91Ó°ÊÓ

An airplane flies on a level path. There is a pressure difference of 500 Pa between the lower and upper surfaces of the wings. The area of each wing surface is about \(100 \mathrm{m}^{2} .\) The air moves below the wings at a speed of \(80.5 \mathrm{m} / \mathrm{s} .\) Estimate (a) the weight of the plane and (b) the air speed above the wings.

A water tower supplies water through the plumbing in a house. A 2.54 -cm- diameter faucet in the house can fill a cylindrical container with a diameter of \(44 \mathrm{cm}\) and a height of \(52 \mathrm{cm}\) in 12 s. How high above the faucet is the top of the water in the tower? (Assume that the diameter of the tower is so large compared to that of the faucet that the water at the top of the tower does not move. \()\)

The volume flow rate of the water supplied by a well is $2.0 \times 10^{-4} \mathrm{m}^{3} / \mathrm{s} .\( The well is \)40.0 \mathrm{m}$ deep. (a) What is the power output of the pump - in other words, at what rate does the well do work on the water? (b) Find the pressure difference the pump must maintain. (c) Can the pump be at the top of the well or must it be at the bottom? Explain.

Using Poiseuille's law [Eq. (9-15)], show that viscosity has SI units of pascal-seconds.

A viscous liquid is flowing steadily through a pipe of diameter \(D .\) Suppose you replace it by two parallel pipes, each of diameter \(D / 2,\) but the same length as the original pipe. If the pressure difference between the ends of these two pipes is the same as for the original pipe, what is the total rate of flow in the two pipes compared to the original flow rate?

A hypodermic syringe is attached to a needle that has an internal radius of \(0.300 \mathrm{mm}\) and a length of \(3.00 \mathrm{cm} .\) The needle is filled with a solution of viscosity $2.00 \times 10^{-3} \mathrm{Pa} \cdot \mathrm{s} ;\( it is injected into a vein at a gauge pressure of \)16.0 \mathrm{mm}$ Hg. Ignore the extra pressure required to accelerate the fluid from the syringe into the entrance of the needle. (a) What must the pressure of the fluid in the syringe be in order to inject the solution at a rate of $0.250 \mathrm{mL} / \mathrm{s} ?$ (b) What force must be applied to the plunger, which has an area of \(1.00 \mathrm{cm}^{2} ?\)

(a) What is the pressure difference required to make blood flow through an artery of inner radius \(2.0 \mathrm{mm}\) and length \(0.20 \mathrm{m}\) at a speed of \(6.0 \mathrm{cm} / \mathrm{s} ?\) (b) What is the pressure difference required to make blood flow at \(0.60 \mathrm{mm} / \mathrm{s}\) through a capillary of radius \(3.0 \mu \mathrm{m}\) and length \(1.0 \mathrm{mm} ?\) (c) Compare both answers to your average blood pressure, about 100 torr.

(a) since the flow rate is proportional to the pressure difference, show that Poiseuille's law can be written in the form \(\Delta P=I R,\) where \(I\) is the volume flow rate and \(R\) is a constant of proportionality called the fluid flow resistance. (Written this way, Poiseuille's law is analogous to Ohm's law for electric current to be studied in Chapter \(18: \Delta V=I R,\) where \(\Delta V\) is the potential drop across a conductor, \(I\) is the electric current flowing through the conductor, and \(R\) is the electrical resistance of the conductor.) (b) Find \(R\) in terms of the viscosity of the fluid and the length and radius of the pipe.

A sphere of radius \(1.0 \mathrm{cm}\) is dropped into a glass cylinder filled with a viscous liquid. The mass of the sphere is \(12.0 \mathrm{g}\) and the density of the liquid is \(1200 \mathrm{kg} / \mathrm{m}^{3} .\) The sphere reaches a terminal speed of \(0.15 \mathrm{m} / \mathrm{s} .\) What is the viscosity of the liquid?