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(III) A patient is to be given a blood transfusion. The blood is to flow through a tube from a raised bottle to a needle inserted in the vein (Fig. $56 ) .$ The inside diameter of the $25-$$\mathrm{mm}$ -long needle is 0.80 $\mathrm{mm}$ and the required flow rate is2.0 $\mathrm{cm}^{3}$ of blood per minute. How high $h$ should the bottle be placed above theneedle? Obtain $\rho$ and $\eta$ from the Tables. Assume the blood pressure is 78torr above atmospheric pressure.

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1.04$m$

Physics 101 Mechanics

Chapter 13

Fluids

Fluid Mechanics

Cornell University

Hope College

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.

03:47

A patient is to be given a…

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In a blood transfusion, bl…

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Intravenous transfusions a…

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blood transfusion is being…

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A blood transfusion is bei…

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Intravenous infusions are …

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[GO] ? A blood transfusio…

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A patient is given an intr…

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A person is donating blood…

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The aorta is approximately…

So here we're going to use Prosperity's equation. We want to find essentially the change in height so we can say that here the volumetric flow rate is equaling pi times the radius to the fourth power multiplied by the change in pressure. Divided by eight times the viscosity of blood multiplied by out. Ah, and we can then say that here piece of two is equaling piece of one plus eight times the viscosity of blood multiplied by the length al times cute D volumetric flow rate divided by pi. Times are to the fourth power and this would simply be equaling the density of blood multiplied by G times, the change in height or the gauge or the the gauge pressure. And so we can sew for Delta H. And we see that Delta H is equaling. I will say one over the density of blood times G, and then this would be multiplied by piece of one plus eight times like believable over at it. On the new line, don't age equaling one over the density of blood times the acceleration due to gravity g most applied by piece of one plus eight times the discuss city of blood multiplied by the length times. Cue the volumetric flow rate divided by pi r to the fourth power and so we can now solve. So Delta H will be equaling one over the density of blood 1050 kilograms per cubic meter multiplied by 9.80 meters per second squared. This would be multiplied by well, put it down here. 78 millimetres of mercury multiplied by 133 pass cows for every millimeter of mercury, this would be a plus eight times the viscosity of blood four times 10 to the negative third task ao seconds. This would be multiplied by 2.5 times 10 to the negative second meters and then this would be multiplied by the volumetric flow rate of 2.0 times 10 to the negative sixth meters cubed divided by 60 seconds and then this entire term would be divided by pi times the radius to the fourth power 4.4 times 10 to the negative third meters to the fourth power close parentheses and we find that the change in height Delta H is equaling approximately 1.4 meters. This would be our final answer. That is the end of the solution. Thank you

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