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

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Surface tension of N non-mixing fluids

I am a mathematician, not a physicist, so please be gentle with me if I write something wrong. Consider a bounded, regular container $\Omega$, which is filled with the fluids $F_1,...,F_N$ which do ...
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664 views

Dimensional Analysis: Buckingham Pi Theorem Using a Matrix

I have the following problem - which is basically that $\omega = f(g,h,l)$ now the book claims that the two $\pi$ terms as follows $\pi_1 = \omega \sqrt{\frac{l}{g}}$ and $\pi_2 = \frac{h}{l}$. Now we ...
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200 views

Surface Tension of a Liquid - When a liquid body is acclerating

As far as I understand it (which admittedly isn't very far), surface tension forces are made up by the tension-attractive forces of molecules at the liquid-gas/vacuum interface, such as those between ...
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239 views

Shear, viscosity and expansion of universe

What is the meaning of expansion, shear and viscosity in context of universe? How can we conclude a result after getting a numerical value of above terms?
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519 views

A water drop in a falling lift

Consider a lift, which is at rest in an homogeneous gravity field. There is a thin layer(with thickness $h$) of water on the floor of the lift. At some moment a single cable, supporting the lift, ...
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156 views

Time evolution of wave spectrum

A useful way of thinking (not only) oceanic waves is to consider them as a superimposition of linear modes: the elevation η of the sea surface is given by: 1: $\eta({\bf x}, t) = ...
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28 views

Fluid dynamics - immiscible liquids

Question: A U-tube of uniform cross-section is partially filled with a liquid I. Another liquid-II, which does not mix with liquid I is poured into one side. It is found that the liquid levels of the ...
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39 views

Is there an equilibrium for water and air in a tank?

I'll try my best to explain my question with examples because I don't have much knowledge on the theory. So say that I had a block of water in air, a cube of water, that is dropping. If the cube ...
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86 views

Propellers and the Speed of sound

I was reading this website that described a novel wind turbine technology and it has this quote: In the mid-20th century, open propeller-driven planes with piston engines reached performance ...
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29 views

Variable area manometer duct

How does one measure the pressure at the end of the manometer tube when the manometer tube itself is having a variable area?
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94 views

Simple expression for transitional pressure force

Consider a simple, circular orifice with an upstream, high gas pressure and downstream, normal atmospheric pressure. Consider also a flat circular plate that can be positioned anywhere along the ...
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57 views

What does centre of lift depend on?

I've read in many places that centre of lift is about quarter chord of the wing and that post-stall lift (the part developed on lower surface) has centre midchord. The later makes sense; the pressure ...
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37 views

Understanding velocity gradients in fluids

So I'm having trouble understanding velocity gradients conceptually, I have little physics training passed physics 101 (I'm a biologist), but I'm currently working in an endothelium research lab with ...
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52 views

Calculate Euler equations of fluid dynamics without division?

I'm working on the calculation of the Euler equations with the finite volume method. Unfortunately I'm not allowed to do a division. So I'm wondering if there's a form which does not need a division. ...
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268 views

Relationship Between Stream Function and Velocity Potential

My understanding is that a velocity potential is a scalar function whose gradient yields the x and y components of a flow's velocity vector. Velocity potential can be graphed, where lines of ...
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61 views

Does the lift created by a wing change when the slats are deployed?

This is a conceptual question as much as an empirical one, but the question is: Does the lift of a wing change when the slats (or any other leading edge device) are deployed? I am stipulating that the ...
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67 views

Steady flow in fluid dynamics?

Steady flow is the condition in which the flow velocity profile does not vary with time. Mathematically this is translated to $\frac{\partial \mathbf{v}}{\partial t} = 0$, for example in the ...
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151 views

Integrating the divergence of a velocity field (Fluid Mechanics)

I'm looking more for verification of my answer as I'm not 100% sure how valid my integration is here: If I have a 2-D incompressible fluid velocity field given by ...
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187 views

Center of mass of a cylinder from which liquid is flowing out

A cylindrical container is of mass M, radius R and height H. The cylinder is filled with a liquid of density D. The base of the cylinder has an outlet tap of radius r through which the liquid can flow ...
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61 views

Constant mass flux in fluid dynamics?

OK so I am having a conceptual crisis about Hydrodynamics. 1) Since mass should be conserved, is $\frac{dm}{dt}=0$ ? 2) But I know that the formula $\rho_1u_1A_1 = \rho_2u_2A_2$ exists... and ...
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60 views

Modeling Water Surface Impact

I have a project that is to model the wave equation in a pond due to a pebble being thrown in. The project is quite simple as all we really have to model is the wave equation with an initial ...
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71 views

Pressure at the front and back of a fan

I have a fan which is inside a duct. When the fan is off, the pressure at the front and back of the blade remains the same. Now when it is running, the velocity of the air below will be more because ...
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51 views

Minimum amount of fluid to experience turbulence?

Turbulence is a challenge to model and simulate: "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the ...
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30 views

No-slip condition when one fluid flows through another

What sort of no-slip zone is in place when liquid water flows from a faucet through air at room temperature? Does the water drag a layer of air molecules along with it?
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85 views

How to caculate the pressure of a fluid when there is no gravity

Well for example we put a ball filled with water, with a density of $1\cdot 10^3 kg/m^3$, in space. How to calculate the pressure the water is exposed to?
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114 views

Energy conservation at a the end of a hose pipe?

I am trying to figure out the energy balance at the end of a hose pipe with water pouring out. Applying Bernoulli's equation inside the pipe we have three energy terms: Kinetic energy, "pressure" ...
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183 views

Spontaneous motion in a wind tunnel

Suppose that a hollow truncated cone is placed in a wind tunnel with a steady wind speed $V$. The cone is placed in such a way that it's base of area $A_1$ faces the wind (rather than the other side ...
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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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365 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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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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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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85 views

Fluid Virtual Mass

In this paper of Lighthill, the author studies the motion of a fish in a constant flow field $U$, modelling the movement of the fish as a deforming, rotationally symmetric, rigid surface in an ...
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78 views

Initialize a traveling wave in a 1D gas?

I am trying to initialize a traveling wave for a 1d simulation as one can see from the attached figure. Such that it will be traveling to the right. However, I cannot initialize the right velocity ...
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145 views

Do electromagnetic fields interact with air pressure?

I would like to know whether electric and magnetic fields interact with air pressure. Do changes in magnitude or direction of such fields increase or decrease the air pressure in a given volume of ...
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412 views

Is it possible to extract nitrogen from the air via a centrifuge

I was thinking about how they have cans of compressed nitrogen for filling paint cans, and also that they sometimes will blow nitrogen in to food containers before sealing them, and that got me ...
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253 views

Compressible flow - subsonic to supersonic and the 2nd law of thermodynamics

I'm reading chapter 16 in Fluid Mechanics by Kundu. It is stated (figures 16.16 and 16.17) that in a constant area duct flow with heating or friction, to go from subsonic conditions to supersonic ...
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140 views

Surface Water Drainage - Grate Inlet Capcity

The situation is a grated drain across a driveway entrance (so a thin long drain) if I know the roughness of the upstream surface (ie mannings roughness), the slope of the surface upstream (which is ...
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118 views

Visualisation of vortex flows

Are there examples of vortex flows (eg: von Karman vortex street or large eddies) which are visualized in a way apart from displaying where the mass is displayed? I can imagine there to be a display ...
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271 views

Aerofoil Theory Project

I'm doing a project (dissertation) on the mathematics of Aerofoil Theory. I wonder if I could get some advice on a possible structure. I'm new to fluid dynamics, so it's quite hard to know where to ...
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193 views

Ship wake height

It is well known that a ship traveling in a deep water produces wake. Far from the aft of the ship, these wake are called a Kelvin wake. I found the mathematical expression of the shape of the wake, ...
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391 views

Is the convective heat coefficient always dependent on heat flux and delta T?

I'm having a difficult discussion with a colleague because I'm running heat flow simulations for a small heater (5 mm^2 area), and I insist that if we're going to run more electrical power through the ...
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230 views

Isentropic vs Total pressure

I am confused between these two quantities: Isentropic pressure and Total pressure. Are they the same?
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1k views

Definition of Buoyancy Flux

I've seen in some papers the definition of buoyancy flux as follows $$B = g \frac{\rho_a-\rho_0}{\rho_0}Q$$ where $g$ is the gravity acceleration, $\rho_a$ is the density of the ambient fluid, ...
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578 views

Book recommendations for fluid dynamics self study [closed]

I have my bachelors degree in engineering science: computer science, option electrotechnic. I have a good understanding of basic mechanics and dynamics, calculus (differential equations). The books ...
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96 views

Is this the reason solids suspended in turbulent fluids don't settle?

While I know (and can observe) that solids don't settle easily in a turbulent flow, I struggle with understanding why exactly this is the case. Here' my problem: Conceptually, turbulence means high ...
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1k views

Why is pressure gradient assumed to be constant with respect to radius in the derivation of Poiseuille's Law?

Poiseuille's Law relies on the fact that velocity is not constant throughout a cross-section of the pipe (it is zero at the boundary due to the no-slip condition and maximum in the center). By ...
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188 views

Power in hydraulic analogy

In hydraulic analogy one compares electrical circuits with water circuits. For the electric case the formula $P = U \cdot I$ for the electric power holds. The analogous formula for water flow would ...
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169 views

Acceleration of a steady line vortex

In a question, I have to find the acceleration of a fluid parcel in a steady line vortex. I am given that $u_\theta=\frac{A_0}{r}$. So for a steady line vortex, the parcels are following circular ...
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477 views

How to calculate flow rate from given stream function

I am stuck on a homework question, all because I dozed off in class. I understand what a stream function is but I don't know how to apply it to calculate the flow in pretty much anything. Here's the ...
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95 views

Water ripples and nonzero divergence

In 2-d, one ripple would mean the velocity of water particles move out radially forming a circular wavefront. The Navier Stokes equations say the divergence of velocity has to be zero, but this ...