Fluid Dynamics -- a spherical particle immersed in water

In summary, the conversation discusses a spherical particle in water experiencing random collisions with surrounding water molecules. Half of the molecules push the particle to the right and the other half to the left, causing a "collision force" that cancels out on average. This leads to the question of whether the particle will still be driven to move. Further questions are raised about the specific situation, such as the size and placement of the particle in the water. The expert summarizes that although the particle will move, the specific circumstances may affect the direction and magnitude of its movement.
  • #1
Prashant Bagga
New user has been reminded to show the Relevant Equations snd show their initial work on the solution

Homework Statement



Consider a spherical particle immersed in water. It will experience random collisions with the surrounding water molecules. Suppose there are such water molecules around the particle. Half (n/2) of the water molecules will push the particle to the right and the other half to the left. On average, this “collision force” (force arising from collisions) vanishes. Does this mean that the particle will not be driven to the right or to the left?

Homework Equations


not sure

3. The attempt at a solutiIn
I know the particle will move. But I am not sure how to explain that using equations.
 
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  • #2
I have the following questions:

1. Is the spherical particle contained in a tank/beaker/vessel?
2. What is the size of the particle comparing to the tank's size?
3. Is the particle immersed in the middle or near the walls of the tank?

How do you know that the particle will move?
 
  • #3
This is kind of like a problem in flipping coins. Even though a coin turns up heads half the time and tails half the time, that does not mean that the cumulative number of heads cannot be greater than the cumulative number of tails at any given time.
 
  • #4
DoItForYourself said:
I have the following questions:

1. Is the spherical particle contained in a tank/beaker/vessel?
2. What is the size of the particle comparing to the tank's size?
3. Is the particle immersed in the middle or near the walls of the tank?

How do you know that the particle will move?

Sir, we are not informed about any of those situations.
 

1. What is fluid dynamics?

Fluid dynamics is a branch of physics that studies the movement and behavior of fluids, such as liquids and gases. It involves the analysis of forces and motion in relation to the fluid's properties, such as density, viscosity, and pressure.

2. How does a spherical particle behave in water?

A spherical particle immersed in water will experience a drag force due to the friction between the particle and the surrounding fluid. The behavior of the particle depends on its size, shape, and the properties of the fluid, such as its viscosity and density.

3. What is the drag force acting on a spherical particle in water?

The drag force on a spherical particle in water can be calculated using the drag equation, which takes into account the particle's velocity, fluid density, viscosity, and the particle's size and shape. The drag force increases with increasing velocity and particle size, and decreases with increasing fluid viscosity.

4. How does the behavior of a spherical particle in water change with increasing fluid velocity?

As the fluid velocity increases, the drag force on the spherical particle also increases, resulting in a decrease in the particle's velocity. This is because the fluid exerts a greater force on the particle, slowing it down. At high velocities, the drag force may become greater than the particle's weight, causing it to reach a terminal velocity where it no longer accelerates.

5. What is the significance of studying fluid dynamics?

Fluid dynamics has many practical applications, such as in engineering, meteorology, and biology. It helps us understand and predict the behavior of fluids in various situations, such as in air and water flow, weather patterns, and blood flow in the human body. This knowledge is crucial for designing and optimizing structures and systems, as well as for understanding natural phenomena.

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