i don't know packing it with soda straws or something like that it's still a bigger area and you're still going to have the law of continuity apply so whether this is just one output pipe or if you were to branch it into a whole bunch of little outputs what would matter is the total cross section and if it's greater on the output end than on the input end then you would expect the flow to be slower so if we return to our relationship for flow speed on this graph it's listed as flow velocity we just forget about the velocity we just call this flow speed if the flow speed changes in this pattern where we have a decrease in the capillaries if i were to ask you say a test question before you're viewing this lecture you know what affects the flow speed you might think something like well pressures or maybe resistance or something like that but here we see the law of continuity is all we need to understand this pattern if we have a decrease in speed that predicts an increase in the cross-sectional and if you have an increase in speed there should be a decrease in cross-sectional area like right here you see that increase and in fact if you measure the cross-sectional area of all of these vessels you get a pattern that you would predict from the law of continuity it looks like this now what this shows is essentially a mirror image of cross-sectional area and in every single position here if you were to take the product of these two quantities you would get the same value you'd get a flat line with respect to position so there's high speed in the left heart in the major arteries and as that speed decreases we have a correlated increase in cross-sectional area and there is more than correlation there's causation here it's because of this increase in cross-sectional area that you get the decrease in speed now you might be puzzled by this because you might say well capillaries are awfully small certainly smaller than the aorta how is it that the cross-sectional area is bigger for the capillaries and the answer to that question is it's the total cross-sectional area that matters okay so you would take the cross-sectional area of the average capillary and multiply it by the total number of capillaries and there are so many of them that the total area of the capillaries is much greater than the aorta and it's for that reason that you have the drop in speed now the veins also have a lower cross-sectional area than the total in the capillaries and as a consequence you get a speeding up of of the flow that continues into the right heart where again you've got a decrease in cross-sectional area and increase in speed and then the capillaries you have a repeat again in the lungs where there's an increase in the total cross-sectional area a decrease in the flow speed exactly where you want it for exchange and in fact if you compare even the two sides of the heart you can understand differences in velocity from just cross-sectional area so note here we've got a slower speed of flow in the right heart than in the left heart you might think that has something to do with musculature pressures or whatever no it can be explained purely by cross-sectional area where you have a higher cross-sectional area in the right heart despite its thinner walls it's larger in cross section than you have in the left heart you can think of the law of continuity as being the thumb over the garden hose effect as you put your thumb over the opening to a garden hose you are reducing the cross-sectional area and so that the product of cross-sectional area and speed remains the same the speed will go up as the cross-sectional area goes down so the question was what determines the flow speed in different regions of the body the answer comes from a consideration of the law of continuity regional differences in speed are generated by differences in the total cross-sectional area