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Specific weight is a useful property that tells us how heavy a liquid is for each unit volume. Think of it as the weight of the liquid per square foot or cubic meter. It is mathematically defined as the weight divided by the volume. In this example, the specific weight given is 85.3 lbs/ft³. Specific weight is dependent on gravity. That's why the units involve weight (like pounds) rather than mass. If gravity changes, the specific weight changes, even if the liquid itself does not.

• It helps in determining how substances compare when sitting in a fluid.
• It helps in engineering designs where weight of the liquid affects the structure, like in dams and tanks.

Density is a fundamental concept in fluid mechanics, referring to mass per unit volume of a substance. In our previous exercise, we calculated it for a liquid whose specific weight is 85.3 lb/ft³. To find the density, we rearrange the formula for specific weight: \[gamma = \rho \times g\]where \(\gamma\) is specific weight, \(\rho\) stands for density, and \(g\) is acceleration due to gravity.
Using Earth’s standard gravity \(g = 32.2 \text{ft/s}^2\), the density \(\rho\) is determimed as follows:

• Rearrange formula to \(\rho = \frac{\gamma}{g}\)
• Substitute given values \(\rho = \frac{85.3}{32.2} \text{slugs/ft}^3\)
• Calculated value for density is approximately \(2.65 \text{slugs/ft}^3\)

This calculation is essential in various applications, like determining how a liquid will behave when mixed with another or how much pressure it will exert in a container during movement.

Specific gravity is another important term that tells us how dense a substance is relative to water. It's a dimensionless quantity, meaning it has no units. It compares the density of a liquid to the density of water, often making it more intuitive to understand how dense a liquid really is.

Formula: \(SG = \frac{\text{Density of liquid}}{\text{Density of water}}\)

For our exercise, the specific gravity was determined by first converting density from slugs to lbs:

• Given \(\rho_{\text{liquid}} = 2.65 \text{slugs/ft}^3\)
• Convert this to lbs: \(2.65 \times 32.2 = 85.3 \text{lb/ft}^3\)
• Density of water \(\approx 62.4 lb/ft^3\)
• Thus, \(SG = \frac{85.3}{62.4} \approx 1.37\)

This means the liquid is 1.37 times denser than water. Understanding specific gravity helps in predicting how a substance will interact in different environments, like whether it will float on water or sink.

Acceleration due to gravity, denoted as \(g\), is an essential constant in physics and fluid mechanics. On Earth, its standard value is \(32.2 \text{ft/s}^2\), which means every second, a freely falling object would increase its velocity by 32.2 ft/s. This constant is crucial when calculating specific weight and density.
Here's why it's important:

• It allows us to relate weight, which depends on gravity, to mass, which doesn't.
• It's a determining factor in how fluids exert pressure and buoyancy.

When computing density from specific weight, knowing the current acceleration due to gravity is essential. Often, laboratory measurements of fluids are conducted with Earth's gravity in mind, making calculations consistent. If you were on another planet, both specific weight and density values would change due to different gravitational forces.