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

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What happens to the d/dr term of the continuity equation in cylindrical coordinates?

The derivation of the continuity equation in cyclindrical coordinates should look like this, $$ \dfrac{dm_{cv}}{dt}=\sum \dot{m}_{in} - \sum \dot{m}_{out} $$ where $$ m_{cv} = \rho r ...
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Liquid Flow Over Object

When there is a large object in the bottom of the ocean of height h, the surface of the ocean rises by a height less than h. In fact, if the ocean depth >> h, then the surface will rise negligibly. ...
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2 different density liquids in space

Lets say you are in deep space with basically zero gravity. You have a ball of water floating in front of you. If you carefully injected that ball with a syringe filled with vegetable oil, what ...
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Are standing waves in water exact sine waves?

In many physics demonstrations waves in water are used to illustrate principles of standing waves and wave propagation. After such demonstrations, classes tend to move on to basic problems ...
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Complex potentials in plane polar coordinates - stream function

Determine the stream function and the potential in plane polar coordinates and sketching streamlines. We need to take the value of m=1. I know how to find the stream function and velocity potential, ...
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185 views

Water Waves in the Wake of a Boat

As a boy I noticed that the waves from the wake of my model boat would fan out. If I looked at the end furthest from the boat the front had turned so that it was almost running in the same direction ...
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Air flow through a hole [closed]

If I drill a hole of 1 cm diameter in each of two opposite window frames of my house, assume that the temperature outside is 0 deg C, the atmospheric pressure is 1020 millibar, wind speed is 10 meter ...
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55 views

The relation between the velocity and the static head

I would like to ask about the Bernoulli's principle: as the principle states, increasing the velocity causes a decrease in the pressure. I made an experiment using a duct and 6 manometers and what I ...
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Is viscosity simply “slowing down time”?

The Pitch drop experiment has pitch, a fluid with extremely high viscosity, flowing through a funnel. In 85 years, only 9 drops have fallen. Photographs of the drops, however, show an appearance just ...
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If I accelerate a mass quickly enough through a short distance (i.e. unit step function), would I create wind, sound, and heat?

As far as I know, the movement of air molecules can result in what we call wind, sound, or heat (and maybe some other things I'm not thinking of), depending on the assumptions about its motion. Wind ...
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Hydro-electric gravity problem - Is there a air-resistance-like force affecting water flow down a mountain making placing hydro-electric ?

Say I have a theoretical mountain with a river starting exactly at the peak. Gravity would act on the water, accelerating it down the mountain. There would also be a force limiting the water's ...
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How do you calculate/estimate hypersonic leading edge and skin temperatures?

At lower speeds (below Mach 5-ish), stagnation temperature (TAT) is a very accurate proxy for skin temperature. But at mid/high hypersonic speeds (especially in the thin upper atmosphere where mass ...
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How can Bernoullis be solved without Vectors [duplicate]

Some time ago I asked a question why Dynamic pressure is considered scalar. Why is the dynamic pressure not a vector quantity? This still puzzles me so I hope to give a scenario that doesn't make ...
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What is the exact difference between diffusion, convection and advection?

I have tried to explore the information but still not very clear on the exact difference between diffusion, convection and advection. Can anyone help me out to clear my concept?
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Mass flow rate and force on moving disk

If I understood correctly, the force $F$ related to a given mass flow rate $\dot{m}$ through orifice area $A$ (or, say, on a disk of area $A$) is given by Newton's 2nd law of motion - assuming a ...
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139 views

How does the radius of a pipe affect the rate of flow of fluid?

Poiseuille's law states that the rate of flow of water is proportionate to $r^4$ where $r$ is the radius of the pipe. I don't see why. Intuitively I would expect rate of flow of fluid to vary with ...
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29 views

Water in an evacuated tube travels 10.3 meters. How does less water in the tube not violate some equilibrium condition?

At atmospheric pressure, water in an evacuated tube travels 10.3 meters. Let's say I don't have 10.3 meters worth of water but I only have enough for 1 meter, like in the image. The atmosphere still ...
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Pressure-Velocity relation at a point in a flow

How can we relate pressure and velocity at the same point in a fluid flow? Why does pressure decrease with increase in velocity?
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68 views

Experiment of plume of smoke

If a burning candle is covered by a transparent glass, the flame extinguishes and a steady upward stream of smoke is produced. Which factors will infulence the figure and properties of the plume of ...
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27 views

Influence of a defect on the flow field

I have a long microchannel where flows some water. The reynolds number is much smaller than one. Within the structure of this microchannel there is a big defect. It looks like a bump of size ...
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75 views

hydrostatic pressure on a plane surface

I've been trying to calculate the amount of pressure on a wall of a rectangular structure, that is under sea watter. For example a dam. I can't come to see any example to be able to locate the ...
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Homogeneous turbulence [closed]

I'm trying to demonstrate the Karman-Howarth expression of isotropic turbulence for the velocity correlation functions: $R_{ij}(r)=A(r)r_ir_j + B(r)\delta_{ij}$ since: \begin{align} A(r) r^2 + ...
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217 views

How to calculate the increased pressure drop due to a restriction?

Assume I have a straight pipe with diameter D1 and a volumetric flow, Q flowing through it. The inlet pressure is P1 and the outlet pressure is P2. Now, assume I've added a restriction in the middle ...
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How would swimming in low gravity work?

Sorry I know very little of actual physics, I'm not looking for hard and fast numbers just a general idea of how the mechanics would work. For the sake of argument, say you were on a planet or moon ...
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How does a heated constant volume flow behave, for an expanding flow tube leading into the free atmosphere

I have a helium gas flow with a flow rate that has been set to a constant value ($0.3\,m^3/h$). It's streaming upwards in the picture, and beyond the upper big red dot position, it meets the ...
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244 views

Surface tension and soap bubbles

In a common experiment, you can make a paper clip float on water due to the strong surface tension. Adding just a tiny bit of soap immediately destroys the surface tension and lets the paper clip ...
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In momentum theory, what happens if atmospheric velocity is larger than outflow velocity?

I am currently reading up on aerodynamics, essentially the actuator disk concept and momentum theory as it is described in e.g. Basic Helicopter Aerodynamics by Seddon and Newman. There they assume ...
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Flow through a packed bed

I'm given a situation where a horizontal tube is filled with metal oxide particles and a reducing gas is passed through it. I'm given all the parameters of the system, including the maximum pressure ...
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242 views

Can a thrown egg chip (or break) a car windshield?

Is it possible to throw an egg with such speed that a car windshield will chip (just like with stone chips?) I have searched around for existing research in the area and have found that the impact ...
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37 views

Tank draining with piston

I am trying to solve a problem which is close to the tank draining (as here Fuel tank draining) but with a piston a the top of the tank which means $p_A$ different of $p_B$. I search the velocity ...
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29 views

Fluid Mechanics Textbook Request [duplicate]

I'm looking for a textbook with which to independently study fluid mechanics. I have been searching a bit by myself, and my problem with what I have found so far is that the texts assumed certain ...
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71 views

Why do flat sheets of paper twist more than paper cones as they fall?

If I cut a 10cm circle out of a piece of paper and drop it, it will twist as it falls, even if it's rigid. If I then cut out a one-quarter wedge of the circle and tape the remaining three-quarters ...
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Are there resources for simulating and/or theoretically describing solitons?

Recently there are striking new ideas emerging on "lower level" dynamics with respect to quantum mechanics involving fluid mechanics principles, including hints of soliton-like aspects to particle ...
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Why do nuclear weapons create a blast wave?

As far as I know, in a nuclear explosion the energy is released in the form of radiation (neutrons, gamma rays, alpha particles and electrons), light and heat. There isn't a chemical reaction that ...
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Evolution of normal of material surface moving at a steady velocity

I need some help with the following question: A material surface moves with the fluid with a steady velocity $\mathbf{U_{o}}$. Show that the unit normal $\mathbf{n}$ to the surface evolves according ...
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Why oobleck does not obey Newtonian dynamics? [duplicate]

In the following post we can see that some guys are walking on Non-Newtonian fluids. As far as I know that, we can not predict the exact amount of strain if we predict some forces. therefore the curve ...
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169 views

Conventional definition of ideal fluid

According to Landau&Lifshitz, an ideal fluid is one with zero viscosity and a negligible thermal conductivity. This is also the FR.wikipedia version: En mécanique des fluides, un fluide est ...
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Solving inhomogeneous Stokes equation

I want to solve the Stokes inhomogeneous equation, i.e. $$\nabla^2 \vec v -\nabla P = \vec f(r,\theta)$$ $$\nabla\cdot\vec v=0$$ where $\vec f$ is irrotational, i.e. $\partial_y f_x - \partial_x ...
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35 views

Height dependancy when adding volume from below to a fluid column

Suppose there is a fluid column of height H and there is a screw already inserted from outside the column entering through the bottom of the column. The screw has a total length L and only 0.1*L is ...
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82 views

What forces act on an object submerged in flowing fluid in an enclosed environment (i.e pipe)?

Let's say we have a pipe with water flowing through it and obstacle is inserted into the pipe and is rigidly fixed to the inner wall so that it does not get washed away. What forces are exerted by ...
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Limits for the linear wave equation

In acoustics and continuum mechanics the following wave equation (for Speed of Sound $c$) for the pressure field $p$ is well-known: $\partial_t \partial_t p = c^2 \Delta p$. This wave equation can be ...
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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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Density of an astrophysical ring of fluid around a star

*An equilibrium ring of isothermal fluid orbits a star at radius R. In the plane of the ring, mechanical equilibrium results from a balance of centrifugal force and the gravitational force of the ...
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Micro gripper for conveying tiny objects

Figure below shows a micro gripper used for conveying very small objects (i.e. the spherical object in Figure) and putting them in desired place using capillary force principal in a liquid bridge. To ...
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What is the essential concept behind the difference in the fundamental solutions of the Stokes and Poisson equations?

The fundamental solutions, i.e., the solution with a point source, of the Poisson's equation and the Stokes equations in 3D are: $$\nabla^2 f=\delta(\boldsymbol x) \ \Longrightarrow\ G(\boldsymbol ...
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67 views

Can I tell where a leak is in a vertical water pipe based on the water pressure at the bottom?

I have a buried water line with a leak in it and I want to locate approximately where it is. The line runs uphill to a storage tank. I've isolated the leak to one section of the pipe. The diameter of ...
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55 views

Decrease in system pressure do to gas dissolution?

A system of fixed volume contains two fluids as illustrated in the figure below, in equal volumes. Their pressures are both equal and high (much greater than atmospheric pressure). Initially the ...
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What happens to running water in sub-zero environment?

Many rivers in sub-zero winter temperatures don't freeze (photo). For simplicity let's discuss a (small) water pipe/canal with uniform cross section, inclined by an angle $\theta$. It seems that: ...
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How much energy to overcome surface tension and create air bubble at an air/water interface

here is my question. Hope you'll help me ;-) Consider a test-tube, almost completely filled with water, and closed with a stopper. Turn it over and then remove the stopper. If the diameter of the ...
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112 views

Can an air bubble in a liquid be faster than its terminal velocity

The title says it pretty much. I am wondering if an air bubble in a liquid can move faster (relative to the surrounding liquid) than its terminal velocity?