Tag: q&a

Reader Question: How to Get Started in Fluid Dynamics
unboundid-deactivated20131116 asks:
Hi. I’m a freshman engineering student at UCSD, and I was hoping to get more into fluid dynamics. Could you possibly give a quick shake-down of what I should look into if I’m just kind of starting? I want to either work in studying specifically fluid dynamics or in studying interactions of oil and petroleum.
Glad to hear that you’re interested in fluid mechanics! I usually answer these kind of questions privately, but I’m going to go ahead and publish my answer here because I think the advice is useful for any undergraduates interested in fluids.
First of all, most engineering courses of study won’t cover fluid mechanics–outside of pipe flow–until the junior or senior-level courses. This is because, unlike many other engineering topics, fluid mechanics relies heavily on foundational material in other subjects. Although fluid mechanics is still essentially F = ma, writing and manipulating the fundamental equations requires advanced calculus. So you will definitely benefit from paying a lot of attention in your math courses, especially vector calculus and differential equations. I also highly recommend learning to solve differential equations numerically using tools like Matlab or Mathematica. These are super useful skills for just about any form of engineering, but they can really pay off in fluid mechanics.
Now, while this classroom work is very important, you don’t have to wait until you’ve finished four semesters of calculus and physics before getting into fluid mechanics. Look up the professors at your school and the research they do. Find some topics/projects you want to learn more about, and go meet with those professors. In my experience, professors are willing to have undergraduates–yes, even freshmen–volunteer in their labs. I can’t guarantee that you’ll get paid, but I can tell you that you will learn a lot, especially from the graduate students you will probably be assisting. As you gain experience, you’ll gain responsibility. Right now, my research group has a sophomore preparing to be the lead on a new data collection campaign in one of our best research wind tunnels.
Many professors recruit their future graduate students this way. And, if it turns out that you don’t want to work in that lab through graduate school, you will still have a leg up getting into grad school because you’ll have significant research experience and a professor who can write you a strong recommendation, having seen your work. You could even have co-authorship on a publication, and that sort of achievement is going to look good on your resume, whether you pursue graduate school or an industrial job.
In short: talk to professors about their research and find a lab where you can become a part of that research. The earlier you do this, the more impressive the results by the time you graduate. Good luck!
January 30, 2012
Reader Question: Froude vs. Reynolds
@spooferbarnabas asks: I was wondering what the difference is between Froude’s number and Reynold’s number? they seem very similar
Fluid dynamicists often use nondimensional numbers to characterize different flows because it’s possible to find similarity in their behaviors this way. The Reynolds number is the most common of these dimensionless numbers and is equal to (fluid density)*(mean fluid velocity)*(characteristic length)/(fluid dynamic viscosity). The Reynolds number is considered a ratio of total momentum (or inertial forces) to the molecular momentum (or viscous forces). A small Reynolds number indicates a flow dominated by viscosity; whereas a flow with a large Reynolds number is considered one where viscous forces have little effect.
The Froude number, in contrast, focuses on resistance to flow caused by gravitational effects, not molecular effects. It is defined as (mean fluid velocity)/(characteristic wave propagation velocity). Initially, it was developed to describe the resistance of a model floating in water when towed at a given speed. As the boat’s hull moves through the water, it creates a wave that travels forward (and backward in the form of the wake), carrying information about the boat–much like pressure waves travel before and behind a subsonic aircraft. The speed of the wave created by the boat depends on gravity (see shallow water waves). The closer the boat’s speed comes to the water wave’s speed, the greater the resistance the boat experiences. In this respect, the Froude number is actually analogous to the Mach number in compressible fluids.
I hope that helps explain some of the differences!
February 10, 2011
Reader Question: Hot Air Balloon Physics
lazenby asks:
and boyancy in air? is the lifting capacity of a hot air balloon equal to the modulo of the weight of the air in the balloon with the weight of the same volume of air outside the balloon?
for that matter, does the lift of a big helium weather balloon decrease as air pressure, and so weight of the air outside the balloon, drops? and is this exactly counterbalanced by the lessening density of the helium in the balloon?
all of these things keep me awake.
Hopefully you won’t be sleepless much longer. Buoyancy in air follows the same principles as buoyancy in water. Determining the lifting capacity of a balloon is a matter of determining how heavy the balloon can be before the buoyant force is equal to the weight. See the free body diagram and little derivation below to see what the maximum payload mass is for a helium balloon. You can click on the picture to enlarge it.
The second part of your question raises some interesting points. As a balloon’s altitude increases, the atmosphere around it gets colder and less dense, all of which should reduce the buoyant force. At the same time, the balloon itself expands to equalize the pressure inside and outside of the balloon, which should increase the buoyant force. (At some point the pressure drops sufficiently that the tensile strength of the balloon material is unable to cope with that expansion and the balloon bursts, but we’ll ignore that here.) For this problem, we’d want to know what payload the balloon can carry without losing lift, and, with a couple assumptions, that’s pretty easy to figure out. I’ve done that derivation below.
The real key to the calculation is assuming that the helium in the balloon maintains the same temperature as the air outside. Since balloons rise slowly, this seemed a more reasonable assumption than imagining that the balloon remains warm compared to its surroundings. That calculation is doable as well but requires more than a couple lines, unfortunately! Thanks for your questions!
January 13, 2011
Reader Question: Swimming and Buoyancy
aniiika asks:
How does buoyancy relate to swimming?
Buoyancy is the force that enables a swimmer to float in the water, even when still. Buoyant force is equal to the weight of the fluid displaced by the swimmer; in other words, the density of the fluid multiplied by the volume of the swimmer that is submerged.
Different people float at different heights in the water depending on many factors, such as body shape, amount of fat, and how much air is in their lungs. All of these things affect a person’s volume and/or density, thereby affecting the buoyant force they experience.
Because a person’s body is not fully submerged their center of buoyancy–the point where all buoyant forces on the body can be represented by a single force–does not coincide with the center of mass (sometimes referred to as center of gravity). Where those forces are relative to one another determines the stability of a person floating in the water. Everyone’s center of buoyancy is higher than their center of mass, so people always float stably in an upright orientation. Our legs, for example, don’t float as well as our torsos, so, when floating horizontally, one’s legs will tend to sink.
Swimmers can control their buoyancy to their advantage by actually pressing their upper chests further into the water. This tends to bring one’s hips closer to the surface and can reduce drag (#).
January 11, 2011
Mach Diamonds
Joe asks:
Why does this rocket have that repeating pattern in its exhaust? I’m amazed that it’s so stable for so far as distance from the nozzle.
Excellent question! The diamond-shaped pattern seen in the rocket’s exhaust is actually a series of reflected shock waves and expansion fans. The rocket’s nozzle is designed to be efficient at high altitudes, which means that, at its nominal design altitude, the shape of the nozzle is such that the exhaust gases will be expanded to the same pressure as the ambient atmosphere. At sea level, the nozzle is overexpanded, meaning that the exhaust gases have been expanded to a lower pressure than the ambient. The supersonic exhaust has to reach ambient pressure, and it does so through an oblique shock right at the exit of the nozzle. However, the oblique shock, in addition to raising the pressure, turns the gases toward the exhaust centerline. To ensure flow symmetry, two additional oblique shocks form. But then the exhaust is at a higher pressure than ambient. Expansion fans form to reduce the pressure, but those, too, affect the direction the exhaust gases flow. The pattern, then, is a series of progressively weaker oblique shocks and expansion fans that raise the exhaust gas pressure to that of the ambient atmosphere.
December 13, 2010
Reader Question: Oswald de Waele
fyeahhexagons-deactivated201103 asks:
Could you do a quick post explaining the Oswald de Waele relationship please? Thanks!
Sure! The Oswald-de Waele relationship (a.k.a. a power-law fluid) is an attempt to generalize the relationship between shear stress and shear rate in fluids. For a Newtonian fluid, that relationship is linear:
This relationship describes many fluids–like air or water–very well. But there are plenty of non-Newtonian fluids as well, both shear-thinning (paint, shampoo, ketchup) and shear-thickening (oobleck). The Oswald-de Waele relationship approximates the behavior of these fluids using:
Values of n less than one correspond to shear-thinning (or pseudoplastic) fluids; a value greater than one is a shear-thickening (or dilatant) fluid. And n = 1 corresponds to a regular Newtonian fluid. #
December 9, 2010
Reader Question
aeronode-deactivated20130828 asks:
What’s your academic/professional background? (Just curious.)
Fair question! I am a fourth-year PhD student in aerospace engineering, focusing (naturally) on fluid dynamics. I have a bachelor’s and master’s degree, both also in aerospace engineering. My master’s thesis focused on turbulence and my current work is in high-speed aerodynamics.
December 7, 2010