Question

Express the density of water in the English units of pounds per cubic foot.

Short answer

The density of water is approximately 62.43 lb/ft³.

Step-by-step solution

Identify the Density of Water in Metric Units

The density of water is commonly known to be approximately 1 gram per cubic centimeter (g/cm³) in metric units.

Convert Grams Per Cubic Centimeter to Kilograms Per Cubic Meter

Since there are 1000 grams in a kilogram and 100 centimeters in a meter, we convert 1 g/cm³ to kg/m³: \(1 \, \text{g/cm}^3 = 1000 \, \text{kg/m}^3\).

Convert Kilograms to Pounds

Use the conversion factor for mass: 1 kilogram equals approximately 2.20462 pounds. So, \(1000 \, \text{kg/m}^3 = 1000 \times 2.20462 \, \text{lb/m}^3 = 2204.62 \, \text{lb/m}^3\).

Convert Cubic Meters to Cubic Feet

Since 1 meter equals approximately 3.28084 feet, 1 cubic meter equals \((3.28084)^3 = 35.3147\) cubic feet.

Calculate the Density in Pounds Per Cubic Foot

Divide the density in pounds per cubic meter by the number of cubic feet in a cubic meter: \(\frac{2204.62 \, \text{lb/m}^3}{35.3147 \, \text{ft}^3/\text{m}^3} \approx 62.43 \, \text{lb/ft}^3\).

Key concepts

Metric to English Units

The conversion process from metric to English units involves several steps, especially when dealing with physical properties like density. Let's explore how to convert the metric density of water into English units.

First, identify the standard metric units. Water's density is typically given as 1 gram per cubic centimeter (g/cm³). In metric terms, this can also be equated to 1000 kilograms per cubic meter (kg/m³).

The challenge arises in translating these units into the English system. Here, mass is measured in pounds, and volume is measured in cubic feet. The conversion process involves:

• Converting kilograms to pounds: 1 kilogram equals approximately 2.20462 pounds.
• Converting cubic meters to cubic feet: 1 cubic meter equals around 35.3147 cubic feet.

By applying these conversions, you can express physical quantities such as density in a format familiar to users of the English measurement system.

Conversion Factors

Conversion factors are fundamental in moving between different unit systems. Understanding and utilizing these is crucial, especially when converting metric measurements to their English equivalents.

For instance, in the density conversion we examined, two primary conversion factors were essential:

• Mass: from kilograms to pounds, with 1 kilogram being approximately 2.20462 pounds. This conversion factor allows you to translate metric weights into the English system seamlessly.
• Volume: from cubic meters to cubic feet. Since 1 meter equals 3.28084 feet, a cubic meter equals 35.3147 cubic feet.

These conversion factors serve as multipliers to scale the quantity from one set of units to another accurately.
Without accurate conversion factors, calculating physical properties across different unit systems would be prone to errors.

Density of Water

Understanding the density of water is a fundamental concept in both physical science and everyday applications. In the metric system, water is well-known for its density of 1 gram per cubic centimeter (g/cm³) or equivalently 1000 kilograms per cubic meter (kg/m³).

The density of water represents how much mass of water exists in a given volume. It's important in various scientific calculations, engineering applications, and even day-to-day activities, like cooking.

When translated to the English system, as we explored, this metric density converts to roughly 62.43 pounds per cubic foot (lb/ft³). This might seem like an arbitrary figure, but it is crucial for various practical applications like understanding buoyancy, fluid dynamics, and cooking measurements.

Water's defined density is also a baseline for the density of other liquids and solids. It provides a reference point for scientists and engineers who need to understand the behavior of different substances in relation to water.