Fluid Mechanics Density problems

In summary, the first conversation discusses the concept of density and how it is calculated using mass and volume. The second conversation applies this concept to find the density of a suspended object. The third conversation introduces the idea of buoyancy and how it can be used to determine the average density of a person floating in the ocean.
  • #1
Susan
1
0
Is this correct?

A 6-kg piece of metal displaces 1 liter of water when submerged. What is its density?
Density = mass/volume 1 liter of water = 1000 cm3 = 1 kg
Ans: 6 kg / 1000 cm3 = .006 cm3


How would this one work out?
When a 2.0-kg object is suspended in water, it ‘masses’ 1.5 kg. What is the density of the object?
I'm guessing:
Density = mass/volume = 2.0 kg/1.5 kg = 1.333
Or 2.0 kg/ 1500 cm3 = .00133 cm3

Now I'm totally lost on what to do:

A vacationer floats lazily in the ocean with 90% of his body below the surface. The density of the ocean water is 1.025 kg/m3. What is the vacationer’s average density?
 
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  • #2
The buoyant force is equal to the weight of the water displaced (Archimedes principle). That allows you to do a force balance from which you can ultimately determine the volume of the swimmer!
 
  • #3


Your calculations for the first two problems are correct. For the third problem, we need to use the equation Density = mass/volume. We know the density of the ocean water (1.025 kg/m3) and we can assume that the vacationer's body has the same density as water (since they are floating). So, we can set up the equation as follows:

1.025 kg/m3 = mass/volume

We know that 90% of the vacationer's body is below the surface, so we can assume that 90% of their volume is also below the surface. This means that their volume above the surface is 10% of their total volume. We can represent this mathematically as:

Volume = 0.1 x total volume

Now we can substitute this into our equation to solve for the vacationer's average density:

1.025 kg/m3 = mass/(0.1 x total volume)

We can rearrange this to solve for mass:

mass = 1.025 x 0.1 x total volume

And we know that mass is equal to the weight of the vacationer, so we can represent this as:

weight = 1.025 x 0.1 x total volume

Finally, we can divide both sides by the total volume to solve for the vacationer's average density:

average density = weight/total volume = (1.025 x 0.1 x total volume)/total volume = 0.1025 kg/m3

So, the vacationer's average density is 0.1025 kg/m3.
 

1. What is fluid mechanics?

Fluid mechanics is a branch of physics that studies the behavior of fluids (liquids and gases) at rest and in motion. It involves the study of properties such as viscosity, pressure, and density to understand how fluids interact with their surroundings.

2. How is density related to fluid mechanics?

Density is a key property in fluid mechanics as it determines how much mass is present in a given volume of fluid. It affects the flow and behavior of fluids, as well as their buoyancy and ability to exert pressure. Density is also used in equations to calculate other properties of fluids, such as viscosity and pressure.

3. What are some common density problems encountered in fluid mechanics?

Common density problems in fluid mechanics include calculating the density of a fluid, determining the density of a mixture of fluids, and understanding how changes in density affect the flow or behavior of fluids. Other common problems involve using density to calculate properties such as pressure, viscosity, and buoyancy.

4. How is density measured in fluid mechanics?

Density can be measured in fluid mechanics using various methods, such as a hydrometer or a density meter. These instruments measure the mass and volume of a fluid to determine its density. Density can also be calculated using the density equation, which involves dividing the mass of a fluid by its volume.

5. How does the density of a fluid affect its flow?

The density of a fluid has a significant impact on its flow. A higher density fluid will typically flow slower and with more resistance compared to a lower density fluid. This is because a higher density fluid has more mass and therefore requires more energy to move. Density also plays a role in determining the viscosity of a fluid, which affects its ability to flow smoothly.

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