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

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Feeling the Breeze

This question is based on an odd phenomenon I noticed last week. Since then, I've been collecting more data to try to get an accurate picture of the facts. Each morning, I go to my bus stop. It's on ...
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1answer
41 views

Flow velocity out of a pipe

For a compressible homoentropic gas is the flow velocity out of the pipe the same as the velocity into the pipe?
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3answers
156 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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2answers
124 views

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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1answer
77 views

Laminar flow in low-permeability material. Which is faster, gas or a liquid?

I consider a simple low-permeability material $(k \sim 10^{-18}\;\text{m}^2)$. Now I either apply a gas (e.g. nitrogen) pressure or liquid (water) pressure of - let's say $10\;\text{MPa}$ - on one ...
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1answer
104 views

Time inversion for Euler equation in fluid dynamics

Consider Euler equation for continuum body: $$\frac{\partial u^i}{\partial t}+\mathbf u\cdot \nabla u^i=- \frac{1}{\rho} \frac{\partial p}{\partial x^i} $$ where $\rho$ is the mass density, $p$ is ...
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0answers
44 views

Derivation of the equation of motion of a viscous fluid by Landau & Lifshitz

I am trying to follow Landau and Lifshitz, from the Volume 6 (Fluid Mechanics) of the Course of Theoretical Physics, on their derivation of the momentum equation for a newtonian viscous fluid, but I ...
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2answers
749 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
522 views

Calculating Reynolds number for a viscous droplet

I'm trying to develop a very basic scaling law/unit analysis for viscous droplet formation, and I'd like to get some rough numerical values of the Reynolds number to play with. To be specific, I'm ...
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1answer
63 views

Capillary action meniscus height in a tube fitted inside another tube?

I was thinking about how would capillary action change in a tube (classic example) and in a tube fitted inside another tube (considering water as the liquid involved). Height of liquid column: ...
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1answer
160 views

Considerations and questions for a DIY heat pipe; how to choose a working fluid?

I plan to build a DIY heat pipe! For more info on what a heat pipe is, see Wikipedia. I would like to use it to cool a desktop graphics card I have. I am having trouble deciding how to choose the ...
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1answer
467 views

Pressure loss in a syringe

I'm currently working on a problem which is really giving me some issues. The problem concerns the force required to expel water from a syringe. We have a 20 ml syringe (which is $2\times10^{-5}$ ...
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1answer
80 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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4answers
166 views

Particles scattering on fluids: breakdown of the effective continuum description

When does the macroscopic continuum description of a medium like a fluid break down? Say I'm interested in a scattering process of some particles with momentum $p$ and energy $E$ off a fluid of ...
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0answers
36 views

Woodstove coppertubing heat exchanger [closed]

I am trying to use the excess temperature of my wood stove's stack to heat a copper tube heat exchanger with water running through it. The water is piped through my concrete floor for radiant floor ...
2
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1answer
61 views

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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1answer
294 views

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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3answers
2k views

Wind generators - why so few blades?

Why commercial wind generators usually have just 2-3 blades? Having more blades would allow to increase power OR decrease diameter. Decreased diameter would also reduce stress due to different wind ...
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1answer
91 views

Vortex shedding

So I was reading about vortex shedding, and got to know that it causes the building to resonate. Is there any way to use this resonance to generate electricity (maybe use quartz?) I am trying to make ...
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1answer
58 views

Motion with damping involving both $-v^2$ and $-v$ terms

I'm trying to solve for the motion of a particle, accounting for both viscous and drag forces. (There is no potential) The total resistance by medium is modeled by: $\vec{F}=-(\mu_1v + ...
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7answers
3k views

Does it take significantly more fuel to fly a heavier airplane?

I was reading in the papers how some-airline-or-the-other increased their prices for extra luggage, citing increased fuel costs. Now I'm a bit skeptical. Using the (wrong) Bernoulli-effect ...
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0answers
37 views

Static,total and velocity pressure at a point

I have a past exam question that I am stuck on. $200$m$^3/s$ of air is entering a shaft of $5m$ diameter, the density is $1.18$kg/m$^3$, and I have shock loss of factor $X=.5$ I want static, ...
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1answer
53 views

Darcy Flow in porous material - consider porosity in cross-section area?

According to Darcy's Law, the volumetric flow rate Q of a fluid occuring due to a pressure difference $\Delta p$ over a distance L and through a cross-sectional area A of a porous medium (volume V) ...
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1answer
100 views

Torque on a rotational cylinder in viscous fluid

I've been stuck on what I'm pretty sure is a simple part of a larger question. It's a cylinder (radius a) spinning in a viscous fluid. It's rotating at rate $\Omega$ .During this question we get that ...
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1answer
249 views

Finding Surface Tension of water at certain Temperature and Pressure

So the question is: Using the Young-Laplace Equation (if applicable), find the surface tension (dynes/cm) for water at 20 degrees Celsius with 2.5 psi. Round to the nearest tenth. ...
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1answer
36 views

Fluid mechanics problem

I have a $2D$ fluid parcel with coordinates $(0.5,-0.5), (-0.5,-0.5), (0.5,0.5)$ and $(-0.5,0.5)$ and this parcel is deformed by a steady flow field of $u=ay$ and $v=0$, defined on the basis ${(1,0), ...
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33 views

Vorticity and circulation in fluid mechanics

Given a fluid element whose circulation was determined counter-clockwise, how can I calculate the Vorticity of the element? The circulation is $$\Gamma = (\frac{\partial u_2}{\partial ...
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2answers
84 views

What makes laminar cascade break?

Near my house there is a mall that have a cascade, which has a pratically constant flow, and doesn't seem to have perturbations (at least near the edge where water falls), between its two levels. ...
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2answers
318 views

Why does tea rises in the pot but water don't?

I was wondering when I boil water in a pot it only shakes too much while boiling. But I could not figure out why tea rises in the pot when we boil it. it is also a liquid but it starts rising up till ...
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2answers
436 views

Difference resultant aerodynamics force on an airfoil and a flat plate

From basic airfoil theory the following free body diagram can be determined for a two dimensional asymmetric airfoil: Here the direction of the resultant force is governed by the geometry of the ...
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1answer
173 views

Pipe in a flowing river problem

I'm working on a certain problem in fluid mechanics, which isn't really my strongest area. The problem is as follows: Curved pipe is partially submerged in a flowing river so that one end is pointing ...
2
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1answer
55 views

Relationship between Connection and Material Derivative

Suppose $D\subset \Bbb R^3$ contains a fluid and that $f : D\times \mathbb{R}\to \mathbb{R}$ is a time dependent function defined on the fluid region. In that case, the material derivative is defined ...
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1answer
44 views

Weight held by jet stream of water

Consider a bucket of weight $W$, held in air by a jet stream of water from the ground (moving vertically upwards) at height $h$. The water is fired from the ground at the rate of $\mu$ (units ...
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1answer
115 views

Feynman's derivation of Bernoulli (part of it)

OK, so what's up with the $\Delta M$ here? I don't get it. In fact, my textbook doesn't even put it in. I don't think it is a type-o because he continues on with the explanation. If anything I got ...
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1answer
94 views

Why viscosity is diffusive?

I'm studying fluid mechanics in more depth during my Ph. D. and there is something related with the diffusive term that has been bothering me for a long time. Looking at the convection diffusion ...
3
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1answer
60 views

Why do we need the material derivative?

I'm studying fluid mechanics, and I got the impression that the material derivative is nothing more than "differentiating along a path" and so I got confused on why do we need it. Basically, let ...
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2answers
74 views

Microscopic source of pressure in an incompressible fluid

The pressure of a fluid can be explained microscopically in terms of molecules bouncing off the walls of a container. The molecules have a certain mass and speed, so when they bounce they transfer a ...
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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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1answer
26 views

How to find the required inlet velocity/pressure to achieve 0.5 m/s in one part of the underground tunnel? [closed]

I have this problem here related with tunnel and ventilation. As you can see at the picture below, it is a top view of the tunnel. The tunnel has an inlet and an outlet. The air flows from the inlet ...
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1answer
38 views

Why do we use time-dependent regions in this derivation?

I'm studying fluid mechanics and I have the following doubt: on the book, the author first deduces the differential form of the equation of balance of momentum. First he argues that if the fluid is ...
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1answer
116 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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1answer
168 views

Absolute Viscosity of Water at certain temperatures

I just started my class on fluid mechanics. There's a problem that requires absolute viscosity $u$ of water at 25C. I looked up my table in the book and I only have it for water at 20C and 30C. I ...
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2answers
43 views

Bulk Modulus, How are these formulas equivalent?

Bulk Modulus is defined as $$ B = \frac{VdP}{-dV}$$ Where $V$ is volume and $P$ is pressure. It is also defined as, $$ B = \frac{\rho dP}{d\rho}$$ Where $\rho$ is density. Question: How are these ...
5
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1answer
124 views

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 ...
3
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1answer
67 views

Mathematical model of a fluid: which viewpoint is the standard one?

I've been studying fluid mechanics and I have some doubts on the mathematical model of a fluid. First we let $D\subset \mathbb{R}^3$ be a region in three-space filled with a fluid. This region has as ...
6
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2answers
2k views

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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2answers
56 views

What forces of stress really represent?

I'm studying fluid mechanics and the book says the following: For any continuum, forces acting on a piece of material are of two types. First there are forces of stress, whereby the piece of ...
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2answers
218 views

Branching lemon drop “smoke rings”

This might be hard to ask, but here goes nothing. I recently poured a cup of water into a black coffee cup. There was a light source--not very bright--above the cup. Anyways, I was squeezing a ...
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1answer
466 views

Sixth Power Law

The Law: The size of a solid material that can be carried by a (water) stream is proportional to the sixth power of its velocity. I have just discovered that I read this law long time ago (it has ...
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2answers
68 views

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 ...