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

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Does irrotational imply inviscid?

Let us consider a 2D irrotational flow, such that $\nabla\times\boldsymbol u =\boldsymbol 0$. Defining the stream function such that $\boldsymbol u =\nabla\times\psi \boldsymbol n$ where $\boldsymbol ...
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1answer
126 views

Transport theorem derivation question

I am trying to rigorously go through some fluid mechanics proofs and theorems. I am currently going through a proof related to the transport theorem and I am having trouble with a step. The steps in ...
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Hit a bottle of beer on the top with another causes the first to spit all the gas, why?

So, on the other day me and my colleges were discussing the following phenomena: Pick two open bottles of beer. With the bottom of the first, hit the second on the bottleneck, in the following way: ...
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Shape of Fan Blades

How is the shape of the blades of an air fan determined? Trial and error, or is there a theory behind it? What are they trying to maximize, volume of air dislocated per rotation?
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Why does smoke go out the window of the car - and what if there's wind blowing instead of the car moving?

When driving a car while smoking with the window open (safety and legal issues aside), I've noticed that the smoke tends to go outside the window. Why does the smoke go outside? If the car is ...
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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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781 views

How deep is the Great Red Spot?

The Great Red Spot (GRS) is a very persistent storm system that's easily visible through a telescope on the surface of Jupiter. But what is the three-dimensional structure of the GRS, and how deep ...
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Whistle Physics

I'm looking for a simple explanation of how a whistle operates. I know that forcing air over a sharp lip can set up a wave in a resonating cavity, but how? "Most whistles operate due to a feedback ...
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Is there a way to fill Tank 2 from Tank 1 through Gravity alone?

I am a newbie in water system design but I am currently faced with the exact situation below on my land, and I need to know whether gravity alone is sufficient in order to fill Tank 2 from Tank 1, as ...
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What about negative Pressure?

Here is something I see : Let's say the ideal fluid(water here) of density $\rho$ is drawn from a source by a motor and thrown upwards with a velocity $v$. Now we take the power of motor be ...
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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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6k views

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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1answer
952 views

Pendulum with water dripping out

Consider a pendulum, consisting of a string of length $l$ tied to a ball of negligible mass and radius $r$. The bob is filled with water, which has density $d$, and the pendulum is given a small push ...
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647 views

Hydrostatic pressure on a teapot spout

The phenomenon where water flows on the outside side of a teapot spout is named "The teapot effect", and occurs due to a difference in pressure between water and the atmosphere. Consider the image of ...
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1answer
511 views

Viscosity/Entropy ratio and unitary evolution in quantum gravity

Calculations of the shear viscosity of the quark-gluon plasma (QGP), observed in heavy ions collisions, are performed via the AdS/CFT correspondence [ref1]. One finds that the shear viscosity of the ...
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1answer
200 views

Fluids in thermodynamic equlibrium

I am reading about the Euler equations of fluid dynamics from Leveque's Numerical Methods for Conservation Laws (Amazon link). After introducing the mass, momentum and energy equations, some ...
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When is a flow vortex free?

To solve problems in fluid dynamics one states often the assumption that the flow is vortex free i.e. $rot(u) = 0$ It is a basic assumption which is needed for potential flow problems etc.. My ...
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1answer
351 views

Fuel tank draining [closed]

A cylindrical fuel tank is being drained from the bottom as in this picture : Conservation of flow rate : $v_A = \frac{S_B}{S_A}v_B = \alpha v_B$ Assuming that $z_B = 0$, Bernoulli's theorem ...
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2k views

How much lift does an airplane get from its wings, vs the rest of the airframe?

Consider a big commercial airliner, like a 727, 747, or a 787. At cruising altitude, under standard conditions, how much of the lift of the aircraft comes from the wings, and how much from the rest ...
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137 views

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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3answers
4k views

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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3answers
203 views

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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3answers
2k views

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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2answers
529 views

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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1answer
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Properties of Fluids-theoritical confusion

I am having a very basic confusion on how we calculate the height of atmosphere when we assume that the density does not change with altitude(density remains 1.29 kg/m$^3$). I want to know why we say ...
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3answers
249 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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Why does a nuclear explosion have directionality?

It just occurred to me that almost all images I've seen of the (in)famous mushroom cloud show a vertical column rising perpendicular to the ground and a horizontal planar ring parallel to the ground. ...
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What exactly is the difference between advection and convection?

After reading Wikipedia articles on advection and convection, I still cannot determine whether there is a consensus on a difference between these two terms. Sometimes, the term convection seems to ...
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731 views

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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233 views

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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1answer
680 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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1answer
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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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1answer
951 views

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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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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1answer
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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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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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562 views

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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750 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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1answer
564 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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2answers
602 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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2answers
709 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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5answers
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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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2answers
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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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1answer
513 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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1answer
329 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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4answers
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Calculate water flow rate through orifice

I'm not very good with fluid physics, and need some help. Imagine the following setup with water contained in-front of a wall with an opening on the bottom: How do I calculate the water flow $Q$?. ...
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2answers
229 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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3answers
266 views

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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1answer
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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 ...