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Chapter 10: Q3Q (page 260)
A small amount of water is boiled in a 1-gallon metal can. The can is removed from the heat and the lid is put on. As the can cool, it collapses and looks crushed. Explain.
The pressure difference across the wall of the metal can collapse it and makes it look crushed.
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(II)What is the volume rate of flow of water from a 1.85-cm-diameter faucet if the pressure head is 12.0 m?
A 3.2-N force is applied to the plunger of a hypodermic needle. If the diameter of the plunger is 1.3 cm and that of the needle is 0.20 mm, (a) with what force does the fluid leave the needle? (b) What force on the plunger would be needed to push fluid into a vein where the gauge pressure is 75 mm-Hg? Answer for the instant just before the fluid starts to move.
Giraffes are a wonder of cardiovascular engineering. Calculate the difference in pressure (in atmospheres) that the blood vessels in a giraffe’s head must accommodate as the head is lowered from a full upright position to ground level for a drink. The height of an average giraffe is about 6 m.
Two ships moving in parallel paths close to one another risk colliding. Why?
(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.
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