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Chapter 1: Problem 17

Hydraulic engineers in the United States often use, as a unit of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre of land to a depth of \(1 \mathrm{ft}\). A severe thunderstorm dumped \(2.0\) in. of rain in \(30 \mathrm{~min}\) on a town of area \(26 \mathrm{~km}^{2}\). What volume of water, in acre-feet, fell on the town?

Short Answer

Expert verified
1,073.33 acre-feet

Step by step solution

01

Convert area to acres

First convert the town's area from \(26 \ \text{km}^2\) to acres. Use the conversion factor \(1\ \text{km}^2 \approx 247.105 \ \text{acres}\). Multiply the town's area by this conversion factor: \[26 \ \text{km}^2 \times 247.105 \ \text{acres/km}^2 = 6,424.73 \ \text{acres}\]
02

Convert rainfall depth to feet

Convert the depth of rainfall from inches to feet. Use the conversion factor \(1 \ \text{inch} = \frac{1}{12} \ \text{feet}\). Multiply the depth of rainfall by this conversion factor: \[2.0 \ \text{inches} \times \ \frac{1}{12} \ \text{feet/inch} = \frac{2.0}{12} \ \text{feet} = 0.167 \ \text{feet}\]
03

Calculate volume in acre-feet

Now, calculate the volume of water that fell on the town by multiplying the area in acres by the depth of the rain in feet: \[6,424.73 \ \text{acres} \times 0.167 \ \text{feet} = 1,073.33 \ \text{acre-feet}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Introduction to Unit Conversion
Unit conversion is a critical tool in physics and engineering. It helps in transforming measurements from one unit to another, ensuring consistency and accuracy. For instance, in the given exercise, we convert kilometers squared (km虏) to acres and inches to feet. These conversions facilitate accurate rainfall volume calculations.
Remember, conversion factors are crucial here. For area, we use: 1 km虏 鈮� 247.105 acres. For length, we use: 1 inch = 1/12 feet. Engaging with unit conversions not only enhances your problem-solving skills but also aids in grasping multiple disciplines seamlessly.
Basics of Hydraulic Engineering
Hydraulic engineering focuses on the movement and storage of water. In this field, precise volume calculations are vital. Engineers may use units like acre-feet to describe large volumes of water, which makes managing resources more practical. An acre-foot is the volume needed to cover one acre to a depth of one foot.
Such units simplify the calculation of water volumes in large-scale applications. Like in our problem, determining how much rainfall collected over a large area can be efficiently solved using these principles. Understanding these basics helps in tackling real-world hydraulic problems effectively.
Understanding Volume Calculation
Volume calculation in physics involves determining the space occupied within a bounded area. In the exercise, this involves converting atmospheric precipitation's depth (in inches) over a defined area (in km虏) into acre-feet. Here's a step-by-step refresher:
1. **Convert Area**: By converting the area from km虏 to acres, we get units that are more manageable for water volume calculations.
2. **Convert Depth**: Transforming rainfall depth from inches to feet helps in utilizing easily convertible consistent units.
3. **Calculate Volume**: Finally, multiplying the area in acres and depth in feet yields the volume in acre-feet.
This logical approach ensures accurate results and is a valuable skill in various fields, from environmental science to urban planning.

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Most popular questions from this chapter

Discuss the question: "Is 500 feet big or small?" Before you do so, carry out the following estimates. (a) You are on the top floor of a 500 -ft-tall building. A fire breaks out in the building and the elevator stops working. You have to walk down to the ground floor. Estimate how long this would take you. (Your stairwell is on the other side of the building from the fire.) (b) You are hiking the Appalachian Trail on a beautiful fall morning as part of a \(10 \mathrm{mi}\) hike with a group of friends. You are walking along a well-tended, level part of the trail. Estimate how long it would take you to walk \(500 \mathrm{ft}\). (c) You are driving on the New Jersey Turnpike at \(65 \mathrm{mi} / \mathrm{hr}\). You pass a sign that says "Lane ends 500 feet." How much time do you have in order to changelanes?

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