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

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Explicit form of the entropy production in hydrodynamics

I'm trying to understand how hydrodynamics arise from a precise, mathematical formulation of thermodynamics, learning mostly from Landau's "Hydrodynamics". So Landau starts from formulating the ...
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Why should fluids be confined for Pascal's Law to be applicable

When is Pascal's law about fluid pressure propagation applicable? Is it applicable to a closed circular pipe with a pump rotating the fluid, but not to a tub of water. Most statements require only ...
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Mathematical Reasoning for Fluid Pressure as a Scalar

This question from a while ago and answers/comments to this question from earlier today both make heavy mention of the fact that fluid pressure is a scalar. Although this information was surprising ...
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Probability distribution in phase space and Liouville's theorem?

We can define a probability distribution over phase space (say 1D) $\rho(x,p)$ such that, for example, $$\langle x\rangle = \int x \rho(x,p) dxdp$$ etc. It can be shown here that such a distribution ...
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What is the velocity area method for estimating the flow of water?

Can anyone explain to me what the Velocity Area method for measuring river or water flow is? My guess is that the product of the cross sectional area and the velocity of water flowing in a pipe is ...
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Finding an equation relating the mass of a blade of a wind turbine to its velocity

I'm writing up my physics coursework and I thought I'd try and find an equation described in the title. This is my attempt: Is it correct?
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Why airplanes fly: the final truth

The questions about the reasons the aircraft fly are frequent among scientist, since the high school until now, even if I work on the other side of fluid mysterious world (the Low Reynolds numbers ...
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231 views

Navier-Stokes system

I have to study this system which name is Navier-Stokes. Can you explain please what means that $p$, $u$ and $(u \cdot \nabla)u$. What represents in reality? Tell me please, how should I read the ...
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How does liquid in a ball affect its rotational acceleration down a ramp?

Suppose we have a shell with mass $M$ and radius $R$. If we let that roll without slipping down a ramp of angle theta to the horizontal, we can easily find the acceleration of the shell the instant ...
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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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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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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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Deriving shallow water equations from Euler's equations

I would like to derive the one-dimensional shallow water equations from Eulers's equations. This works perfectly for the conservation of mass. Especially the meaning of the longitudinal fluid ...
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Fluid in a rotating cylinder

I have been wondering why a fluid in a rotating container has a parabola shape? Is it possible to prove this mathematically?
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632 views

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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Why does pressure act as a source for the gravitational field?

I'm asking for a qualitative explanation if there is one. My own answer doesn't work. I would have guessed it's because when a gas has pressure the kinetic energy adds to the rest mass of a given ...
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Effect of water pressure on sinking objects

As I understand, water pressure increases as we go towards bottom of the ocean. So if an object* is thrown into water and it starts sinking with some speed, does the sinking object's acceleration ...
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Why do liquids separate in space?

I've seen videos of people in space (on ISS) who squeeze a bottle or something and liquid comes out, it then separates into smaller balls. Why is this surely it should stay pretty much together ...
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Problem understanding basic sail mechanics

I am trying to understand the physics behind a single sailed boat. I have read the following questions Sailing against the wind. Is this a fair model? What exactly is the 'lift' of a ...
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393 views

Why does a container with fluid make different sounds at different fluid levels?

Have you ever noticed that when you are filling a container with fluid. As it approaches the top, it makes a different sound? You can tell by listening when your about to reach the top. Why is this?
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Solving the Young-Laplace equation for arbitrary axisymmetric geometry

Say I have a non-ellipsoidal soap bubble and I want to numerically analyse the pressure in the inner lobe of this bubble here: The Young Laplace equation gives the pressure difference across a ...
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554 views

How does Earth's interior dynamo work?

I'm interested in getting a basic physical understanding of how Earth's magnetic field is generated. I understand that it's a "dynamo" type of effect, driven by convection currents in the molten outer ...
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641 views

When does a pot not spill?

What shape for the edges of a pot and what surface properties are best for a tea pot not to spill? Apart from the cross-section from the side, how does the radius of curvature as seen from above play ...
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Is it possible to accelerate air to supersonic speeds? What would it look like?

The speed of sound is the rate that disturbances in air propagate through it. Is it possible to have a wind that itself is moving at supersonic speeds relative to stationary winds around it? Or ...
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Flow of liquid among branches

If water is flowing through big pipe is branched into 4 branches of small pipe. Lets say the flow is around 4 m/sec. I have the following questions: What will be the flow rate in each of the ...
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487 views

Fluid Mechanics from a variational principle

It is possible to define a good variational principle to describe Fluid Mechanics? if so, what is the correct treatment of the issue. I guess something like: $$I=\int d^4x \left(\frac{1}{2}\rho ...
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207 views

What is the theoretical justification for a fluid flow's being irrotational?

I am not a fluid dynamicist, and I really just began thinking about this problem as my curiousity drew me into building an answer for the question What really allows airplanes to fly?. It is very ...
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How to compute the speed necessary for an airplane to fly?

I give some physics lessons to a friend. She asked me a question that I am unable to answer. Could you help me ? A plane has a weight of $2\times10^6$kg. The surface of the wing is $1200 \text{m}^2$. ...
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How far will water squirt out from a hole in a can?

Say you have a bottle of water filled up to a height H. A small hole is drilled in its side at a height d, so that water squirts out. The squirting water travels in an arc as it falls, covering some ...
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125 views

Why do vapour cones form around jet fighters?

Apparently this phenomenon has nothing to do with jets breaking the sound barrier and has something to do with the Prandtl-Glauert singularity as described on Wikipedia. But, the Wikipedia article ...
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249 views

How Reynolds number was derived?

I'm studying fluid dynamics and recently the formula $Re=\frac{\rho vd}{\eta}$ was presented to me. I'm curious to know how Reynolds came up with this relations between this different variables. Did ...
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Is turbulence due to the inertia of the fluid?

Turbulence is the time-dependent chaotic behavior seen in many fluid flows. Why is it generally believed that turbulence is due to the inertia of the fluid?
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257 views

What equations/constants were used to calculate the Kármán Line for Earth?

I am interested in how the original value of ~100 km was calculated for the Kármán line of earth. What equations and constants would need to be used to reproduce this value? Note: By constants, ...
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36 views

How does a piezoelectric drop generator work?

In a piezoelectric drop generator used for generating a single droplet which is 0.5 mm in diameter, there is a piezo-actuated brass diaphragm to generate droplets (for example here or here). What is ...
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Could a fish in a sealed ball, move the ball?

If you had a glass ball filled with water, completely sealed and containing a fish, could the fish move the ball?
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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 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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Sailing against the wind. Is this a fair model?

I was ruminating the explanations about how boats can sail against the wind (or "into the wind"), and wondered if one could devise a simple mechanical model without hydrodynamics involved. Imagine a ...
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767 views

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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Distance a curveball travels?

I've seen some discussions regarding the movement of a spinning object, say a curveball. However, all have been largely qualitative. I was wondering if anyone has seen or worked through a ...
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570 views

Why can, or can not, a perfectly incompressible fluid exist?

Water is normally assumed to be an incompressible fluid - for example in the context of calculations involving water pressure. I wondered whether that is strictly true, or an approximation? Later I ...
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Home experiment question

I want to make a home experiment where I roughly explain the phenomenon of water remaining in a straw if you close one end of the straw. So I'm thinking that the weight of the water is pulling it ...
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Deuterium density in seawater

I heard today that deuterium for nuclear fusion could be extracted from the Oceans, in which it is present in "heavy water." I heard this claim: "Deuterium is distributed uniformly with Ocean ...
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How far can water rise above the edge of a glass?

When you fill a glass with water, water forms a concave meniscus with constant contact angle $\theta$ (typically $\theta=20^\circ$ for tap water): Once you reach the top of the glass, the water-air ...
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Non-Newtonian Fluid Stop a Bullet?

I just saw a YouTube video about Non-Newtonian fluids where people could actually walk on the surface of the fluid but if they stood still, they'd sink. Cool stuff. Now, I'm wondering: Could a pool ...
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Why does your car lurch toward an oncoming truck as it passes you?

I notice that the larger the truck the greater the magnitude of the lurch. Can anyone give a physical explanation to this?
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Is it possible for wind to break the sound barrier?

I understand that in nature wind would never get high enough, but I am just curious as to whether physics would allow this to occur or not.
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Integrating pressure over a surface

Consider the 2D airfoil below. In engineering (and maybe physics) you will often see something like the following as an expression for the pressure force acting on a surface (in this case a curve ...
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What does the Froude number represent?

While reading on Wikipedia, I read the following The Froude number is defined as: $$\mathrm{Fr} = \frac{v}{c}$$ where $v$ is a characteristic velocity, and $c$ is a characteristic water ...
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atmospheric phenomenon? What causes condensation trails to converge?

This air plane just caught my eye. Two contrails apparently are flowing backward, slightly off-centered and then ultimately converge, giving the overall shape of a very narrow rhomboid parallelogram, ...