Chapter 10: Q46P (page 260)
(II)A fish tank has dimensions 36 cm wide by 1.0 m long by 0.60 m high. If the filter should process all the water in the tank once every 3.0 h, what should the flow speed be in the 3.0 cm diameter input tube for the filter?
The flow speed in input tube for the filter is \(0.028\;{\rm{m/s}}\).
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Two ships moving in parallel paths close to one another risk colliding. Why?
Intravenous transfusions are often made under gravity, as shown in Fig. 10–55. Assuming the fluid has a density of \({\bf{1}}{\bf{.00\;g/c}}{{\bf{m}}^{\bf{3}}}\)at what height h should the bottle be placed so the liquid pressure is (a) 52 mm-Hg, and (b) \({\bf{680\;mm - }}{{\bf{H}}_{\bf{2}}}{\bf{O?}}\)(c) If the blood pressure is 75 mm-Hg above atmospheric pressure, how high should the bottle be placed so that the fluid just barely enters the vein?
(II) If the base of an insect’s leg has a radius of about \(3.0 \times 1{0^{{\bf{ - }}5}}\;m\) and the insect’s mass is 0.016 g, would you expect the six-legged insect to remain on top of the water? Why or why not?
(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.
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.
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