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(II) Poiseuille's equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, Re, exceeds approximately $2000 .$ Re is defined as$$R e=\frac{2 \overline{v} r \rho}{\eta}$$where $\overline{v}$ is the average speed of the fluid, $\rho$ is its density, $\eta$is its viscosity, and $r$ is the radius of the tube in which the fluidis flowing. (a) Determine if blood flow through the aorta islaminar or turbulent when the average speed of blood in theaorta $(r=0.80 \mathrm{cm})$ during the resting part of the heart'scycle is about 35 $\mathrm{cm} / \mathrm{s}$ . (b) During exercise, the blood-flowspeed approximately doubles. Calculate the Reynolds numberin this case, and determine if the flow is laminar or turbulent.

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(a) laminar(b) turbulent

Physics 101 Mechanics

Chapter 13

Fluids

Fluid Mechanics

Emmanuel O.

October 25, 2020

Cornell University

University of Michigan - Ann Arbor

McMaster University

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.

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(II) Poiseuille's equ…

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Poiseuille's equation…

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Poiseuille's law rema…

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Poiseuille’s law remains v…

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07:34

A common parameter that ca…

04:18

Assuming that blood is an …

03:27

Blood flow The shape of a …

02:12

Blood flow In Example 3.3 …

03:44

Blood Flow As blood moves …

so here for party we want to find Reynolds number. Ari is, uh, Reynolds number is he noted, as Ari, and this would be equal to two times the average velocity times the radius times row, the density. This would be divided by new the viscosity. So this would be equaling two times 0.35 meters per second, multiplied by the radius 0.80 times 10 to the negative second meters, and this would be multiplied by the density of 1050 kilograms per cubic meter. This would be divided by the viscosity of four times 10 to the negative third Pascal seconds. And we find that the Reynolds number four part A is equaling 1470 approximately at this speed. Now we can say that this is going toe. We have, ah laminar flow. And so for part B. Now, um, these velocity is simply doubled. We know that the Reynolds number is directly proportional to the average velocity. So if the velocity is double, the Reynolds number now becomes essentially 22,000, 940. Royal's number is unit list. And at this ah, speed. Now we have turbulent flow. That's the end of the solution. Thank you. For what

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