Ch 12: Fluid Mechanics

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th Edition

Ch 12: Fluid Mechanics

Problem 16

Chapter 12, Problem 16

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.

Verified step by step guidance

Step 1: Understand that the problem involves calculating the gauge pressure required to lift water to a certain height in a straw. Gauge pressure is the pressure relative to atmospheric pressure.

Step 2: Use the formula for pressure due to a column of fluid: \( P = \rho g h \), where \( \rho \) is the density of the fluid (water in this case), \( g \) is the acceleration due to gravity, and \( h \) is the height of the fluid column.

Step 3: Substitute the known values into the formula. For water, \( \rho \approx 1000 \, \text{kg/m}^3 \), \( g \approx 9.81 \, \text{m/s}^2 \), and \( h = 1.1 \, \text{m} \). Calculate the pressure \( P \) exerted by the water column.

Step 4: Recognize that the gauge pressure inside the lungs must be lower than atmospheric pressure by the amount calculated in Step 3 to lift the water to the given height. Therefore, the gauge pressure is negative because it is below atmospheric pressure.

Step 5: Explain that the negative gauge pressure indicates a partial vacuum created by the person sucking on the straw, which reduces the pressure inside the straw below atmospheric pressure, allowing the atmospheric pressure on the water surface to push the water up into the straw.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gauge Pressure

Gauge pressure is the pressure relative to atmospheric pressure. It is measured using a gauge that reads zero at atmospheric pressure. In this scenario, the gauge pressure inside the lungs must be lower than atmospheric pressure to draw water up the straw, indicating a negative value relative to the atmosphere.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It increases with depth in the fluid. To suck water up a straw, the pressure difference between the inside of the straw and the atmospheric pressure must overcome the hydrostatic pressure exerted by the column of water.

Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the weight of the air in the Earth's atmosphere. It acts on the surface of the water in the cup. To lift water up the straw, the pressure inside the straw must be lower than atmospheric pressure, allowing atmospheric pressure to push the water up into the straw.

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Textbook Question

The liquid in the open-tube manometer in Fig. 12.8a is mercury, y₁=3.00 cm,and y₂=7.00 cm. Atmospheric pressure is 980 millibars. What is (a) the absolute pressure at the bottom of the U-shaped tube; (b) the absolute pressure in the open tube at a depth of 4.00 cm below the free surface; (c) the absolute pressure of the gas in the container; (d) the gauge pressure of the gas in pascals?

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Textbook Question

A rock has mass 1.80 kg. When the rock is suspended from the lower end of a string and totally immersed in water, the tension in the string is 12.8 N. What is the smallest density of a liquid in which the rock will float?

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Textbook 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.)

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Textbook Question

Hydraulic Lift II.The piston of a hydraulic automobile lift is 0.30 m in diameter. What gauge pressure, in pascals, is required to lift a car with a mass of 1200 kg? Also express this pressure in atmospheres.

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Textbook Question

A 950-kg cylindrical can buoy floats vertically in sea-water. The diameter of the buoy is 0.900 m. Calculate the additional distance the buoy will sink when an 80.0-kg man stands on top of it.

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Textbook Question

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.)

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