Category: Reader Questions

Reader Question: General Audience Fluids Books
nothing43-blog-blog asks:
Do you know any good books on fluid dynamics? Not textbooks or handbooks, but more along the lines of what you’d find in the “popular science” section of the book store – accessible to a larger audience. Or maybe a good “history of fluid dynamics” book?
That’s a great question! To be honest, I really haven’t seen any general audience fluid dynamics books–fluid dynamics is a field I like to refer to as “the physics physicists gave up on”–but that doesn’t mean there aren’t any. I know fluid dynamics shows up in Feynman’s books (which are excellent reading regardless), and I read a great biography of G. I. Taylor written by G. K. Batchelor that discusses Taylor’s life and contributions to fluid mechanics through two World Wars and the aftermath. Van Dyke’s Album of Fluid Motion is a classic that’s not heavy on technical material. I’ll look into a couple of others as I get hold of them and post any suggestions I have. In the meantime, does anyone else have some general fluid dynamics reading suggestions?
March 2, 2011
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: Surface Tension vs. Viscosity
lazenby asks:
How can superfluid liquid Helium have zero viscosity while retaining surface tension? (assuming something like surface tension is required for a liquid to form drops)
The short answer is that surface tension and viscosity are two totally separate properties for a fluid. To illustrate how one can exist without the other in a superfluid, we’ll imagine two different scenarios. For the first, imagine that you have a narrow vertical pipe. Any fluid you put in the pipe will flow downward due to the force of gravity. If you put water through the pipe, you’ll get some rate of outflow. Now imagine putting something like molasses through the pipe. Even with the same external forces on it, the molasses will never move through the pipe as quickly as the water does. This is because the molasses has higher viscosity and resists flowing. In a force balance, viscosity would act like friction, opposing the downward motion of the fluid.
Surface tension arises from a different balance of forces. Now imagine that you have a stationary droplet of one fluid (A) floating in a different fluid (B). Deep inside the droplet, each molecule of Fluid A is being pulled on all sides by other identical molecules of Fluid A. A molecule at the surface of the droplet, though, doesn’t experience that neighborly pull on all sides; it experiences different intermolecular forces from Fluid B. Our imaginary droplet is stationary, though, so all the forces on it and all the forces on its individual molecules have to balance, otherwise there’d be acceleration. Surface tension acts along the interface by pulling molecules of Fluid A in toward one another–much like the elastic of a balloon–thereby balancing the forces in the droplet and equalizing the force across the interface between Fluid A and Fluid B. (Illustration credit: Wikipedia)
In the superfluid, this balance of forces across the interface between air and helium-3 must still exist, despite the superfluid’s lack of viscosity.
January 20, 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
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
Reader Question
loscheiner asks:
So the video about the ooblek was clearly filmed at CU Boulder. Do you go to school here?
Also, you should enable disqus comments or replies to your posts!
Nope! I have connections to three different universities (one of which has been featured here), but none of them is CU Boulder. I just found that video on YouTube.
November 7, 2010