19. Fluid Mechanics

BIO. There is a maximum depth at which a diver can breathe through a snorkel tube (Fig. E12.17) because as the depth increases, so does the pressure difference, which tends to collapse the diver's lungs. Since the snorkel connects the air in the lungs to the atmosphere at the surface, the pressure inside the lungs is atmospheric pressure. What is the external– internal pressure difference when the diver's lungs are at a depth of 6.1 m (about 20 ft)? Assume that the diver is in fresh-water. (A scuba diver breathing from compressed air tanks can operate at greater depths than can a snorkeler, since the pressure of the air inside the scuba diver's lungs increases to match the external pressure of the water.)

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?

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 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?

An iron bolt is used to connect two iron plates together. The bolt must withstand shear forces up to about 3600 N. Calculate the minimum diameter for the bolt, based on a safety factor of 7.0.

(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?

The container shown in FIGURE EX14.11 is filled with oil. It is open to the atmosphere on the left. What is the pressure difference between points 1 and 2? Between points 1 and 3?

Ear Damage from Diving. If the force on the tympanic membrane (eardrum) increases by about 1.5 N above the force from atmospheric pressure, the membrane can be damaged. When you go scuba diving in the ocean, below what depth could damage to your eardrum start to occur? The eardrum is typically 8.2 mm in diameter. (Consult Table 12.1.)

The container shown in FIGURE EX14.11 is filled with oil. It is open to the atmosphere on the left. What is the pressure at point 1?

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?

(II) While exploring a sunken ocean liner, a small robot submarine measured the absolute pressure at the level of the ship to be 413 atmospheres. Calculate the magnitude of the force due to the water on a viewing port of the submarine at this depth if the viewing port has a surface area of 0.0100 m².

A barrel contains a 0.120-m layer of oil floating on water that is 0.250 m deep. The density of the oil is 600 kg/m³. (a) What is the gauge pressure at the oil–water interface? (b) What is the gauge pressure at the bottom of the barrel?

There is a maximum height of a uniform vertical column made of any material that can support itself without buckling, and it is independent of the cross-sectional area (why?). Calculate this height for ordinary steel (density 7.8 x 10³ kg/m³).