Skip to main content
Ch. 13 - Fluids
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 13 - FluidsProblem 92
Chapter 13, Problem 92

A ship, carrying fresh water to a desert island in the Caribbean, has a horizontal cross-sectional area of 2240 m² at the waterline. When unloaded, the ship rises 8.55 m higher in the sea. How much water (m³) was delivered?

Verified step by step guidance
1
Determine the volume of water displaced by the ship when it rises. The volume of displaced water is equal to the product of the cross-sectional area of the ship at the waterline and the height it rises. Use the formula: V=A⋅h, where A is the cross-sectional area and h is the height the ship rises.
Substitute the given values into the formula. The cross-sectional area A is 2240 m², and the height h is 8.55 m. The formula becomes: V=2240⋅8.55.
Recognize that the volume of water displaced by the ship is equal to the volume of water delivered, as the ship rises by the same amount when the water is unloaded.
Perform the multiplication to calculate the volume of water delivered. This will give the result in cubic meters (m³).
Ensure the units are consistent throughout the calculation and confirm that the final volume is expressed in cubic meters, as required by the problem.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
6m
Was this helpful?

Key Concepts

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

Buoyancy

Buoyancy is the upward force exerted by a fluid that opposes the weight of an object immersed in it. According to Archimedes' principle, the buoyant force on an object is equal to the weight of the fluid displaced by the object. In this scenario, the ship's rise in water level when unloaded indicates a change in the volume of water displaced, which is crucial for calculating the volume of water delivered.
Recommended video:
Guided course
11:06
Intro to Buoyancy & Buoyant Force

Volume Displacement

Volume displacement refers to the amount of fluid that is moved out of the way when an object is submerged in it. For the ship, the volume of water displaced when it is loaded with fresh water can be calculated using the change in height it rises in the water and its cross-sectional area. This relationship is essential for determining how much water was delivered to the island.
Recommended video:
Guided course
05:21
Volume Thermal Expansion

Cross-Sectional Area

The cross-sectional area is the area of a particular section of an object, perpendicular to a specified direction. In this case, the ship's horizontal cross-sectional area at the waterline is given as 2240 m². This area is used in conjunction with the change in height of the ship to calculate the volume of water delivered, as the volume can be found by multiplying the area by the height change.
Recommended video:
Guided course
08:10
Calculating the Vector (Cross) Product Using Components
Related Practice
Textbook Question

A drinking fountain shoots water about 12 cm up in the air from a nozzle of diameter 0.60 cm (Fig. 13–67). The pump at the base of the unit (1.1 m below the nozzle) pushes water into a 1.2-cm-diameter supply pipe that goes up to the nozzle. What gauge pressure does the pump have to provide? Ignore the viscosity; your answer will therefore be an underestimate.

<IMAGE>

Textbook Question

You are watering your lawn with a hose when you put your finger over the hose opening to increase the distance the water reaches. If you are holding the hose horizontally, and the distance the water reaches increases by a factor of 4, what fraction of the hose opening did you block?

Textbook Question

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

2
views
Textbook Question

A hydraulic lift is used to jack a 960-kg car 52 cm off the floor. The diameter of the output piston is 18 cm, and the input force is 380 N. What is the area of the input piston?

1
views
Textbook Question

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?

1
views
Textbook Question

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?

1
views