The amount of water in reservoirs is often measured in acre-ft. One acre-ft is a volume that...

Question:

The amount of water in reservoirs is often measured in acre-ft. One acre-ft is a volume that covers an area of one acre to a depth of one foot. An acre is 43,560 ft{eq}^2 {/eq}. Find the volume in SI units of a reservoir containing 26.0 acre-ft of water.

Unit Conversion:

The basic types of physical quantities (such as mass, length, and charge) are called dimensions. In order to measure these dimensions, we need standard units (such as kilograms, feet, or Coulombs). We can convert between different units if they measure the same dimension.

For example, let's consider how to convert between inches and centimeters. One inch is equal to 2.54 cm, so the fraction {eq}\frac{1 \ in}{2.54 \ cm} {/eq} is equal to one (it is a thing divided by itself, which is always equal to one). So, we can multiply this fraction by any quantity without changing the value of that quantity (because multiplying a number by one results in the same number. Let's see what happens when we multiply this conversion factor by 7 cm:

{eq}L = 7 \ cm (\dfrac{1 \ in}{2.54 \ cm}) {/eq}

Notice that there is a {eq}cm {/eq} in the numerator and denominator that we can cancel out.

{eq}L = 7 (\dfrac{1 \ in}{2.54})\\ L = 2.76 \ in {/eq}

This is how we can convert between units: by choosing the appropriate conversion factor and multiplying it by the original quantity.

Answer and Explanation:

The answer is {eq}32,100 \ m^3 {/eq}.

We can solve this problem using unit analysis. First, for simplicity, let's convert the volume from acre-ft to...

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Unit Conversion and Dimensional Analysis

from Chemistry 101: General Chemistry

Chapter 1 / Lesson 2
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