Question
QUESTION: I'm a high school student and I'm doing a research paper on the feasibility of the application of streamlined structures in the interior of a solar convection tower.

My knowledge in fluid dynamics is very basic, more like for high schoolers with all the formulas and the like. It would be better would like to solicit answers from an expert in the field.

So, my questions are:

- What are streamlines? How do they work?
- How do physical objects affect airflow? In regards to the type of material used, shape, and length?
- Is their such a formula that can compute on how physical objects affect the flow of fluids? The nearest equation I could get is the R=Av formula but I'm not sure if it is applicable.
- Lastly, can I use Bernoulli's equation in my study?

ANSWER: Hi Yrza - If we imagine that tiny colored dots are imbedded in a fluid, the path that those dots take as the fluid flows around a body or along a duct are called streamlines. But the flow has to be smooth. If it becomes turbulent, we no longer have streamlines. In other words, streamlines are the paths taken by smooth flow; the path being always parallel to the velocity vector at each point.

Physical objects cause fluid streamlines to change direction and the flow to accelerate or decelerate depending on the pressures that develop on the object. Simple examples are a ball in flight, or a wing in flight. The objects alter the flow and the flow alters the motion of the object. Of course shape, size, density, orientation (angle of attack) of the object all have a big effect on the flow and the aerodynamic forces.

The study of fluid mechanics involves the study of many important equations, too many to discuss here. But usually we can trace them back to basic physics such as Newton's laws of motion. A simple example is:

L = cl rho (V^2)/2  S

where L = wing lift, cl = lift coefficient (a number that depends on wing shape and angle of attack), rho = air density, V = airspeed, S = wing area (cross section)

I don't recognize your equation without some definition of the the variables. Bernoulli's equation is an important equation that you can use to relate fluid pressures and velocities along streamlines. But you have to stay on a streamline to make it work correctly. Aerodynamicists use Bernoulli's law often, because they may know the velocities on a wing and wish to compute the pressures (or lift force) or they know the pressures and wish to compute velocities.

Good luck in your studies. I am sorry to hear about the suffering and damage from the typhoon.

Paul

---------- FOLLOW-UP ----------

QUESTION: I thank you for your condolences with the suffering caused by the typhoon, Sir Paul. My country has went through this many times, rest assured, we'll get back on our feet again.

What do you mean by, "But you have to stay on a streamline to make it work correctly.", sir?

As for R=Av formula, sir, according to my high school physics textbook would go like:

M1 = M2 or P1V1 = P2V2

Since: V = X/T and X = VT, therefore;

P1(Ax)1 = P2(Ax)2

P1A1(VT)1 = P2A2(VT)2

Thus, the final equation is: P1A1V1T1 = P2A2V2T2

The reason why it was R=Av, sir, according to my textbook is "Because mass and density are constant and the time of travel will be the same for both ends, this leads to the equation of continuity  as: A1V1 = A2V2."

"Because Av is a constant, then it's product is considered as the rate of flow or amount of fluid moving through the tube at a period time, therefore: R = Av."

Can you explain this equation to me, sir, in layman's terms?

Another question, sir, is that aside from the previous formula you gave me, what other formulas can you suggest?

And from your point of view, Sir Paul, since I want to get the opinion of an expert in this field, do you think that my study is feasible? If we are to base your opinion from your experiences and knowledge as an aeronautics engineer.

OK - imagine flow along a duct that passes through a venturi. If we know the pressures (total and static) and velocity on the centerline, for example, upstream of the venturi then we can compute the pressures and velocity in the venturi using Bernoulli's law and the continuity equation. But we have to stay on the centerline because that is the streamline we chose. If we move off the centerline in the venturi we will find different pressures and velocities not as easily related to the upstream values. We cannot move across streamlines if we want to use Bernoulli's law.

Your equation of continuity is based on the fact that in steady state flow along a duct, the volume rate of flow at any cross section must be equal to the volume rate of flow in every other cross section. A1V1 = A2V2 where A1 is cross section area at station 1, V1 is velocity at station 1 and similarly for station 2. This is very logical. It is easy to imagine putting 1 cubic meter of fluid into the duct at a certain rate (m^3/second) and seeing the same cubic meter/second coming out the other end during steady state conditions. The areas can be different and the velocities can be different, but the volume flow rate must be constant. (Density is assumed constant at low speeds.)

As for formulas, I suggest you get an aerodynamics book and see what you can find. The drag equation might be good to look for. As for your project, it is always good to optimize fluid mechanics, but I know nothing of what you are trying to do so can give no specific suggestions.

Paul
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 9 Politeness = 10 Comment Thanks, Sir Paul! :D I really appreciate the help and the info you gave me.

Aeronautical Engineering

Volunteer

#### Paul Soderman

##### Expertise

Aeronautics, Aerodynamics, Fluid Mechanics, Aeroacoustics, Noise Control, Muffler Design, Wind Tunnel Research.... I know nothing about India - do not ask about schools, jobs, application requirements, career choices, etc. for India. Please, no text message verbiage; I prefer full words in full sentences. Thanks.

##### Experience

38 years as research engineer at NASA

Publications
AIAA, NASA

Education/Credentials
B.S. and M.S. Aeronautical Engineering - U. of Washington, Graduate work Standford U.

Awards and Honors
AIAA Associate Fellow (American Institute of Aeronautics and Astronautics)