This exercise. We have an artery that decreases in its diameter from D to the prime. The prime is 75% of D. So the private 70 0.75 D and in question A, we have the develop metric flow rate of the blood is the same in both situation. So Delta neither the t easy go to doubt of the prime. No, the tea. And we want to calculate how the pressure the difference in pressure in in the artery changes. So once you calculate Delta P prime, that's the difference in pressure after the decrease in the diameter of the artery as a function off the people. That's the difference of the That's the difference between off of the pressure before the decrees. So what I'm going to do is to use coarse as law which says that the volumetric flow rate is even by high over age times. Don't the p over l Aita l is the length of the artery. Aita is the disgust of the blood times the radius of the artery to the fourth and I'm gonna isolate about a P here to get eight over pie Aito l over our to the fourth daughter V though the tea And when I write it just little differently as eight. Tito el over high ah dot of either the tea TV. No, the tea all of these times went over are to the fourth notice that in both situations we have both before and after the decrease. This I wanted to hear 88 l over pied out of, you know, the tea is constant. Okay, so I'm gonna just call it, see, and we're gonna have that. The pee equals constant over our to the fourth. Okay. S o, this is the very of that API. That's before the decrease in the diameter. And let's calculate that a p prime, that's a p prime. It's gonna be see over 0.75 are to the fourth. Noticed that since the diameter was decreased by said that by 25%. Then so was the radius. This is gonna be 3.16 see over our to the fourth. But see over our to the fourth is Delta P is the original difference in pressure. So this is gonna be three points. 16 belt api. Okay, so we have the results that that'll be prime is 3.16 about a P. Or in other words, if we want the the percentage of increase, the difference in pressure was increased by 216%. Okay, now we move on to question V. And here, uh, were asked what happens if the difference in pressure was kept constant so that the P prime equals that api? What happens to the volumetric flow rate? So now what we want to do is to calculate Delta v Prime, not a t as a function of the outer vdot. Okay, So, uh, again, I'm gonna use pose as a creation. I'm just gonna write it, uh, again here, which is higher age that a p over L Aita are to the fourth. So now what's constant? Is this guy here that I wouldn't call D? Okay, this is a constant. So delta V that a t is de times are to the fourth. Okay, this constant, because the peace constant, Ellis Constant and Aitor is constant. So we have that doubt, Avi, though the tea is de are to the fourth. And this is the initial volumetric flow rate. The final volumetric flow rate is gonna be the out of you primed at the tea, which is D times 0.75 are to the fourth, which is 0.32 d r to the fourth. And since d r to the fourth is that I ve delta t We have 0.32 and out of E. Delta t case of the results, uh, is here that if you prime equals dealt it, that would be a prime over that. A t is 0.32 Delta veto the tea. Yeah, if we want the decrease in in percentage 81 minus 0.32 0 When? 68. So the decrees is 68% and this concludes there exercise.