19. Fluid Mechanics

Intro to Pressure

Open Question
(II) A wind blowing over the flat roof of a house causes the roof to lift off the house. If the house is 6.2 m x 12.4 m in size, estimate the weight of the roof. Assume the roof is not nailed down.
Multiple Choice
A large warehouse is 100 m wide, 100 m deep, 10 m high:
a) What is the total weight of the air inside the warehouse?
b) How much pressure does the weight of the air apply on the floor?
Multiple Choice
A tall cylindrical beaker 10 cm in radius is placed on a picnic table outside. You pour 5 L of an 8,000 kg/m³ liquid and 10 L of a 6,000 kg/m³ liquid into. Calculate the total pressure at the bottom of the beaker. (Use g=10 m/s².)
Multiple Choice
A wooden cube, 1 m on all sides and having density 800 kg/m³ , is held under water in a large container by a string, as shown below. The top of the cube is exactly 2 m below the water line. Calculate the difference between the force applied by water to the top and to the bottom faces of the cube (Hint:calculate the two forces, then subtract. Use g=10 m/s².)
Multiple Choice
At point A, a hose ejects water at a speed of $5.10 m/s$ . Point B is upstream from, and 30.0cm above, the outlet. If the water is moving at $2.40 m/s$ at point B, what is the internal pressure of the water at B? Use $101.3 kPa$ for atmospheric pressure and $1000 {kg/m}^{3}$ for the density of water.
Multiple Choice
The pressure gradient in a pipe carrying water is $600 Pa / m .$ What pressure gradient would be required to maintain the same flow rate in the same pipe if it were carrying olive oil? Treat the flow as the flow of a viscous fluid. The viscosity of water is $1.0 \times 10^{- 3} Pa \cdot s$ and the viscosity of olive oil is $8.2 \times 10^{- 2} Pa \cdot s$ .
Multiple Choice
Suppose the average speed of blood in the aorta is $0.26 m/s$ , and the diameter is 2.0 cm. What is the pressure gradient in this aorta due to the viscosity of blood (assume a human body temperature)?
Multiple Choice
The deepest known point on Earth is called the Mariana Trench, at ~11,000 m (~36,000 ft). If the surface area of the average human ear is 20 cm2, how much average force would be exerted on your ear at that depth?
Open Question
BIO. The lower end of a long plastic straw is immersed below the surface of the water in a plastic cup. An average person sucking on the upper end of the straw can pull water into the straw to a vertical height of 1.1 m above the surface of the water in the cup. (a) What is the lowest gauge pressure that the average person can achieve inside his lungs? (b) Explain why your answer in part (a) is negative.
Open Question
Exploring Venus. The surface pressure on Venus is 92 atm, and the acceleration due to gravity there is 0.894g. In a future exploratory mission, an upright cylindrical tank of benzene is sealed at the top but still pressurized at 92 atm just above the benzene. The tank has a diameter of 1.72 m, and the benzene column is 11.50 m tall. Ignore any effects due to the very high temperature on Venus. (b) What force does the Venusian atmosphere exert on the outside surface of the bottom of the tank?
Open Question
A closed container is partially filled with water. Initially, the air above the water is at atmospheric pressure (1.01×10^5 Pa) and the gauge pressure at the bottom of the water is 2500 Pa. Then additional air is pumped in, increasing the pressure of the air above the water by 1500 Pa. (a) What is the gauge pressure at the bottom of the water?
Open Question
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/m^3. (a) What is the gauge pressure at the oil–water interface? (b) What is the gauge pressure at the bottom of the barrel?
Open Question
Oceans on Mars. Scientists have found evidence that Mars may once have had an ocean 0.500 km deep. The acceleration due to gravity on Mars is 3.71 m/s^2. (a) What would be the gauge pressure at the bottom of such an ocean, assuming it was freshwater? (b) To what depth would you need to go in the earth's ocean to experience the same gauge pressure?
Open Question
BIO. 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.)
Open Question
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.)