Skip to main content
Ch 12: Fluid Mechanics
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 12: Fluid MechanicsProblem 18
Chapter 12, Problem 18

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
1
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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
5m
Was this helpful?

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.
Recommended video:
Guided course
09:27
Pressure Gauges: Barometer

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.
Recommended video:
Guided course
17:04
Pressure and Atmospheric Pressure

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.
Recommended video:
Guided course
17:04
Pressure and Atmospheric Pressure
Related Practice
Textbook 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. What force does the Venusian atmosphere exert on the outside surface of the bottom of the tank?

1
views
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?

1
views
Textbook Question

A closed container is partially filled with water. Initially, the air above the water is at atmospheric pressure (1.01×105 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. What is the gauge pressure at the bottom of the water?

1
views
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.)


1
views
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.

1
views
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.)

2
views