What is the Geometric Balance of an Object in a Fluid Flow?

In summary: Dear Clausius:You are incorrect. The first picture is a subcritical flow, which is analogous to subsonic compressible flow. The wave is reaching zones of upstreaming fluid. When the flow is critical (incompressible and free surface flow) or sonic (compressible flow) the wave speed is the same than the free stream velocity, and so one should see an steady front of waves just in front of the body nose. As you may check the Froude / Mach angle in this cases is 90º. As a cautionary note, I am comparing free surface flows with compressible flow because both behaviors are similar as far as changes in flow phenomena made by the two most important numbers ( Fr
  • #1
Raparicio
115
0
Dear Friends,

I have a problem on fluid mechanics that I can't solve.

The question is one boat that has great velocity. In front of it, it's created a wave because of the boat. Now, imagine that this boat has greater and greater velocity. The angle of the wave in the front, at great velocity, will be more orthogonal to the trajectory of the boat.

Now imagine that one circle of this wave arrounds the boat. The lines of flux that enter this circle, will be the same they go out (conservation of mass), well, how can be calculated this?

There's one formula that says shows the flux that enter and go out one surface is the same that enters and go out the volume. It could be calculate with the navier-stokes formula and the conservation of the mass.

The question is about an object that is into a flow, that is arrounded by this flow, and finally one geometric balance.

best reggards.
 
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  • #2
Raparicio said:
Dear Friends,

I have a problem on fluid mechanics that I can't solve.

The question is one boat that has great velocity. In front of it, it's created a wave because of the boat. Now, imagine that this boat has greater and greater velocity. The angle of the wave in the front, at great velocity, will be more orthogonal to the trajectory of the boat.

Now imagine that one circle of this wave arrounds the boat. The lines of flux that enter this circle, will be the same they go out (conservation of mass), well, how can be calculated this?

There's one formula that says shows the flux that enter and go out one surface is the same that enters and go out the volume. It could be calculate with the navier-stokes formula and the conservation of the mass.

The question is about an object that is into a flow, that is arrounded by this flow, and finally one geometric balance.

best reggards.

I am not too sure about what you want to calculate. I don't know what circle are you referring to. Maybe some picture would help a bit. Anyway, no matter how is the control surface you have defined, the integral mass conservation law is:

[tex]\oint_S \overline{v}\cdot \overline{dS}=0[/tex]

The problem you are describing is a typical free surface flow. IF and only IF the boat velocity is less than the propagation speed of the superficial waves, there will be such circles around the boat (i.e. the Froude number is less than unity). As you may have seen on TV or in some pictures, usually there is a weak around the boat which has the shape of an opened triangle such a shock wave. This means the flow is supercritical in upstream the boat and transforms into a subcritical one just downstream of an small hydraulic jump. See my figure attached:
 

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  • #3
Dear Clausius:

The question is similar that first picture. It's like an airplane, flying at the same velocity of the sound: it generates arround it, a wave that is increasing in the time, always more radius, but never pass it. The doppler efect it's very strange in this example.

There are 2 questions that I want to understand:

1) how to calculate the doppler efect exactly at the velocity of sound
2) what's the effect of a sphere, going at a very great velocity, that makes arround it a great wave that is bigger than the sphere, and is composed of water.
3) If it exists any calculations that we can establish one balance between this mass that envolves sphere and what is arrounding it.

I don't know how to calculate it.
 
  • #4
Raparicio said:
Dear Clausius:

The question is similar that first picture. It's like an airplane, flying at the same velocity of the sound: it generates arround it, a wave that is increasing in the time, always more radius, but never pass it.

You're wrong. The first picture is a subcritical flow, which is analogous to subsonic compressible flow. The wave is reaching zones of upstreaming fluid. When the flow is critical (incompressible and free surface flow) or sonic (compressible flow) the wave speed is the same than the free stream velocity, and so one should see an steady front of waves just in front of the body nose. As you may check the Froude / Mach angle in this cases is 90º.
As a cautionary note, I am comparing free surface flows with compressible flow because both behaviors are similar as far as changes in flow phenomena made by the two most important numbers ([tex] Fr=U/\sqrt{gH}[/tex] and [tex] M=U/c[/tex]).

Raparicio said:
There are 2 questions that I want to understand:

1) how to calculate the doppler efect exactly at the velocity of sound

Just at sonic flow, same particle just upstream the body nose would sense a wave length 0, because no pressure information can reach upstream zones.
Don't be surprised the equations for frequency will give you a singularity. The critical /sonic flow is singular and unsteady effects are very important in these cases.


Raparicio said:
2) what's the effect of a sphere, going at a very great velocity, that makes arround it a great wave that is bigger than the sphere, and is composed of water.

I haven't understood nothing. Escríbelo en español a ver si entiendo lo que quieres decir.
 
  • #5
Imagine one object at the same velocity of sound (exactly mach 1), and now translate this waves to another "fluid". It's the most approached I can explain.
 

Related to What is the Geometric Balance of an Object in a Fluid Flow?

1. What is fluid mechanics and why is it important for understanding an object's behavior?

Fluid mechanics is the study of how fluids (liquids and gases) behave and interact with objects. It is important for understanding an object's behavior because most objects in our daily lives are either surrounded by or interacting with fluids. Understanding how fluids move and exert forces on objects is crucial for designing and engineering various systems, such as airplanes, ships, and pipelines.

2. How does viscosity affect an object's movement in a fluid?

Viscosity is a measure of a fluid's resistance to flow. An object moving through a fluid with high viscosity will experience more resistance and will move slower compared to a fluid with low viscosity. This is because high viscosity fluids have stronger internal forces that oppose the object's movement.

3. What is Bernoulli's principle and how does it apply to fluid mechanics of an object?

Bernoulli's principle states that as the speed of a fluid increases, its pressure decreases. This principle applies to the fluid mechanics of an object by explaining the relationship between fluid speed and pressure. For example, when an object is moving through a fluid, the fluid on top of the object moves faster than the fluid underneath it, resulting in lower pressure on top of the object. This creates a net upward force, known as lift, which is important for understanding the flight of airplanes and the lift of wings.

4. Can an object float in a fluid and what factors determine its ability to float?

Yes, an object can float in a fluid if its weight is equal to the weight of the fluid it displaces. This is known as Archimedes' principle. The factors that determine an object's ability to float in a fluid include its density, shape, and volume. Objects with lower density and larger volume are more likely to float in a fluid.

5. How does the shape and size of an object affect its drag force in a fluid?

The shape and size of an object can greatly affect its drag force in a fluid. An object with a streamlined shape, such as an airplane, will experience less drag compared to a blunt object with a larger surface area. This is because the streamlined shape allows the fluid to flow smoothly around the object, while a blunt object creates more turbulence and resistance. Additionally, larger objects will experience more drag compared to smaller objects because they have a larger surface area for the fluid to push against.

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