The quantitative study of how fluids (gases and liquids) move.

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Why do galaxies and water going down a plug hole spin?

We all experience things spinning, whether it's water down a drain, the earth on its axis, planets round the sun, or stars in a galaxy - even electrons round an atom. But why is spin so common in ...
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How to estimate the Kolmogorov length scale

My understanding of Kolmogorov scales doesn't really go beyond this poem: Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity. ...
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Why does water flow out of an upside-down bottle? (Rayleigh Taylor Instability)

I am currently reading the excellent book An Indispensable Truth: How Fusion Power Can Save the Planet by Francis F. Chen and I came across this explanation. The Rayleigh–Taylor Instability ...
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Why does a transformation to a rotating reference frame NOT break temporal scale invariance?

Naively, I thought that transforming a scale invariant equation (such as the Navier-Stokes equations for example) to a rotating reference frame (for example the rotating earth) would break the ...
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The Galileo thermometer: why do the bubbles float in the middle of the tube?

If the water were uniform temperature, it would have uniform density, so a bubble should either be all the way at the top (if it's lighter than water) or all the way at the bottom (if heavier). But in ...
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What is enstrophy?

In turbulence, the enstrophy of a flow in a domain $\mathcal{D} \subset \mathbb{R}^{D}$ $$ \mathcal{E} = \int_{\mathcal{D}} |\vec{\nabla} \times \, \vec{v}|^2 d^{D}x $$ appears sometimes, it's cool ...
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What does the quantification of causes and effect look like, for clouds in offshore wind turbine wakes?

At Horns Rev windfarm off the coast of Denmark, sometimes in winter, clouds appears in the wake of the turbines. I've only seen photos of the phenomenon when the wind direction is exactly aligned with ...
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Explanation that air drag is proportional to speed or square speed?

A falling object with no initial velocity with mass $m$ is influenced by a gravitational force $g$ and the drag (air resistance) which is proportional to the object's speed. By Newton´s laws this can ...
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A fly in an accelerating car

A fly is flying around in a car, the fly never touches any surface in the car only fly’s around in the air inside the car. The car accelerates. does the fly slam in to the rear window. or does the fly ...
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Conservation Vs Non-conservation Forms of conservation Equations

I understand mathematically how one can obtain the conservation equations in both the conservative $${\partial\rho\over\partial t}+\nabla\cdot(\rho \textbf{u})=0$$ ...
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How does a hole's size affect the distance that water will squirt

I took a bucket, drilled 2 different sized holes on the side near the bottom and filled it with water. The stream of water the proceeded from the larger hole traveled further than the stream from the ...
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Water pressure in free fall

The increasing water pressure as you go deeper is generally explained in terms of the weight of the water column above the observation point pressing down. The question, then, is what would happen if ...
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Why does the water level equalize in a series of tubes?

Say I have a series of tubes (not the internet) looking like this, where w represents water: ...
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Differences in the behaviour of pinching a garden hose and closing a tap

Let's say you have a garden hose connected to an ordinary water tap which is opened fully. If you pinch the end of the hose, water leaves the hose at a higher speed (and this can be useful while ...
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316 views

Strange behaviour of water drops on a heated pan

I did an experiment in my home and I was surprised by the results. I heated a pan without anything in it. After some time it became very hot and I took some water (2 drops) and put it into the pan. It ...
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802 views

How much effect does the Bernoulli effect have on lift?

I understand that the Bernoulli effect is a flawed explanation for the cause of lift, and does not cause much at all, but how much? Is there any experimental data on the force caused by the ...
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897 views

Friction term in Navier-Stokes equation

The friction term in Navier-Stokes equation assumes that the viscosity coefficients are the same for the longitudinal and transverse directions. This doesn't seem intuitive, because the former is ...
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Would a solution to the Navier-Stokes Millennium Problem have any practical consequences?

I know the problem is especially of interest to mathematicians, but I was wondering if a solution to the problem would have any practical consequences. Upon request: this is the official problem ...
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water flow in a sink

When one turns on the tap in the kitchen, a circle is observable in the water flowing in the sink. The circle is the boundary between laminar and turbulent flow of the water (maybe this is the wrong ...
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finding equation of a water droplet

I have a water droplet which is falling down through its gravity. I've supposed that my droplet is an ellipsoid and I want to find the equation that represents this ellipsoid in XYZ coordinate system. ...
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Why aren't airplanes like golf balls?

Ok this is a silly question but here it goes Although it is good to have a laminar flow of the air around the object for low drag but the laminar flow is prone the phenomena called separation (sounds ...
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What is the microscopic picture for warm air rising?

The usual explanation for warm fluids rising past cooler ones is that the warmer fluid has a lower density. I'm trying to understand what this looks like at a molecular scale. The density seems to ...
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859 views

How much of the forces when entering water is related to surface tension?

When an object enters water with high velocity, (like in Why is jumping into water from high altitude fatal?), most of it's kinetic energy will be converted, eg to accelerate water, deform the object ...
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681 views

Why water in the sink follow a curved path?

When you fill the sink with water and then allow the water to be drained, the water forms a vortex.. And then it starts to follow a curved path downwards by effects of gravity.. Why this phenomena ...
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Physical Explanation for “Kolmogorov -5/3 spectrum” in Fluid Mechanics

According to Kolmogorov, the energy spectrum function of a turbulent fluid is given as, $E(k)=C\epsilon^{\frac{2}{3}}k^{\frac{-5}{3}}$ where $\epsilon$ is the energy flux and $k=\frac{2\pi}{r}$ ...
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Physics of how the cochlea isolates frequencies along its length?

Can anyone explain the separation of frequencies along the basilar membrane of the cochlea please? (equations would be nice) I understand it being related to the resistance caused by fluid in the ...
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Boundary layer theory in fluids learning resources

I'm trying to understand boundary layer theory in fluids. All I've found are dimensional arguments, order of magnitude arguments, etc... What I'm looking for is more mathematically sound arguments. ...
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How do subgrid-scale parametrisations in climate models work?

Global Circulation Models typically have grids of 100-300km on a side. There are obviously lots of atmospheric processes that happen at smaller scales than this. Convection, cloud formation, the ...
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How can I understand a Vortex Tube and its efficiency?

A Vortex Tube takes a pressurized input stream, most typically of a gas, and creates two output streams with a temperature differential. Apparently, it has been described as a Maxwell's Demon. Both ...
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What can wavy patterned sand tell about the Fluid that formed it?

Sand on the bottom of the ocean as well as sand on the low-tide beach often forms wavy patterns. Do the parameters of these wavy patterns have any relation to the water and waves that formed them? If ...
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What is the symmetry associated with the local particle number conservation law for fluid?

According to Noether's theorem, every continuous symmetry (of the action) yields a conservation law. In fluid, there is a local particle number conservation law, which is ...
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Zigzag flow of water along a vertical glass window

I've observed this behavior many times. When it rains, the rainwater will form vertical channels along a glass window. The flow of water is mostly confined within these vertical channels and the ...
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Equation derivation for skipping rocks

oWhy can rocks skip over water? For instance, if you conduct an experiment where you drop both rocks from the same height, but give one considerable acceleration in the x direction, one will fall in ...
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Self Stirring Boiling Liquid

A couple of weeks ago, a friend and I were brewing a new batch of beer. We boil our wort in a turkey fryer. Pretty standard setup for beginners. Anyway, our wort was getting pretty close to boiling ...
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Fluid Mechanics with calculus on manifolds

Fluid Mechanics is a branch of physics that uses a lot of vector calculus in $\mathbb{R}^3$ to describe phenomena mathematically. Calculus on manifolds, however, is the straightforward generalization ...
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Lagrangian Coordinates in Fluid Flow

I apologize if this is not the right place to ask this question: I am currently reading a paper by Y. Brenier, where for the fluid flow he introduces a Lagrangian label $a$ instead of the vertical ...
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Why can't helicopters reach mount everest?

Is there a reason why people can't just take the helicopter to mount Everest? Why is it that helicopters can't reach that high?
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Conserved quantities and total derivatives?

I am having a bit of a crisis in understanding of the physical meanings of total derivatives. When a quantity $\rho$ (be it a vector or a scalar) is said to be conserved, then (mathematically) ...
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What equation of state is needed for liquid states?

I'm familiar with the ideal gas law $$PV=nRT$$ but I don't think it applies to liquids like water. If I'm wrong, please correct me! If I'm right, then what equation of state applies to liquids such ...
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Why do non-Newtonian fluids go hard when having a sudden force exerted on them?

You can dip your hands into a bowl of non-Newtonian fluid but if you are to punch it, it goes hard all of a sudden and is more like a solid than anything else. What is it about a non-Newtonian fluid ...
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Why is there a space between the flame and the nozzle on the space shuttle?

Why is there some space between the flame and the nozzle on the space shuttle? (see above picture)
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What does the Reynolds Number of a flow represent physically?

What does the Reynolds Number of a flow represent physically? I am having trouble understanding the meaning and the utility of the Reynolds number for a certain flow, could someone please tell me how ...
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How is viscosity described on the molecular level?

What is the 'molecular' origin of the viscosity? The molecular origin of elasticity is almost clear for me: at the very bottom the 'elasticity' comes from the attraction and repulsion between atoms ...
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How to make the bubbles in my soda drink last longer?

I would like to make the bubbles in my soda drink last longer. For example, one good thing to do is to keep the bottle shut when you don't drink. But what else I can do? Should I try to minimize the ...
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How does the divergence theorem justify the integral form of the continuity equation?

I vaguely understand the continuity equation (at least its integral form), but I don't really understand the differential form of the continuity equation. I'm having trouble understanding how to ...
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Can air bubbles sink at extreme depths? [duplicate]

I was thinking earlier about air bubbles in water. if you had a bubble of air (say in a balloon) then as you take it down in water the bubble shrinks because of the pressure and because it is ...
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What is Relativistic Navier-Stokes Equation Through Einstein Notation?

Navier-Stokes equation is non-relativistic, what is relativistic Navier-Stokes equation through Einstein notation?
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In terms of scale, where does the concept of Reynold's number cease to have meaning?

The Reynolds number is classically described in terms of pipe geometries but its use has also been usefully extended to other more complex surface geometries to predict transitional flow behavior. But ...
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How is the water meniscus at the edge of a capillary tube

Suppose we have a capillary tube in which water can rise to a height of x cm. If we dip the tube such that the height above the surface is less than x, then how will the water meniscus be at the edge ...
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General procedure for solving fluid flow problems

Could someone help me devise a short series of steps for solving an arbitrary fluid flow problem? Often the most difficult part of these problems is just figuring out what path to take in solving ...