19. Fluid Mechanics

How high would the level be in an alcohol barometer at normal atmospheric pressure?

(III) A beaker of liquid accelerates from rest, on a horizontal surface, with acceleration α to the right. How does the pressure vary with depth below the surface?

Intravenous transfusions are often made under gravity, as shown in Fig. 13–59. Assuming the fluid has a density of 1.00 g/cm³, at what height h should the bottle be placed so the liquid pressure is 52 mm-Hg?

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Intravenous transfusions are often made under gravity, as shown in Fig. 13–59. Assuming the fluid has a density of 1.00 g/cm³. 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?

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A bicycle pump is used to inflate a tire. The initial tire (gauge) pressure is 210 kPa (30 psi). At the end of the pumping process, the final pressure is 310 kPa (45 psi). If the diameter of the plunger in the cylinder of the pump is 2.5 cm, what is the range of the force that needs to be applied to the pump handle from beginning to end?

Estimate the total mass of the Earth’s atmosphere, using the known value of atmospheric pressure at sea level.

When a person drives or hikes to a higher altitude, and even more during descent, volume changes of trapped air in the middle ear can cause ear discomfort until the middle-ear pressure and exterior pressure are equalized. If a rapid descent at a rate of 7.0 m/s or faster commonly causes ear discomfort, what is the maximum rate of increase in atmospheric pressure (that is, dP/dt) tolerable to most people?

When you ascend or descend a great deal when driving in a car, your ears “pop,” which means that the pressure behind the eardrum is being equalized to that outside. If this did not happen, what would be the approximate force on an eardrum of area 0.20cm² if a change in altitude of 1120 m takes place?

A marble column of cross-sectional area 1.4m² supports a mass of 22,000 kg. By how much is the column shortened if it is 8.6 m high?

Parachutists whose chutes have failed to open have been known to survive if they land in deep snow. Assume that a 75-kg parachutist hits the snow with an area of impact of .030m² at a velocity of 55 m/s, and that the ultimate strength of body tissue is 5 x 10⁵ N/m². Assume that the person is brought to rest in 1.0 m of snow. Show that the person may escape serious injury.

A 25-kg object is being lifted by two people pulling on the ends of a 1.15-mm-diameter nylon cord that goes over two 3.00-m-high poles that are 4.5 m apart, as shown in Fig. 12–93. How high above the floor will the object be when the cord breaks?

Suppose a 65-kg person jumps from a height of 3.0 m down to the ground. Estimate the stress and determine if the tibia will break in a stiff-legged landing (d = 1.0 cm).

Show that inside a soap bubble, there must be a pressure ∆P in excess of that outside equal to ∆P - 4γ/r, where r is the radius of the bubble and γ is the surface tension. [Hint: Think of the bubble as two hemispheres in contact with each other, one on the left and one on the right; and remember that there are two surfaces to the bubble, outside and inside. Note that this result applies to any kind of membrane, where 2γ is the tension per unit length in that membrane.]