College Physics: A Strategic Approach (4th Edition)
4th Edition
ISBN: 9780134609034
Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher: PEARSON
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Textbook Question
Chapter 15, Problem 82GP
When the heart pumps blood into the aorta, the pressure gradient—the difference between the blood pressure inside the heart and the blood pressure in the artery—is an important diagnostic measurement. A direct measurement of the pressure gradient is difficult, but an indirect determination can be made by inferring the pressure difference from a measurement of velocity. Blood is essentially at rest in the heart; when it leaves and enters the aorta, it speeds up significantly and—according to Bernoulli’s equation—the pressure must decrease. A doctor using 2.5 MHz ultrasound measures a 6000 Hz frequency shift as the ultrasound reflects from blood ejected from the heart.
a. What is the speed of the blood in the aorta?
b. What is the difference in blood pressure between the inside of the heart and the aorta? Assume that the patient is lying down and that there is no difference in height as the blood moves from the heart into the aorta.
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(a) The heart pumps blood into the aorta at a rate of 4
the aorta's diameter is 2.1 cm.
Calculate the average speed of blood if
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(b) The aorta branches many times until the blood finally reaches the smallest branch: the capillaries.
Each capillary has an average diameter of 6.9 μm and the blood slows down to 0.5
the number of capillaries in the body. Does this answer look reasonable?
mm
Calculate
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(c) For what duration of time is a red blood cell in a capillary if the average capillary length is 1 mm?
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(d) Why does the blood need to flow much slower through the capillaries than the aorta?
○ A. The capillaries are thin and might burst.
○ B. There must be sufficient time for the exchange of substances to occur across the cell
membrane of the capillaries.
O C. There is a smaller cross-sectional area.
○ D. None of these.
The density ρ of a fluid changes proportionally with depth from the surface h according to the following formula: ρ(h) = ρ0 + ch. where ρ0 is the density of the fluid at the surface (h = 0), and c is a constant.
a)Write an expression for the gauge pressure p as a function of the depth.
b)A pressure gauge is placed at a depth of 6.3 m in a fluid with density that varies with depth as described above. The constant c is 720 kg/m4. The density of the fluid at h = 0 is 0 kg/m4. What pressure, in pascals, would the gauge read?
A fluid sits in a tank whose top is open to atmosphere . This fluid has a density that increases linearly as a function of depth
p = Po + ay , where Po is the density at the top of the fluid and a is a measure of how that fluid's density changes as a function of
height. Which of the following is the correct functional form for gauge pressure as a function of depth?
Choice A: (po + ay) gh
Choice B: PogY
Choice C: Pogy +agy?
() gu
Potay
GY
Choice D:
Chapter 15 Solutions
College Physics: A Strategic Approach (4th Edition)
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