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

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Vorticity - Paradox

I am having trouble grasping the concept of vorticity. Above is a picture of fluid element under deformation (rotational). Say we ignore the vertical motion, which is $\frac {\partial {v}}{\partial ...
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244 views

Curvilinear coordinate system around body of revolution

In Boundary-Layer Theory by Schlichting he gives the boundary-layer equations for a body of revolution according to the paper by Boltze$^1$. Unfortunately, this paper is in German. He apparently uses ...
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4answers
505 views

In the formula for the mass of a drop of water on the end of a tube, is r internal or external radius?

In the formula for the mass $m$ of a drop of water forming on the end of a vertical capillary tube, $$m = \frac{2\pi r \gamma}{g},$$ does $r$ refer to the internal or external radius of the ...
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234 views

Can a human body supercavitate to survive water impact?

Inspired by this analysis of a human (OK, Captain America) hitting water feet first at terminal velocity, I'm wondering if supercavitation would be possible and whether it would improve your chances ...
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406 views

Viscosity coefficients

I'm using the 2nd edition of "Transport Phenomena" by Bird and Stewart. I am having trouble with one of the equations: $$\tau_{ij} = \sum_k \sum_l \mu_{ijkl} \frac{\partial v_k}{\partial x_l} $$ ...
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110 views

What does k denote in this equation?

Recently, I was attempting to compare the rate of flow of different liquids using the formulas given below: $$P = \rho g h$$ $$ \frac{dh}{dt}\varpropto h$$ $$ \frac{dh}{dt} = -k h $$ $$ ...
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315 views

The criteria for potential flow theory

I am learning aerodynamics. In this course a potential flow is denoted that a flow in which the rotation is zero everywhere. But the book told me that we can add vortex into a flow field, and we can ...
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455 views

Why does cornstarch and water mixed together become solid when put under stress? [duplicate]

Here is one of the many videos on youtube showing how a cornstarch and water mixture can become very hard when put under stress. I haven't found a good explanation of why it behaves the way it does. ...
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350 views

Velocity field induced by vortex points along ellipse

I'm investigating the velocity field induced by a continuous distribution of 2D vortex points distributed along an ellipse $\{a\cos\theta,b\sin\theta\}$. I'm interested in the field inside the ...
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1answer
462 views

periodic boundary conditions for vortex in a square lattice

I am trying to follow this paper and track the dynamics of vortex motion on a discrete (square) lattice. The idea is to simulate the time evolution of the Gross-Pitaevskii (GP) equation, which reads ...
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1answer
116 views

Distribution of pressure inside a capsule

How would pressure of an ideal gas be distributed over the inside of a capsule (a cylinder with semi-spheres on the ends)? What about the strain on the material? Is there a general formula for how ...
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89 views

CMB anisotropies and tightly coupled limit

Sorry if this is a technical question. I am studying the origin of CMB anisotropies and the tightly coupled limit of the Boltzmann equations. We have a fluid composed of ionized electrons and photons. ...
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980 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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329 views

Swimming and forces

I was told that the total integral of the stress over the surface of a swimmer (i.e. the total force exerted by the swimmer on the fluid) always vanishes, because there are no external forces applied ...
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631 views

Limitations of drag equation

The magnitude of the air resistance for objects with Reynolds numbers greater than 1000 is given by the formula: Why it does not hold for objects with lower Reynolds numbers? Can I use this ...
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2answers
2k views

Will the siphoning effect help a system pump water upwards if the water's entry and exit points are at the same height?

I am looking to pump water from a pool up to a roof for solar heating (black plastic tubing) and then back into the pool with the original source water. Does the gravitational force of the water ...
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2answers
1k views

What would be an appropiate shape for a parachute?

I'm trying to design a parachute that minimizes the descent velocity, but I'm not sure what shape I should use. From what I've read, ellipse-shaped parachutes are too aerodynamic and minimize drag, ...
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2answers
372 views

Why is there a wave on the water surface when I put something in the water?

We've started doing waves in our physics class, but we're doing things very quickly and the teacher doesn't explain anything. And I don't understand why waves work. I was thinking that when I fill a ...
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1answer
3k views

What is the shear stress of a fluid?

One book defines the shear stress $\tau$ of a (Newtonian) fluid as $$\tau = \eta \frac{\partial v}{\partial r} $$ where $\eta$ is the viscosity. There is not much context, so I've made some guesses. ...
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1answer
3k views

How to calculate the projected area at different angles/vectors?

Please help me with the following. I want to know if there is an equation/set of equations to find out the projected area of a (3-D) cube when it is oriented at different angles of attack to the fluid ...
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2answers
233 views

Mixing of fluid in a rotating barrel

A barrel/drum with a diameter of 60cm is rotating at 20RPM to get a good mixing of the fluid contained (type thick oil). At what RPM should a barrel of 30cm rotate to get the same mixing efficiency ...
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2answers
41 views

Hourglass fluid mechanics issue with Bernoulli's equation

I know that I'm thinking about this problem wrong, but I've been pondering it for a while and can't understand something. On my fluid mech. exam I had a problem that asked to determine the radius of ...
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1answer
38 views

What amount of force could be created by a person “swimming” in air?

Had a question on a physics test, a person is at rest on a frictionless surface and can not throw anything, can they move? I said yes, by "swimming" against the air and got docked because "it ...
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1answer
44 views

vorticity not zero - why

I am quite new to fluid dynamics and I cannot seem to understand the concept of vorticity. It is defined as $\nabla\times\vec{v}$ where $\vec{v}$ is the velocity vector. Now (working in cartesian ...
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2answers
124 views

How does a rising bubble take a dome-like shape?

Since I have swam on the swim team for most of my life, I am very familiar with bubbles. I know a raindrop falling through the sky gets its shape because it is the most aerodynamic shape, but how come ...
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46 views

Friction in a fluid

when an object is moving in a fluid(air for example), the air will resist the object's movement: molecules of the air will collide with the surface of the object (no slip condition) and then we will ...
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57 views

Difference between finite volume, characteristic method and plug flow models of a pipe

I have to model pipes (of a district heating network) with ODE's. My background is computer-science, so it is not that easy for me to understand different approaches. Finite volume approach. Method ...
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1answer
109 views

Physical intuition on vortex sound generation

Whenever a fluid has a nonzero vorticity, it looses some of its energy in a form of sound wave. Formally is this mechanism described by Lighthill's equation or some related model (like e.g. Curle's ...
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46 views

Why does rolling down opposite windows create a breeze?

If, while driving, I roll down both of the front windows an inch or two, it mainly creates some turbulence around the window. By symmetry we shouldn't really expect anything different. However, if I ...
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1answer
175 views

Problems implementing Lattice Boltzmann method

I want to make a basic 2D implementation of the Lattice Boltzmann method (in javascript) to simulate gas/fluid flow, but I have run into some problems and I can't seem to find the cause of it. ...
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2answers
146 views

Show that the boundary layers diffuse out from the plate with speed $\sqrt{\frac{\nu}{t}}$ [closed]

I was wondering if somebody would be able to help me with this problem. I know how to solve it using dimension arguments but I'm unsure what is meant by transformation techniques. Any help would be ...
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1answer
65 views

Unsmooth behavior of water waves

I happened to come across this rather interesting picture of a very deformed (or perhaps intricate) wave. The structure looks like it illustrates a superposition of multiple waveforms, as intuitively ...
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265 views

Why is the solution to the Blasius boundary layer problem self-similar?

In every course or textbook that I encountered so far, the authors transform the Navier-Stokes equations of the Blasius boundary layer problem into the Blasius ODE. The problem with many of those ...
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2k views

Distance traveled by a water jet

I helped my kid in a science fair project, where we punctured holes in a water bottle at various heights and then measured the distance traveled by the water jets before they hit the ground. The ...
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3answers
14k views

What is basically the difference between static pressure and dynamic pressure?

What is basically the difference between static pressure and dynamic pressure? While studying Bernoulli's theorem, I came before these terms. The law says: When the fluid flows through a small ...
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180 views

“Where” does dissipated enstrophy go?

We are all familiar with the kinetic energy dissipation and how it is converted into heat which can either be radiated away or go into the internal energy of the system. In the enstrophy transport ...
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2answers
147 views

Will the box move if I blow air inside it?

Suppose that I have a box in space and it is filled with air in it. I keep a fan at one end and blew the air to other end. The air will hit the box with some velocity, so it should move. I know that ...
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202 views

Solving flow equations with less information

Suppose we consider the flow of a fluid through a channel, considered to happen in a plane. We want to consider the region $D = [0,L]\times [-a,a]\subset \mathbb{R}^2$ representing the piece of the ...
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1answer
604 views

Difference between a “source dipole” and a “force dipole”

I know quite well what a dipole is and in general what multipole moments are (in the context of, for instance, electrodynamics). What I find myself confused by is something called a "force dipole" in ...
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109 views

How stable are Benard Cells when the thermal gradient begins decreasing?

I've found lots of information on the formation of Benard Cells and convection currents but very little information about what happens to the self-organized structures when the energy gradient being ...
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1answer
90 views

In a column of fluid does density vary?

In a column of fluid does density vary?
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189 views

Rigorous definition of pressure in a fluid

We briefly introduced some terms at the start of my Fluids class, and one of them was pressure. I'm looking for a rigorous definition of pressure. Wikipedia gives this definition for pressure: $p = ...
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1answer
108 views

How to design windy area - what variables?

When you're walking around malls or parking structures, or a building corner, you'll sometimes notice areas with consistent windiness. I was wondering what positions, angles, wind direction, ...
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2answers
222 views

Is it possible to limit water flow this way and how is this effect called?

I needed to propose a mechanism to store water and keep water flow at the same level with 100% passive equipment. Here's what I came up with. If you turn a water reservoir upside down and put in ...
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1answer
129 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
197 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
189 views

Why do hydraulic jumps form?

I know that a hydraulic jump is formed when a zone of supercritical flow discharges into a zone of subcritical flow, but why exactly is a hydraulic jump formed? From a mechanical point of view, are ...
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1answer
302 views

Simulation of fluid flow using Euler equation

I have been looking on Euler's equations for a while and can't grasp one thing. Suppose we have initial system state with volumes of fluid "hanging" in air (time is frozen and equal to zero), each of ...
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205 views

Examples of nearly perfect fluids and gases

When learning for physics (hydrodynamics and gases) I wanted to know what would be examples of nearly perfect fluids (no surface effects and no friction) and perfect gases (only elastic collisions and ...
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4answers
309 views

Computing the force generated by a sail on a boat

This is a follow up question to the question I asked yesterday: Problem understanding basic sail mechanics I am focusing purely on the Newtonian aspect of motion and I am computing this as ...