Questions tagged [fluid-dynamics]
The quantitative study of how fluids (gases and liquids) move.
7,234 questions
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Why does flowing water produce what sounds like white noise?
Why does flowing water produce what sounds like white noise? Is this due to a certain type of turbulence? Is there a proof that it white (or pink or Brown?) noise?
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Curious about entropy and information theory in Bohmian mechanics
I've been playing around with Bohmian mechanics in electronic systems. I really like the interpretation of particle trajectories in terms of the continuity, Hamilton Jacobi equation and guiding ...
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Trouble understanding the boundary conditions for the Blasius boundary layer equation
In Section 7.2.1 of Bergman's Fundamentals of Heat and Mass Transfer, there is a derivation of the Blasius equation
$$ 2 \frac{\mathrm d^3 f}{\mathrm d \eta^3} + f \frac{\mathrm d^2 f}{\mathrm d \eta^...
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How to find pressure in pipe contraction for compressible high speeds flow?
Air with density ρ, absolute pressure P1 flows through a pipe with velocity v₁ and cross-sectional area A₁, and then enters a contraction with area A₂. A1/A2=10. We need to determine the pressure P₂ ...
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Does the no-slip boundary condition contradict Bernoulli's equation here?
Imagine inviscid, incompressible steady-state fluid flow around a cylinder like in the diagram below so that it flows around the cylinder symmetrically about the x-axis:
According to the no-slip ...
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Temperature of flowing water
Water's temperature is given by (average K.E. of molecules) $=3/2 \ k_{B}T$, so my intuition is that flowing water molecules will gain additional kinetic energy from flowing, leading to a huge ...
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Has someone ever obtained a relative trajectory being exactly the Coriolis formula without a background centripetal force (as gravity)?
In geophysics and many other cases, the Coriolis formula is clearly linked to a background centripetal force.
Read Anders Persson (UK MetOffice, EU ECMWF, Sweden SMHI, Uppsala) https://scholar.google....
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Fluid in a rotating cylinder: how is this wrong?
I have recently been working a bunch of hydrostatic problems with accelerating fluids of all kinds. I came across the classic problem of finding the shape of the free surface of a fluid in a rotating ...
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What pressure is used in Bernoulli's equation in fluid-dynamics?
Hereinafter, the term “fluid” will be used to mean “ideal fluid” (i.e., an incompressible fluid without friction).
The fluid flows to the right through a horizontal pipe at a speed $v$. Then Bernoulli'...
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Could cometary non-gravitational acceleration be linked to surface cohesion transitions?
In several comets, including the interstellar comet 3I/ATLAS, a non-gravitational acceleration is observed, i.e., a net thrust not fully accounted for by gravity. While outgassing is known to produce ...
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Why do we have to invoke interfacial displacement in solving the Kelvin-Helmholtz instaility?
Lately I've been studying the Kelvin-Helmholtz instability (KHI) and Rayleigh-Taylor instability (RTI). To be specific, in the incompressible limit.
The equations are the same:
\begin{align}
\frac{\...
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Reconciliation of filtering operation in turbulence
I am studying turbulence more specifically properties of filtering operations given by
$$
U(x, t) = \int_{\mathbb{R}^n} G(r, x) U(x-r, t) dr
$$
with normalization condition
$$
\int_{\mathbb{R}^n} G(r, ...
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How long can electrohydrodynamic (EHD) propulsion last?
In an electrohydrodynamic (EHD) propulsion, I know that there is a thin wire with high voltage (emitter) and a 0-voltage collector. Because of the radial electric field around the thin wire, electrons ...
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Which orientation of a truncated cone will drain faster?
A container is shaped like a truncated cone (frustum) as in cylinder-like shape where one end has a larger radius than the other. Both orientations contain the same volume of water, and the outlet ...
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Which orientation of a truncated cone will drain faster? [duplicate]
A container shaped like a truncated cone (frustum) as in cylinder-like shape where one end has a larger radius than the other. Both orientations contain the same volume of water, and the outlet hole (...
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How does electrohydrodynamic (EHD) propulsion work? [closed]
How does electrohydrodynamic (EHD) propulsion work? In the usual setup there’s a thin emitter wire and a collector electrode. The emitter is held at a high positive voltage, creating positive ions ...
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Convective boundary condition for Lid-Driven Cavity
Can we use convective boundary conditions for a lid driven cavity in a steady incompressible air flow with heat transfer in a lid driven cavity?
Is this type of problem exist for air type of fluid? If ...
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Velocity of efflux when the area of hole is equal to the cross-sectional area of the container
From the equation of continuity and Bernoulli's theorem a formula can be derived for the velocity of efflux when it flows from a hole of area $a$ such that the cross-sectional area of the container is ...
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Squire’s article “The Round Laminar Jet”
I was reading the article "Round Laminar Jet" by H.B. Squire about the Landau jet (for which I can't provide free access, sadly). It models a fluid being discharged into a space containing ...
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Determining depth of seabeds near shore using waves characteristics
Shoaling wave height increases as waves come closer to the beach. By using this property of the wave, it is possible to find the depth of the seabed close to the beach(between when the shoaling of the ...
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Low Mach number expansion
I'm reading the article "Lattice-Boltzmann Simulations of Particle-Fluid Suspensions"
by A. J. C. Ladd and R. Verberg.
In section 5.4 ("Limiting Cases"), the authors note that in ...
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Do fluid streams attract each other ("pinch" or bundle together)?
Do fluid streams (air coming out of two jet engines, one on each wing; hot gas coming out of multiple rocket nozzles, etc.) attract one another ("pinch" or bundle together)?
cf. History of ...
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How can I use Bernoulli’s principle to measure fluid height and energy?
I’m trying to do a small experiment to understand Bernoulli’s principle.
I want to measure how the height of a fluid in a pipe relates to its energy or pressure. I’m not sure:
How to set up the ...
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Pressure conflict when priming a siphon: 1m water column vs. 20cm tank level
I have a question about fluid dynamics that is causing some confusion for me. It relates to the pressures at play when priming a siphon.
The Setup:
Imagine two identical tanks, Tank A and Tank B.
...
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Is shear stress really zero for a fluid in accelerating container?
I am really confused, about the nature of inviscid fluid.
That is
A fluid cannot resist a shear stress.
The confusion seems to arise when we accelerate a fluid like this:
You can see the fluid is ...
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Confusion in Pitot stagnation pressure $(½)ρV²$ with momentum-flux pressure $ρV²$: control-volume derivation and instrumentation implications [closed]
When a Pitot tube faces a uniform incompressible flow we obtain the usual Bernoulli result for stagnation pressure:
$p_{0} - p_{\infty } = (1/2)\rho v_{\infty }^{2}$
so the Pitot gives the dynamic ...
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How much does air in a vehicle dampen the feeling of acceleration?
You're standing on a train. The train starts suddenly, your feet are on the floor so they start moving with the train but the rest of you doesn't. You stumble back a step and catch your balance as ...
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How does static pressure increase from flow turning differ between subsonic and supersonic cases?
When subsonic flow encounters an object (e.g. a wedge airfoil), the flow gradually turns to follow the surface. Because pressure disturbances can propagate upstream, the flow adjusts smoothly, leading ...
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Continuity equation vs Poiseuille's law [duplicate]
In a pipe of diameter 10cm that narrows into a pipe segment of diameter 5cm, my understanding with the continuity equation is that flow remains constant in both segments of the pipe. However, ...
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Dynamics of Snail Balls 🐌🔵
It has been suggested I ask this here instead.
I've read the standard result for a rigid body that rolls without slipping down an incline of angle $\theta$:
$$
a \;=\; \frac{g\sin\theta}{1+\dfrac{I}{...
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When calculating pressure in fluids, will neglecting the tangential component $F_\parallel$ ever lead to significant inaccuracies?
In many school and university textbooks, pressure $p$ is commonly defined as a scalar:
\begin{equation}
p=\frac{F_\perp}{A},
\end{equation}
where $F_\perp$ is the normal component of the force with ...
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Understanding flow rate with equations
I am having trouble understanding the continuity equation alongside Poiseuille's law. I would like to mention a scenario of a syringe with diameter 4cm pushing saline solution into a tube of 1mm ...
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Why does a free-falling liquid jet contract while an upward jet expands, from a molecular perspective?
I’m trying to understand this strictly from the atomic/molecular level, without relying on equations of continuity. Consider this situation:
A vertical water jet is released in free fall (downward).
...
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Pressure gradients vs. Bernoulli: what drives blood flow through a stenosis?
In a vessel stenosis, the static pressure drops locally (e.g. from 100 mmHg to 60 mmHg) and then rises again downstream (e.g. to 80 mmHg). Intuitively, this looks as if fluid should flow backward from ...
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Control volume analysis of the "Blow your own sail" problem
A fan on a cart blows air at a sail as shown. How would you use a control volume analysis to compute the force needed to keep the cart stationary (i.e. compute the 'reverse' thrust)? Obviously there ...
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Compressibility in Stoke's work of Navier-Stokes equations?
Can you explain is equation (12) compressible? Isn't compressible flow when we have term $dρ/dt$?
Here is full Stoke's work: link
photo of equations (12) and (13)
Compressible N-S equations:
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Pitot Tube vs Bunsen Burner
In a pitot tube, the holes to the static pressure chamber are perpendicular to the flow of the surrounding air. In a bunsen burner, the air supply holes are perpendicular to the flow of gas.
From what ...
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Does an Internal Spring Force Contribute to Drag on Parallel Plates?
Consider a simple system of 2 parallel plates joined at one end by a hinge, with a spring under tension, attempting to push the plates apart. The plates are moving through a fluid with enough speed ...
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Are compressible Navier-Stokes equations valid in the incompressible regime?
Are compressible Navier-Stokes equations valid in the incompressible regime or I must use strictly incompressible version of N-S to get correct result?
Original N-S equations works only for ...
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Material Derivative of Infinitesimal Line Element
I am trying to self-learn fluid dynamics from online resources because I am interested in its application to astrophysical environments. I found lecture notes on astrophysical fluid dynamics on arXiv (...
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Has the kinetic energy of falling into the water also been transferred to the water in the pool?
The water falls vertically onto a thin and lightweight iron disc, and then flows horizontally in all directions on the disc. However, the disc does not sink to the bottom of the water. My question is, ...
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Is it possible to construct Smooth solutions for the unsimplified version of the viscid and incompressible Navier-Stokes eqs.? Smooth is essential
There are many exact solutions to the simplified Navier-Stokes equations. However smooth and 3d solutions do still remain elusive.
Is there a way to construct an exact 3d smooth solution generator of ...
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Is the flow of charges in a conductor incompressible?
Let us assume local charge conservation:
$$\frac{\partial \rho}{\partial t}+\boldsymbol \nabla \cdot \mathbf{J}=0\tag{1}$$
$$\mathbf{J}=\rho\mathbf{u}\tag{2}$$
The material derivative used in fluid ...
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Ensuring the stability and validity of a numerical solution for the Fokker-Planck equation
I am developing a finite-difference numerical scheme for solving the Fokker–Planck equation. The scheme is validated by comparing its solutions with histograms constructed from trajectories of the ...
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Reynold's transport theorem in the context of compressible fluids
Reynold's transport theorem states :
$$\frac{d}{dt}\int_{\Omega (t)}q\rho dV=\int_{\Omega (t)}\frac{\partial}{\partial t}(q\rho)dV+\int_{\partial\Omega (t)}q\rho \vec{v_{b}}\cdot d\vec{S}$$
where $q$ ...
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Can the speed of the wind be determined from a photo or video of a flag?
When a flag moves around in a wind of constant speed can we determine wind speed from the flags distorted shape or angle it is flying at?
Perhaps this video of a flagpole vortex can help
Flagpole ...
user439184
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Explaining that surface tension is limited to the surface using thermodynamic/energy arguments
The usual treatment of surface tension for the liquid-vapor interface involves creating a new surface, say of area $dA$, and then defining that the work required to do so, $dW$, divided by $dA$, is ...
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Negligible power to keep a gas of negligible viscosity moving through a tube of varying diameter
It is easy to prove that only negligible power per unit length is needed to keep a gas of negligible viscosity moving at constant velocity through an infinite tube of highly varying diameter, provided ...
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Why does a radiative view‑factor estimate underestimate the “weight shadow” of an airplane by many orders of magnitude?
I recently saw an experiment where a large ground scale registered a transient “weight shadow” as a warplane flew overhead. The experimenter’s results showed a measurable signal — much larger than I ...
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Zero vorticity for ideal flow
My notes state that the given the vorticity equation:
$$\frac{\partial \boldsymbol \omega}{\partial t} + (\mathbf{v} \cdot \nabla)\boldsymbol\omega = (\boldsymbol\omega \cdot \nabla)\mathbf{v} + \nu \...
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