### Adding up resistanceseries andparallel

We had talked a little bitabout the resistance equation that we got from Poiseuille. And the equation lookeda little bit like this. Actually, let mejust replace this. We had 8 times eta, whichwas the viscosity of blood times the lengthof a vessel divided by pi times the radius of thatvessel to the fourth power.

And all this put together givesus the resistancea vessel. So thinking about thisa little bit more, let's assume for the momentthat the blood viscosity is not going to change. It certainly won't changefrom moment to moment, but let's say that, ingeneral, blood viscosity is pretty constant. Now, given that, if I wantto change the resistance,

then I have two variables left. I've got the length of myvessel and I've got the radius. So if I have a vessellike this and let's say it's got a certainradius and length. And let's say that radius isr, and the length is here. And I apply a number. Let's say the number is2 for the resistance. Well, I have two options forchanging that resistance.

If I want to increasethe resistance, I can do two things. So let's say I want toincrease that resistance. And you can look at theequation and tell me what the answer would be. Two things. And I'll actually aw it out. So one thing would be to keepthe radius basically the same,

but make it much longer. Because if I make itlonger, since the L is now, let's say, twice aslong and r is the same, now my resistanceis going to double. So now we go 2 times. And 2 times 2 is 4. So my resistance is 4. OK.

Option 2. Let's say I don't wantto change the length. I keep the length the same. Instead, I could actuallymaybe change the radius. And let's say I half the radius. I make it half of what it was. And I actually worked outthe maththe last one. And it turned out that,if you half the radius