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

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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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Why don't we talk about angular momentum at all in fluid mechanics?

People usually talk about similar (or maybe not?) things like vorticity or enstrophy in fluid mechanics, but no one talks about angular momentum, why?
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Could some design of a propeller be used in both air and water?

Propellers in water are smaller in diameter. They also move more slowly. On the other hand, aircraft propellers are larger in diameter, have narrower blades and operate at very high speeds. An ...
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Why do ice cubes stick together or to the edges of a drinking glass?

I was drinking iced-water from a drinking glass (made of glass) at a restaurant yesterday when I was taking a drink, I noticed that there is very little ice water coming out and then suddenly, the ice ...
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What part of the fan blade actually does the noise generation?

I'm trying to identify the sources of noise in spinning fan blades and what causes them. Is the noise only generated by the lead edge of the blade 'cutting through' air? and different parts of it ...
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How can these fluid dynamical smoke-ring phenomena be explained?

The Navier-Stokes fluid dynamics equations, said that, as Sir William Thomson (or Lord Kelvin) predicted: When two smoke-rings are moving in the same direction, with the same speed, one behind the ...
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Is surface of a solid a streamline?

In fluid dynamics, streamlines are defined as line where at each point flow velocity is tangential to the line. Is it correct to say surface of a solid a streamline? On the surface the velocity vector ...
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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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Polar vs non-polar fluid

In the book "Vectors, Tensors, and the Basic Equations of Fluid Mechanics" by Rutherford Aris I read the following: If the fluid is such that the torques within it arise only as the moments of ...
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Phase Space Flow

Phase space flow shares characteristics with fluid flow such as incompressibility by Liouville's theorem. Extending the similarities one might be curious, does phase space flow have a characteristic ...
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What are the limitations of Smoothed-Particle Hydrodynamics?

I've been excited by some of the possibilities of Smoothed-Particle Hydrodynamics (SPH). I have seen some very exciting demonstrations of their use in 3D graphics, but I am wondering how well the ...
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Could motives aid in the study of the Navier-Stokes equations?

Recently, mathematicians and theoretical physicists have been studying Quantum Field Theory (and renormalization in particular) by means of abstract geometrical objects called motives. Amongst these ...
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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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How can a droplet of liquid float on the surface of the same liquid?

This can happen during the rain, or when pouring water. Sometimes small (1-2 mm) droplets of water float on the surface for some time (a few seconds) before coalescing with the big body of water. A ...
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154 views

Does Liquid Immersion protect against G forces?

I'm under the impression that if an object is immersed in water it can be protected from the effects of Gravity - or in other terms appear to be in a 0G enviroment. Typical examples of this include ...
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Riemann invariants…Any physical interpretation?

I am really new to the CFD simulation, and started some simple algorithms recently. I then got introduced to the Riemann Invariants. Can any one provide some physical interpretation? Also, why is ...
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How do I intuit viscosity in a rotating fluid?

Suppose I have two plates with a viscous fluid in between. I slide them in the same direction (a direction in their own plane), one at $5 \,\text{m/s}$ and the other at $6 \,\text{m/s}$. Due to the ...
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Atmospheric Circulation

What is the simplest simulatable model giving our rotating earth its 3 circulation cells (Hadley, Ferrel, Polar)? The model should also show 1 circulation cell if the earth's rotation were stopped (or ...
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Helicopter, Tricopter, Quadccopter - what's really happening here? Are there generalized advantages on a small scale?

There have been, it seems, a proliferation of quad-copters commercially available. Amazon seriously tried to use them for deliveries. (Search Drone on their website.) The NFL uses one for cameras. ...
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Why Are Normal Shock Waves Unstable in a Converging Channel?

While learning about shock waves in an introductory Gas Dynamics course, it was revealed that normal shocks are unstable if formed in a converging channel. Even if the local conditions ostensibly ...
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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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What's the most efficient strategy to shake a bottle to create a global flow?

Consider a bottle of orange juice with pieces of the fruit gathered at the bottom of the bottle. You need to shake the bottle to evenly distribute the pieces in the bottle. The first part of the ...
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Could the phenomenon of vortex bursting be exploited to reduce wake turbulence?

One of the classic stories in the annals of aerospace engineering is the development (and subsequent redesign) of the F-18 and its Leading Edge Extensions (LEX) due to fatigue problems, problems that ...
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945 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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Sound Propagation using Finite-Difference Time-Domain (FDTD) considering wind effects

I am trying to plot the propagation of sound from a fixed source in a 2D environment using Finite-Difference Time-Domain (FDTD) Method taking into account the effects of the wind velocity. I came ...
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Is a venturi pump feasible at very low pressure?

I need assistance (or experience feedback) in estimating if a Venturi pump would work at low pressure. A boiler under vacuum (10% atmosphere) will produce steam (at a given speed depending on the ...
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At what velocity does sea water leave a pipe run into a fresh water lake (for equal surface levels)?

If I took a fresh water lake* whose surface is exactly as sea level, and connect it to the sea with a pipe filled with sea water, with both ends of the pipe at exactly the same depth from the surface, ...
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What keeps a gas giant from falling in on itself?

There is not enough gravity at the center to start nuclear fusion, but it seems that there would be plenty enough to collapse the planet.
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Why are Navier-Stokes equations needed?

Can't we picture air or water molecules individually? Then, why are Navier-Stokes equations needed, after all? Can't we just aggregate individual ones? Or is it computationally difficult, or ...
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Why do blades of windturbine propellers as comp. to propellers of ships cover very different areas?

This is a thought I asked myself often, but never did real efforts to get an answer. Barsmonsters question about number of fans of a wind turbine made me think of it again Why do blades of aircraft ...
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Why is the answer to this diffusion example unintuitive?

Imagine a linear decrease in concentration from left to right. Using Fick's first law, $J = -D \frac{d \psi}{d x}$ for all x, from left to right, we have the same flux amount because the decrease is ...
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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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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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Exact Solutions to the Navier-Stokes Equations

There are a number of exact solutions to the Navier-Stokes equations. How many exact solutions are currently known? Is it possible to enumerate all of the solutions to the Navier-Stokes equations?
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Why does bad smell follow people (assuming they are not the source)?

When you are sitting in a room where there is a source of bad smell, such as somebody smoking or some other source of bad smell, it is often a solution to simply move to another spot where bad smell ...
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How does one derive the equation for the speed of sound?

In my acoustics books I see $$c^2 = \frac{\mathrm{d}P}{\mathrm{d}\rho}$$ where $c$ is the speed of sound, $P$ is the pressure and $\rho$ is the density. Where does this equation come from? In my ...
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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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Is there an analytical solution for fluid flow in a square duct?

I couldn't find one but assumed it must exist. Tried to find it on the back of an envelope, but got to an ugly differential equation I can't solve. I'm assuming a square duct of infinite length, ...
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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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Wavy stream of liquid

When pouring a liquid into a glass some streams have a wavy shape, like the one in the following photo: (Couldn't find a better picture, sorry.) What causes the stream to be of such a shape?
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Physical interpretation of the Lorenz system

The Lorenz equations $$ \frac{dx}{dt} = \sigma(y-x);\\ \frac{dy}{dt} = x(\rho-z)-y;\\ \frac{dz}{dt} = xy - \beta z $$ were (I believe) the first set of nonlinear equations known to exhibit chaotic ...
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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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Drag on a spinning ball in fluid

I am a physics newbie (high school level) and I am wondering what happens when a spherical object is spinning on the spot in a bunch of gas (no gravity here, just an imaginary physics sandbox). Am I ...
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Intuitive explanation of Poiseuille's law — why $r^4$?

According to Poiseuille's law, the effective resistance of a tube is inversely proportional to the fourth power of its radius (as given by the following equation). $$R = \frac{ 8 \eta \Delta x}{\pi ...
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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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263 views

How to derive a physical model of temperature above the earth surface?

At a point on the surface of the Earth, if I go straight "up" a distance $z$ (radially outward from the Earth), I'd observe a temperature profile $T(z)$. The conventional wisdom from the meteorology ...
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Why does the higher of two medical IV bags empties first?

I'm a nurse, so my physics background is about that of a lay person. Please explain on that level. Ordinarily an Intravenous (IV) fluid bag is one liter. An IV piggyback is usually 2500ml. usually the ...
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Free surface of inviscid fluid flow

The following problem seems like it should have a definite solution, but I've been thinking about it for months and haven't got anywhere. It might not be a well-posed problem, but if it isn't I'd ...
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Analogue of Princeton Companion to Mathematics for Physics?

I would like to know if there are compendiums much like the Princeton Companion to Mathematics for physics (especially classical physics: fluid mechanics, elasticity theory, Hamiltonian formalism of ...
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Do de Laval nozzles have to be asymmetric?

All pictures of de Laval nozzles I've seen have an hourglass shape where the convergent section is shorter than the divergent section. Is this necessary to attain supersonic exhaust velocities, or ...