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

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Air pressure in closed (circular) tube

I have learned that for fluids and gases $P_\text{total}=P_\text{dynamic} + P_\text{static}$. Suppose we have a closed circular tube in a form of ring filled with air under some pressure. In this ...
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217 views

pressure in fluid mechanics of incompressible liquid

Most liquids can be approximated to be incompressible, since the Mach-number is much smaller than 1. That means that the density variations are negligible and from the relation between pressure p and ...
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190 views

When to use ideal gas law in fluid mechanics?

The ideal gas law (aka the equation of state) is given by $$ p/\rho_N = k_BT, $$ where $\rho_N$ is number density. When am I allowed to use this to describe a fluid?
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How to freeze the Niagara waterfalls?

Here is a picture of the usual vigorous Niagara Falls (in the winter). Here is the picture of Niagara Falls frozen in 1933 (in the very cold winter). Here is the picture of Niagara Falls frozen in ...
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119 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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2k views

Festive physics: gold flake vodka

I have a bottle of vodka that has a load of gold flakes suspended in it. It has been sat still for over 24 hours and the flakes are all still suspended within the liquid: they have not risen to the ...
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124 views

Is it possible to use the parabolic shape of a rotating fluid to measure the angular frequency of the rotation of the Earth?

A fluid in a rotating bucket will take on a parabolic shape (for example of some simple derivations of this result see http://en.wikipedia.org/wiki/Bucket_argument). The assumptions that play into the ...
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137 views

Acceleration of particles in a pipe with variable cross section

I am currently making an exercise from Paterson,1983, IV.3.ii. It goes as follows Water flows steadily and incompressibly along a pipe whose area cross section $A(x)$ varies slowly with the ...
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137 views

Maximum liquid velocity in a siphon

According to wikipedia: Siphon, the velocity of liquid in a siphon is equal to $\sqrt{2gh}$, where h is the difference in level between the water surface and the opening of the siphon. But it also ...
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271 views

What is the aperture in the hydraulic analogy of Ohm's law

Note: My question is duplicate of Why doesn't water come out of tap/faucet at high pressure when I turn it on?. None of the answers given there explains how the continuity equation fits properly. ...
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73 views

shear and normal stresses

When we talk about shear stresses in a fluid, we find that the shear stress is given by $$\tau_{xy} = \mu(\partial_y u + \partial_x v) = \tau_{yx}$$ This relation we get when only looking at one side ...
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Does pressure drop across pipe affect flow rate?

Let's say there is a main pipe containing $100\: \mathrm{m^3/hr}$ a fluid of density $750\: \mathrm{kg/m^3}$ and it's gonna be branched into 2 pipes (Pipe A and Pipe B) of the same diameter. If Pipe A ...
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154 views

Units of the PDF in the Lattice Boltzmann Method

In the Lattice Boltzmann method we require (based on mass conservation) that the sum of the distribution functions for a node is equal to the density, i.e. $$ \sum_i f_i = \rho $$ But what units do ...
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958 views

Physical description of momentum flux tensor

In the field of fluid mechanics, what is the momentum flux tensor? Is there an easy explanation for how it "works"?
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142 views

Freezing water in a closed container [duplicate]

We know that density of ice reduces by about 8% during freezing, this means it expands to have little higher volume. But if I fill water in a container (entire volume) which has very low coefficient ...
3
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1answer
100 views

Pressure difference between 2 side of wings of aircraft

I understand why the pressure is reduced above the wings of aircraft, but when I read books and look for information, it says that the air is compressed below the wings, I do not understand why it is? ...
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67 views

What will happen to a compressible fluid filled inside a sealed container when the container begins to accelerate?

Assume the fluid to be air and the container to be a car, will there be a pressure gradient which will result the fluid to stack at one end of the car or there is something else that I'm missing?
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60 views

Noether's theorem in the realm of superfluids

In 1969 Keith Moffat showed helicity conservation for ideal fluids such as liquid Helium. This work is proving seminal in our understanding of turbulent flows and viscous fluids. In the case where ...
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183 views

What is a projection method?

Quoting from Solenthaler et. al. Predictive-Corrective Incompressible SPH (ACM Transactions on Graphics, Vol. 28, No. 3, Article 40, Publication date: August 2009) (PDF link here) These ...
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85 views

How to estimate the time spending along the fluid flow

I have a 2d flow field with a singular point $$\dot x=y-px^2\\\dot y=-x-qy^3$$ where $p,q$ are small parameters. How do I compute the cost time of a particle from $(x_0,y_0)$ to ambient of the ...
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223 views

What kind of energy does superfluidity use?

Liquid helium (and other similar fluids) can "climb up" the walls of their containers. Who does the work in this case, and what kind of energy does it use? I'm sure we can't make a perpetuum mobile ...
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38 views

Streamlines in Boundary Layer

Suppose that a fluid is flowing parallel to and over a flat plate. Obviously, a boundary layer develops in which the velocity ranges from 0 to 99% of the upstream velocity U. Could somebody please ...
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1answer
364 views

Pressure difference in u tube

Suppose you have a U tube filled with a liquid. The height of the liquid column in both the arms of the U tube is not the same. Will the pressure be the same at two points in the two arms of the U ...
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86 views

Relative velocity decomposition

In my fluid dynamics course notes is stated a change in relative velocity can be decomposed: $$\delta \mathbf{v} = \left\{ \begin{pmatrix} \Delta & 0 \\ 0 & \Delta \end{pmatrix} + ...
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3answers
326 views

Is there any solution to the potential flow around a square cylinder?

Potential flow around a circular cylinder is a classic solution. But I am wondering if there is any solution similar to this for the flow past a square cylinder?
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167 views

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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89 views

Rayleigh-Taylor Instability dependence on acceleration direction

I'm trying to bolster my understanding of the Rayleigh-Taylor instability, and I've gotten stuck on the point of which fluid (more or less dense) is being accelerated into the other. Cases of uniform ...
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157 views

Speed of ejection of liquid from revolving tank

Consider a cylindrical tank filled with a liquid. Suppose it has an orifice somewhere at the bottom and the liquid is spurting out of this hole at a certain velocity. Now, if you rotated this cylinder ...
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327 views

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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206 views

Container of liquid in free fall

Imagine a container of liquid in free fall. Why does the liquid fly out of the container. Is there a force exerted by the inside fluid on the surface of liquid which causes this? Also, suppose there ...
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93 views

Does quasi-static motion imply zero energy dissipation?

When a droplet is deposited on a surface with some surface roughness and subsequently tilted it can stick due to pinning (think of droplets on a window after rain). What I am interested in is ...
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1answer
157 views

Do convection currents under the crust affect Earths motion in the solar system?

Whilst browsing through this website I began to wonder whether all of that molten rock underneath the Earth's crust would have a notable effect on how the Earth moves in it's orbit of the Sun. ...
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55 views

Is there a consensus on the definition of wavelength for a solitary wave?

Solitary waves are by definition a wave of single nature so the usual definition for periodic waves does not apply. R. Dalrymple provides a definition but I saw a lot of other websites and papers ...
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89 views

1D wave equation as a function of sound speed

The 1D wave equation is given by $\frac{\partial ^2 p}{\partial t^2}=c^2 \frac{\partial^2 p}{\partial x^2}$ . I found in a reference that for an unsteady gas, where both the gas and sound speeds are ...
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Why are roofs blown away by wind?

Whenever there are high winds, such as in storms, thin metal roofs on sheds as well as concave roofs on huts are sometimes blown away. One explanation provided to me said that the higher velocity of ...
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175 views

Axisymmetric fluid flow

I'm having trouble with a boundary condition. In a fluid mechanics problem, I have flow at $z = \infty$ flowing into a solid plate at $z = 0$ and then flowing radially, and the problem is given as ...
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2answers
726 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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633 views

Force exerted by fluid in circular pipe

Imagine a pipe which is bent to form a circular arc and a liquid is force through this pipe. How will you find the net force exerted by the fluid on pipe? Is the only force acting on fluid centripetal ...
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102 views

Viscosity of water in the presence of solutes

Some physical properties of water change in the presence of solutes: vapor pressure, boiling point, freezing point and osmotic pressure. In particular, these four properties are called colligative ...
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What is the motivation behind $\tau=\mu \frac{\mathrm{d}u}{\mathrm{d}y}$ for Newtonian fluid?

Where does the motivation come from? $\tau$ is the shear stress, $u$ is the velocity and $\mu$ is the shear viscosity. EDIT: Since I wrote the question on phone I wasn't clear enough about what I ...
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420 views

Pressure difference between 2 points in an accelerated fluid

Consider a liquid in a tub and this tub is accelerated. And so the liquid will have a slanted surface. I am clear about finding pressure difference between two points in the fluid having same height ...
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182 views

Capillary action in a slanted tube

Suppose there is a slanted capillary tube and a fluid rises in it. Why does the fluid rise to the same vertical height as when the tube is perfectly vertical? If I'm right surface tension force ...
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204 views

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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363 views

Straw and Water

I drink from a glass of water with a vertical straw. What's the longest straw I can use and still drink water if the ambient pressure is 1 atm? Details and assumptions 1 atm is 101,325 Pa. The ...
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2answers
856 views

Physics of the inverted bottle dispenser

When you invert a water-bottle in a container, the water rises and then stops at a particular level --- as soon as it touches the hole of the inverted bottle. This will happen no matter how long ...
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3answers
923 views

Capillary tube of insufficient length

I was wondering if we have a very thin glass tube placed in a tub of liquid and the portion of the tube outside the liquid is lesser than the height to which the liquid can rise because of ...
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2answers
120 views

The velocity of a cloud?

I noticed an unusually fast moving cloud this morning. My questions: What is the average velocity of a cloud on Earth? What is the greatest ever recorded cloud velocity? What factors affect the ...
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1answer
1k views

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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135 views

Formula for residence time/turnover rate with unsteady state

I'm not sure this is the correct place to ask my question... but maybe someone could still help me. I'm looking for a way to calculate the residence time/turnover rate. I have the production and ...
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1answer
55 views

Pushing water along is it possible to calculate the angle it forms

If I had a static thin (a few mm) film of water lying on a surface and I tried to push a squeegee across the surface in order to move the water. Would the water rise up in front of the squeegee? Would ...