Intro Fluid Dynamics homework question

In summary, the equations from the chapter on fluid dynamics can be used to determine the force necessary to lift a ring with a diameter of 20mm made of fine wire and placed on the surface of water at 20 degrees celsius. Specifically, the equations for shearing stress, kinematic viscosity, change in pressure, capillarity height, bulk modulus, compressibility, and PV^n=constant can all be utilized. However, this problem may also be related to surface tension. The Du Noüy ring method can be used to calculate the force, and the energy equation for surface tension can also be used. Ultimately, the answer is 9.15*10^-3 N.
  • #1
sc0tt
5
0
How much force is necessary to lift a ring, diameter 20mm, made of fine wire, and placed on the surface of water at 20 degrees celsius?
All the equations from the chapter:
Shearing stress = F/A = Viscosity*(velocity parallel/h)
Kinematic Viscosity = viscosity/density
Change in pressure = 4(surface tension/diameter)
Capillarity height = 4Tcos(theta)/(g*diameter*density)
Bulk modulus = -V*(change in pressure/change in V)
compressibility = 1/Bulk modulus
PV=RT
PV^n=constant

I'm learning fluid dynamics on my own for possible research so I don't have any professor or guidance, just a book. This makes solving problems much more difficult. With this problem specifically, I'm lost because I feel like the mass of the ring must be known as part of the problem, but no other information is given. This leads me to believe it has something to do with surface tension, compressibility, or shearing stress (this equation contains force).
My initial reaction was to solve the first equation for force and substitute the second equality in for shear stress. This leaves:
F=A*(viscosity*velocity parallel/h)
but there is no velocity parallel or required height.
The other equations don't seem to be of any help.
The answer the book gives is 9.15*10^-3 N
Thanks for any help,
Scott
 
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  • #2
Sounds interesting, what book are you reading?

I'm quite lost myself when it comes to fluid dynamics, but I'd relate this problem to surface tension. More specifically, the Du Noüy ring: http://en.wikipedia.org/wiki/Du_Noüy_ring_method.

I got the right answer, but using a bit ad hoc methods (well, maybe not, but had you not supplied the answer, I would probably not be writing this reply). I thought of the thing as creating two surfaces (inner, outer) when you begin to lift the ring. I wrote an equation for the energy, and thus obtained the force.

EDIT: And yeah, I ignored the weight of the ring thing, as I suppose if you do these things experimentally, you add a counterbalance to get rid of it + I suppose it's supposed to be very, very light.
 
Last edited:
  • #3
The book is "Introduction to Fluid Mechanics" by Y. Nakayama. so are you saying you don't use any of the equations the book gives? If possible could you please list out the energy equations, my physics is better but i don't see a solution using energy either. Gravitational is mgh, energy from surface tension would be... ?
Thanks
 
  • #4
Well, that's how I would do it, but again, having little experience with fluid dynamics, there might be other, better, solutions.

Energy from surface tension would be the tension times the area, i.e. gamma * 2 * 2*pi*r*h. Differentiate w.r.t. h, and you've got the force, I suppose.
 

Related to Intro Fluid Dynamics homework question

1. What is fluid dynamics?

Fluid dynamics is the study of fluids in motion, including liquids and gases. It involves understanding the behavior and properties of fluids, such as velocity, pressure, and viscosity, and how they interact with solid objects.

2. What is the purpose of this homework question?

The purpose of this homework question is to test your understanding of basic fluid dynamics concepts and principles. It also allows you to apply these concepts to solve real-world problems and develop critical thinking skills.

3. How do I approach solving this problem?

First, carefully read and understand the given problem and its requirements. Then, review the relevant fluid dynamics concepts and equations. Next, make any necessary assumptions and draw diagrams to visualize the problem. Finally, use the appropriate equations and solve for the unknown variables.

4. Can I use any equation to solve this problem?

No, you should only use equations that are relevant to the given problem and its specific conditions. Additionally, you should always check the units and dimensions of the variables to ensure they are consistent.

5. What are some common mistakes to avoid when solving fluid dynamics problems?

Some common mistakes to avoid include using incorrect or irrelevant equations, not accounting for all the forces acting on the fluid, and not paying attention to the units and dimensions of the variables. It is also important to double-check your calculations and ensure they make physical sense in the context of the problem.

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