Questions tagged [fluid-dynamics]

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

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Is there a Lagrangian $L$ (equivalently an action functional $S$) which yields the Navier-Stokes equation?

The Navier-Stokes equation or the Euler equation are usually derived as the conservation laws. However, I wonder if there exists a Lagrangian $L$ or equivalently, an action functional $S[\...
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Would water flow in the following system?

Would water flow in the following system?
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Two bodies of different mass are passing through viscous fluid. Which will achieve terminal velocity faster and why? How to calculate time?

Two bodies of different mass are passing through viscous fluid. Which will achieve terminal velocity faster and why? How to calculate time? My personal thought is that terminal velocity is ...
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Do Maxwell's equations still apply in fluids?

Hi I am trying to build an electrical impedance tomography platform. The problem I'm facing mainly is to come up with an algorithm to calculate the variation of conductivity within the lung tissue ...
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How does gravity affect the formation of vortices?

Context: I understand the axis of vortices can form in any direction (like underwater used by fishes). However, in large vortices in water bodies, for example, in a closed water bottle, the centre of ...
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Helicopter hover flight question

I'm an avionics technician and I work on helicopters. This week I was trying to explain where comes the lift force to some friends. I'm a self-learner but I have a poor physics school background. I ...
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Inaccurate flow rate measurements of an engine diesel fuel due to change of its viscosity

I am measuring the volumetric flow rate of a diesel fuel using "Turbines" flow meter, both in the supply and return fuel lines of an industrial diesel engine (Caterpillar 3512B – coupled ...
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Question to multi-component fluids

I have read these lecture notes: http://geo.mff.cuni.cz/~soucek/vyuka/materials/theory-of-mixtures/theory_of_mixtures-lecture-notes.pdf Now look at page 41: There are 4 different types of mixture ...
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How much can gases expand when heated? [closed]

When heated, how much can a gas expand when heated relative to Temperature? Is there any physical limitation to how much it can expand, at maximum? What if gas is contained in a sphere or cube, how ...
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Does convection occur in microgravity due to pressure gradient?

Context: On Earth, with gravity, when heating a fluid, the particles gain thermal energy and decrease in density, and a difference in density throughout the fluid causes thermal energy transfered by ...
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Why does air not flow backwards in Jet Engines in the combustion chamber? [duplicate]

In jet engines air is taken in, compressed and then fuel is injected and then ignited forcing the turbine to spin powering the compressor. What I am curious about is why the combusted air isn't forced ...
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Jet of water hitting a wall

In my lecture course the following slide was given: Is the justification for the pressure being P0 at a large radius Pascal's principle? Is there anything else that can be said about the fluid flow ...
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Experiment of liquid filled rod doing oscillation is called?

I know this is a weird question but I can't find any reference to this experiment, I have Google a lot and now I need the experts help. There is a physics experiment where a liquid filled rod is ...
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Potential flow involving a sphere

I am currently working on a problem involving a sphere being dragged through a fluid at constant velocity. Working in the rest frame of the sphere I'm told the potential is of the form: $$\frac{k\cos(\...
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A question for expert in geometrical method and Riemannian metrics

I'm a physical oceanographer with great interest in Theoretical Geophysical Fluid Dynamics. I have some ideas on the possibility to derive the so-called: geostrophic equilibrium (i.e. on a rotating ...
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Is incompressible fluid flow isentropic?

I was asked to verify the relation $\partial_t(\nabla \times v)=\nabla \times (v \times (\nabla \times v))$ of an incompressible fluid flow, where $v$ is the flow velocity. I was looking at Landau and ...
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Can we tell anything about the velocity at which a spherical stone falls into a lake based on the sound it makes?

Suppose we have a spherical cow... I mean stone, and we throw it to a lake. Can we tell anything about the velocity (speed and angle) at which it falls based on the sound it makes? And based on a ...
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Molten metal flow due to high currents

It is mentioned in the book "Ampere-Neumann Electrodynamics of Metals", Peter Graneau, that Carl Hering in 1923 operated furnaces by passing high currents through the molten metal pool. He ...
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Why forces exerted by fluids, inside or outside, are always perpendicular?

I was learning about pressure due to fluids when I encountered the lines such as 'liquid layers exert perpendicular force on each other, fluid exert force on a body perpendicular to it in all ...
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Buoyancy versus viscosity

A common problem in casting is removing the air bubbles that might might be in the mold material, like plaster or resin. This is typically done by degassing--putting the mold material under vacuum to ...
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Pressure in a half empty U bend

All of the water in my game will be gravity fed. My current problem I'm trying to solve is if I have a U-Bends like this: ...
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Lifting force and rope tension in the elevator [closed]

İn the beginning T1 = 10N and T2 = 10N. If the elevator starts to move downwards with acceleration a = 2m/s², what values ​​do the tensions in the ropes take T1 and T2, respectively? (The answer is A ...
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Boussinesq Approximation Term in Momentum Equation

According to the Boussinesq equation: $\rho = \rho_o ( 1 - \beta_t ( t – t_o) - \beta_c ( c – c_o ) ) $ So, $\rho \cdot g$ should be equal to : $\rho g = g \rho_o ( 1 - \beta_t ( t – t_o) - \...
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Net force exerted by pressure

Why do the net force $K$ exerted by the pressure of a hard sphere gas according to the Maxwellian distribution on the walls of the container $A \subset R^3$ vanishes? (In the absence of external ...
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How do I expand: $\langle u , \nabla\rangle u$?

I'm studying the Landau (VI) and when he "introduces" the material derivative (he is building up the continuity equation), something like this appears: $(u,\operatorname{grad})u$ (sometimes ...
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Does this patent using venturi effect violate laws of energy conservation? [closed]

Please see this Patent. Overview: Please note : the claim is, an impeller 8s pushing air thru a shroud/channel that is narrowing. Then venturi effect is used to draw more air in. Thus at the exit ...
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Does the continuity equation for fluids simply state that the material derivative of density is 0?

The definition of material derivative is: $$\frac{Df}{Dt}:= \frac{\partial f}{\partial t}+(\vec{v} \ \cdot \vec{\nabla})f $$ And the continuity equation is: $$\frac{\partial \rho}{\partial t}+\vec{\...
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Dual-medium Plateau-Rayleigh Instability

(This is my first question here so I would really appreciate your guidance on how to use SO better!) I’ve been working on the Plateau-Rayleigh instability for some time and I was considering the ...
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Meaning of potentials in Helmholtz decomposition

I am trying to understand the meaning of the potentials $U$ and $A$ arising in the Helmholtz decomposition of a vector field $\vec{V}$: $\vec{V} = \nabla U + \nabla \times A$ Let's focus on the curl-...
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How and where does air that is displaced by a constant moving vehicle flow?

How does air that is displaced by a constant moving car move? When a car is driving with constant speed, there is air displaced in front of the car. Let's say the surface of the car view flat from ...
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Prove that horizontal velocity component equation $u=Ue^{-ky}\cos(ky-\omega t)$ is valid (Stokes problem) [closed]

I was presented with this question in my fluid mechanics lecture, however I am a bit unsure how to solve it. The problem is as follows: Knowing that the bottom plate oscillates with velocity $u=U\cos(...
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How much power is needed to turn a water turbine in reverse if the power produced by the turbine in normal operation is known?

The picture below shows a farm of underwater turbines placed in a river or a sea with important tides. Assuming that at a speed of the water of 4 m/s, one turbine rotates at 60 RPM and produces 100 kW ...
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Would a 100-m tall wave really get reduced to near-zero height by hitting a West Cost style continental shelf, before reaching the actual shore?

This seems to be the conclusion of a 1996 study but the US Defense Nuclear Agency (which was renamed since then). Short shelf there refers to a West Coast style situation, known to allow for higher ...
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Are all turbulent flows chaotic?

I have often read that all turbulent flows are chaotic. I have come across a few explanations on web forums, but are there any authoritative references/textbooks that explicitly cover this question?
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Zel'dovich, Raizer - derive energy equation

Consider following excerpt from Zel'dovich, Raizer, Physics of Shock Waves and High Temperature Hydrodynamic Phenomena: I wonder how exactly can I derive (1.10) from (1.9)? For example, (1.9) ...
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What is average force?

When reading about how to calculate the force exerted from a liquid on the sides of a container it’s said that the average force is equal to 1/2hA x pg what is the meaning of an average force here? ...
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How do I quantify an adhesive's ability to stick in contrast to flow?

Let's say you glue a ball to a shovel. How do you quantify this adhesive's and ball's ability to stick to the shovel, moving at different speeds, in air and then while the shovel digs into the ground? ...
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Force required to move a liquid through a specified opening

If I know the rate of a liquid, the density of that liquid, the velocity of the liquid, and the size of the opening. How would I calculate the force required (in PSI) to move that liquid through the ...
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Calculating hole size on the side of a pipe

I have a fluid channel through which a fluid with known properties (viscosity, density etc.) flows at a known velocity with a known pressure and temperature and mass flow rate. The external pressure (...
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When using pressure energy to state Bernoulli's Theorem, why do we say it's simply pressure?

I was asked this question in my viva and I couldn't answer. I know there's the whole mathematical explaination of this, when we multiply Force/Area with displacement and convert it into Energy/Volume, ...
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Equilibrium of air volume in and out of an inflated bag

I want to use a small squirrel cage fan to blow air into (and inflate) a closed bag. The bag will also have a number of small holes in it to release air at various points across the bag. But, I want ...
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What would be the Stokes hypothesis in a 1D flow?

In this paper, the author derives the Navier-Stokes equation for a Newtonian fluid starting from the Cauchy equation: $$\rho \frac{D\mathbf V}{Dt} = \rho \mathbf{f} + \nabla\cdot\mathbf{T}$$ where $\...
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Can finite element analysis predict whether flow is turbulent?

Finite Element Analysis in Simulation Software to predict the Reynold's number are computed using the formula$=pVD/u$ or there is a finite element method for this? I was just wondering whether it ...
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Young-Laplace Equation

The Young laplace equation relates the pressure difference to the shape of the young surface as ∆P= T(1/R1 + 1/R2) , here r1 and r2 are the principal radii of curvature. How do we determine these ...
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About the formula of the Taylor microscale

I am running simulations of a non-isotropic turbulent flow and I need to compute the Taylor microscale. The formula one can find in the book Turbulent flows (Stephen B. Pope) is : $\lambda = \sqrt{10} ...
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On taking the gradient of a compressible fluid potential

In literature I read: $$\tag{1} \mathbf{q}=(Nd^2)(\rho/\mu)[\mathbf{g}-(1/\rho) \nabla p]=\sigma \mathbf{E}$$ which is valid for liquid generally, and for gases at pressures higher than about 20 ...
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Can we really treat air and water flows the same?

Suppose we push water through a huge (0.1 m diameter) glass pipe and make an experimental Moody chart from slow (0.001 m/s laminar) to fast (10 m/s turbulent) speeds by measuring the pressure gradient....
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Can we use Darcys flow equation through porous media for pipe flow?

I am looking at flow in a pipe with no solid matrix. Therefore, the porosity is always equal to one. For such a set-up, I can use the Direct Numerical Simulations (DNS) on a 2D framework. However, a ...
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Energy-momentum tensor of a perfect fluid flowing at the speed of light?

The general energy-momentum tensor for a fluid is given by (working with $c=1$ convention) $$\begin{equation}\label{T}\tag{1}T^{\mu\nu}=\left(\rho+p\right)U^\mu U^\nu+p g^{\mu\nu}\end{equation}$$ with ...
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Static and stagnation enthalpy / pressure derivation for incompressible flow

I was wondering how one could derive the relationship between static and stagnation pressure in incompressible flow from the relationship between static and stagnation enthalpy. It should be pretty ...
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