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Artery blockage. A medical technician is trying to determine what percentage of a patient's artery is blocked by plaque. To do this, she measures the blood pressure just before theregion of blockage and finds that it is $1.20 \times 10^{4}$ Pa, while in the region of blockage it is $1.15 \times 10^{4}$ Pa. Furthermore, she knows that blood flowing through the normal artery just before the point of blockage is traveling at 30.0 $\mathrm{cm} / \mathrm{s}$ , and the specific gravity of this patient's blood is $1.06 .$ What percentage of the cross-sectional area of the patient's artery is blocked by the plaque?

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70.47$\%$

Physics 101 Mechanics

Chapter 13

Fluid Mechanics

Temperature and Heat

Cornell University

Hope College

University of Sheffield

Lectures

03:45

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids.

09:49

A fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases and plasmas. Fluids display properties such as flow, pressure, and tension, which can be described with a fluid model. For example, liquids form a surface which exerts a force on other objects in contact with it, and is the basis for the forces of capillarity and cohesion. Fluids are a continuum (or "continuous" in some sense) which means that they cannot be strictly separated into separate pieces. However, there are theoretical limits to the divisibility of fluids. Fluids are in contrast to solids, which are able to sustain a shear stress with no tendency to continue deforming.

07:46

A medical technician is tr…

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03:32

Artery blockage. A medical…

10:06

There are two carotid arte…

04:46

Blood with density $1.06 \…

06:13

In an aortic aneurysm, a b…

01:37

Blood pressure. Systemic b…

04:43

all right. In this problem, we want to figure out what percentage of an artery is blocked and we're given the pressure, Um, in the artery before the blockage and inside the blockage. Those were these values here and were given that the density of blood Well, actually, we're given the specific gravity of blood, which translates into ah, 10 city of one point of six times sent to the three kilograms per meter. Cute. And to solve this problem, we're going to rely on continuity which are written here and Bernoulli's equation, which ever in the year. So the subscript 12 notes the portion of the artery bullet before the blockage and subscript two gin notes, a portion of the artery that is blocked and were given that these points here are close together so we can drop the's terms from Bernoulli's equation. Each one is approximately equal teach, too. So, um, in this equation one that I've written, I've re exploited. Excuse me. I have re expressed the area of the blockage in terms of a fraction x of the area of the artery so we can cancel out the area of the artery from both sides and we were given that the speed of the blood in the unblocked portion of the artery is 30 centimeters per second, or 300.3 meters per second. So basically, if we know the value of the two, then we can solve Equation one for X, which is what we're after. And we'll be able to get the two from Bernoulli's equation so the two is going to be equal. Tio, the square root of two over Ro, where row is the density of blood which we've written over here. And, um, we have inside the brackets p one minus p, too. I use different sub scripts over here. Maybe let's change that out for a one. Change this out for too, just to completely avoid confusion. So it's going to be P one minus p too. Plus 1/2 row again, Um, times V one squared, actually. Excuse me at weekends. Well, I'll leave like that. The one just keep in mind is 0.3. So after we solve this equation for V to or I should say after we plug in the numbers to get the value of the two, then the person that's blocked X is just 0.3 over V two, and this comes out to ah, about 70% blockage

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