About this video
The video works through total resistance in a blood-vessel network. Segments in series add up, so the total is larger than any one segment. Branches in parallel combine into a total smaller than any single branch. The worked example combines a parallel section of 2 with segments of 8 and 3 to reach a total of 13.
You'll be able to
- calculate total resistance for vessels in series
- calculate total resistance for vessels in parallel
- explain why parallel branches lower total resistance
Key words
- Resistance
- How strongly a vessel opposes blood flow, set largely by its length and radius.
- Series
- Segments that blood passes through one after another; their resistances add.
- Parallel
- Branches blood can take alternatively; they combine using reciprocals.
- Total resistance
- The overall opposition to flow for the whole network.
- Reciprocal
- One divided by a value; parallel resistances are added as reciprocals, then inverted.
Transcript
Let's say you've got a blood vessel here, and it's a longish blood vessel, and we'll give it a resistance of 8, and it has three branches. Say two big ones and kind of a tiny one in the middle, and this goes straight across. And this has a resistance of 10, and these biggish ones, they have resistance of, let's say, half that.
So they're about 5. And on this side they all come together again and enter a short vessel, and this has a resistance of 3. So my question to you is what is the total resistance of blood going in here and out here? So it's going to have to go through this 8 bit, and then it has three choices here, here, here, or here.
But eventually they all come together again into that 3 bit and then exit out the other side. So what is the total resistance? So what is RT for this? That's the question. And what I'm going to do is I'm going to divide into two parts. Part one, I'm going to figure out in part one what the resistance is for this part right in here.
So I can do that using an equation I introduced in the last video, which was you can basically take RT, which is total resistance for that yellow box, equals 1 over 1/5 plus 1/10 plus 1/5. And I can look at that and tell you the common denominator is going to be 10, right, for all three.
And here the numerator, I've got 2, 1, and 2. So putting it all together I've got 1 over-- what is that-- 5/10, and that equals 10/5, which equals 2. So that tells me that the resistance in this middle yellow box is 2. And that makes sense with our rule, because we said that when things are in parallel, the total resistance is going to be less than any component.
And, in fact, 2 is less than 5, 10, and 5, right? It's less than any of those numbers individually. So we've got now in part two, we have three things in series, right? We basically have something like this. We have 8 and we have 2 and we have 3. So we've got basically three things in a series, and so we simply add those up.
So I'm going to say RT now equals 8 plus 2 plus 3. And so RT equals 13. So if I want to know what is my total RT, my total resistance, I would say it is 13. So that's the answer to this problem, and what I want to get you thinking about is total resistance for the body, the human body, which has obviously more than just a few vessels like I have in this diagram.
We have literally thousands and thousands of vessels.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.