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Chapter 10: Q6Q (page 260)
A submerged can of Coke sink, but a can of Diet Coke will float. (Try it!) Explain.
The density of Coke is greater than the density of the Diet Coke.
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A rowboat floats in a swimming pool, and the level of the water at the edge of the pool is marked. Consider the following situations. (i) The boat is removed from the water. (ii) The boat in the water holds an iron anchor which is removed from the boat and placed on the shore. For each situation, the level of the water will,
(a) Rise.
(b) Fall.
(c) Stay the same.
If cholesterol buildup reduces the diameter of an artery by 25%, by what % will the blood flow rate be reduced, assuming the same pressure difference?
A viscometer consists of two concentric cylinders, \({\bf{10}}{\bf{.20}}\;{\bf{cm}}\) and \({\bf{10}}{\bf{.60}}\;{\bf{cm}}\)in diameter. A liquid fills the space between them to a depth of \({\bf{12}}{\bf{.0}}\;{\bf{cm}}\). The outer cylinder is fixed, and a torque of \({\bf{0}}{\bf{.024}}\;{\bf{m}} \cdot {\bf{N}}\) keeps the inner cylinder turning at a steady rotational speed of \({\bf{57}}\;{\bf{rev/min}}\). What is the viscosity of the liquid?
(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
\({\mathop{\rm Re}\nolimits} = \frac{{2\overline v r\rho }}{\eta }\)
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 fluid is flowing. (a) Determine if blood flow through the aorta is laminar or turbulent when the average speed of blood in the aorta \(\left( {{\bf{r = 0}}{\bf{.80}}\;{\bf{cm}}} \right)\) during the resting part of the heart’s cycle is about \({\bf{35}}\;{\bf{cm/s}}\). (b) During exercise, the blood-flow speed approximately doubles. Calculate the Reynolds number in this case, and determine if the flow is laminar or turbulent.
Why does the canvas top of a convertible bulge out when the car is traveling at high speed? [Hint: The windshield deflects air upward, pushing streamlines closer together.]
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