Questions tagged [fluid-dynamics]
The quantitative study of how fluids (gases and liquids) move.
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In a fluid flow, how do you tell if negative acceleration is deceleration or change in direction?
When solving for the acceleration of a fluid flow, you use the equation: (∂u/∂t)+u(∂u/∂x)+v(∂u/∂y). If the solution at a given u and v are negative, how do you know if the flow has a negative ...
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Name of viscosity formula? [closed]
I am doing a school project comparing viscosity of different brands of honey. The easiest way for me to test viscosity was dropping a ball bearing down a grad cylinder filled with honey. So I used ...
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Freedoms in non-dimensionalization of Navier-Stokes equation and their usage in normalization
When we non-dimensionalize NS equation, we typically take some characteristic scales of length, velocity etc, say the size of the box, average speed of the fluid in the flow direction etc. Once we ...
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Two ways of non-dimensionalizing Navier Stokes equation
I can see two ways of non-dimensionalizing Navier Stokes equation. One of them is from Wikipedia where one can see that the non-dimensionalization is performed by taking $p^*=\frac{p}{\rho U^2}$ where ...
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How can i model natural convection over vertical surface using the Boussinesq approximation?
How can I utilize the Boussinesq approximation and Finite Difference Method (FDM) to model natural convection in a wall where the bottom temperature is higher and the top temperature is lower?
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How does length effect drag?
Section of pipe: 20mm diameter, 2000mm length, hemisphere end cap. Moving horizontally through water, I think that the coefficient of drag would be approx. 0.42.
How would the length of the pipe ...
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What is the name and notation given to the inverse of the inertial resistivity $\beta$ (aka non-Darcy factor or Forchhiemer factor)?
The viscous resistivity $\alpha$ is the reciprocal of permeability $k$. That is, $\alpha=1/k$.
Considering the 1D isotropic non-Darcy equation,
$$\tag{1} -\frac{dp}{dx}=\alpha \mu q+ \beta \rho q^2,$$...
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Pressure variation in a Fluid in rotating cylinder [closed]
It is a well-known result that the pressure variation(between two radial points $r$ and $r_{0}$) in a radial direction in an ideal fluid in a rotating cylinder is given by
$$ \frac{1}{2} \rho \omega^{...
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Meissner effect and Coanda effect
1) I've come up with the Meissner effect in my job recently:
(Magnetic field lines through a conductor vs. field lines through a superconductor)
2) And today I saw a video of Mark Rober explaining ...
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Relation of first adiabatic exponent to adiabatic index
I'm going through a fluid dynamics text and I'm a little confused by a listed relation. The first adiabatic index is defined as
$$ \Gamma_1 = \left(\frac{\partial \ln P}{\partial \ln \rho}\right)_s, $$...
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Confusion on compressible 1D Euler Equations [closed]
Playing around with the 1D (and isothermal) steady state Euler equations and got some absurd results, so I am pretty sure I made a mistake somewhere.
Starting with continuity equation and momentum ...
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How can centerline stagnation streamlines exist?
A stagnation streamline is a streamline that ends on the surface of an object, resulting in a stagnation point. Consider now the stagnation streamline for a symmetric object, which is along the ...
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Would an adhesive surface have more air resistance?
Imagine spreading double-sticky tape all over the surface of a car or a plane. Would there more significantly more aerodynamic drag as a result of the adhesive 'sticking' to air molecules and slowing ...
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Why does the volume of a liquid seem to increase and then rise when you release pressure too fast in a car's cooling system?
So I was pressure testing the cooling system of my car with a kit where you fix a cap, a gauge and a hand pump to the expansion tank and then pressurize the system to 1.5 bars (mostly European cars go ...
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To find the angular velocity of rotating fluid [closed]
How do we compare angular velocity with the rotation of fluid
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Mean first passage time (MFPT)
I want to know the mean first passage time (MFPT) on a unit interval for two boundary conditions (please see attached figures a and b for your reference). This is in the context of the hydrodynamic ...
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Reverse blood flow in an IV
When the IV drip for a patient is completed, the patient's will flow back.
This is apparently due to the pressure difference.
However, IV needles are inserted into veins in the direction of blood flow....
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How to prove this equation in rocket launching? [closed]
Consider launching a satellite into orbit using a single-stage rocket. The rocket is continuously losing mass, which is being propelled away from it at significant speeds. We are interested in ...
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Propagation speed difference between transverse surface waves and underwater longitudinal pressure waves?
Throwing a small stone on the surface of a calm pond of water creates concentric ripples on the water surface starting from the point of impact and travelling outwards like transverse waves.
At the ...
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Can pipes with pressurized fluid act like an electric grid?
Electricity is used for many things. One of the biggest uses is transporting energy, almost instantly, from a power plant to the machines in my home and many others'.
I was wondering if a similar ...
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Open-ended pipe under water, pressure vs. flow when pump starts up
A pipe with a pump and two open ends is placed under water. When the pump is initially turned on, will the pressure at P_out and P_in initially rise/fall, but then stabilize as a flow of water V_flux ...
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Why is this the "no bubbles" condition?
I'm reading through the "Waves" textbook from the Berkley series. In section 7.3, water waves are described. First, the condition that water is incompressible is derived as follows (assuming ...
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Sealed container with half-open gas buoy
Consider a sufficiently rigid and sealed container completely filled with liquid (e.g. water), pressurized at 1 bar, at constant temperature. Inside the container there is a buoy partially filled with ...
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Height of water spurt in Heron's fountain
I'm trying to understand the height of the water spurt in Heron's fountain under ideal conditions (incompressible fluid/gas, no turbulence, no effects of temperature...). Referring to the diagram ...
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Does ambient pressure has an influence in the equilibrium contact angle of a sessile droplet (Laplace-Young Equation)?
Does the equilibrium contact angle depend on the ambient pressure?
I understand that the Young-Dupre equation suggests the contact angle is independent of pressure, as it is determined by surface ...
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Definition of pressure for viscous fluids
Hc verma, concepts of Physics, vol 1 pg 258
We define pressure of fluid at the point A as : $P= F/\Delta S$.
For a homogeneous and non-viscous fluid, this quantity does not depend on orientation of $\...
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How to modify kinetic gas theory to work for macroscopic particles? (2D)
For the first time I framed a question on my own when I was recently playing carrom pool with my cousin and a striking thought ran across my mind!
I was thinking if a square frame is fixed rigidly on ...
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Spatial coordinates in Eulerian specification of velocity field
The Wikipedia page summarized the relationship between Eulerian and Lagrangian specification as follows:
$$\mathbf{u}\left(\mathbf{X}(\mathbf{x}_0,t), t \right) = \frac{\partial \mathbf{X}}{\partial t}...
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Is there an algorithm for real-time fluid simulations with Fluid-structure interaction with viscous fluids?
I'm trying to write a Fluid simulator for my school coding project. I want the Fluid simulator to be able to handle FSI with viscous Fluids in real-time and be 3D. I've been reading a few papers and ...
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How can I derive this thermodynamically equivalent expression for the speed of sound?
Background
In Viscous Fluid Flow by White, the speed of sound for a gas is given as
$$\tag{1-71}
a^2 = \frac{\partial p}{\partial \rho}\big|_s
$$
where the partial derivative is computed at constant ...
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What causes drag crisis?
While reading the Wikipedia article on Drag Crisis, I found:
The drag crisis is associated with a transition from laminar to
turbulent boundary layer flow adjacent to the object.
While, the ...
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Understanding notation for differential mass flow rate of a control volume
Was reviewing some notes on fluid dynamics, and the notes go as follows (conservation of mass for a qubic CV),
$$\frac{dm_{out}}{dt} = \rho u (dydz)_{x+dx} + \rho v (dxdz)_{y+dy} + (similarly,forZ) = \...
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Why does a pitot tube lose its static pressure term?
This is what I mean by a pitot tube:
except, the bent tube should be closed, so there is no velocity in the pitot.
But why is there no height? It's reflected in the Bernoulli equation that the small ...
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Dispersion relation for Rayleigh equation given unbounded vortex sheet
Reference: Drazin and Reid
Consider Rayleigh's equation away from the continuous part of the spectrum, which is governed by $$\phi''-\alpha^2\phi=0.$$ Given the shear flow $U(z)=\text{sgn } z$, one ...
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To find the speed of a beaker that is ejecting fluid, using Bernoulli's equation
I wish to mathematically model the speed of a beaker which is ejecting fluid out of a tiny orifice (area a) at the bottom, as a function of time, t.
[I'll assume the surface area of the beaker to be A ...
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Effect of viscosity in a rolling body and it's contrast to non-viscous fluids
while working on problems related to fluid mechanics i came across a problem in which we were asked to find the kinetic energy of a sphere which is under pure rolling and has non viscous fluid filled ...
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Why doesn't a dark matter halo just collapse to a disc?
According to this and this answer, and as far as I understand these answers, dark matter halos cannot collapse to a black hole because, due to uncoupling from the EM field, they are unable to radiate ...
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Derivation of the exit velocity of water through a hole by force analysis at hole [closed]
As it is the setup with Torricelli's law, consider a hole (of negligible height difference) of area A at a height of h from the top of a cylinder filled with a non-viscous liquid of density $\rho$.
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Why are these balloons attracted when there is air blowing between them?
There are two party air balloons pending by their own weight through strings. When we blow strongly in the pipe, they move to approximate from each other as shown in the picture.
It seems that the ...
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Need help visualizing mass and momentum diffusivity
I'm currently studying various dimensionless numbers. Right now, I'm stuck trying to understand the Schmidt number.
I think I understand what is meant by thermal diffusivity. It's just how fast heat ...
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How to show that the diffusion of a species is given by $\frac{\dot{m}}{A}=-\rho_i D \ln(C_i)$?
I'm reading a textbook on viscous flow which says that you can go from Fick's Law for the diffusion of a species
$$\dot{m_i}/A = -D \nabla \rho_i$$
to an equivalent formulation using the species ...
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Why dows Water in the shower run down glass pane in meanders?
The last days I noticed that after taking a shower (cabin has glass walls, safety glass if it matters) and finally splashing the glass panes for cleaning soap residues off, some of the remaining water ...
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Interchange of Lagrangian/material derivative and volume integral
In hydrodynamics there are two basic approaches. The first is the Eulerian specification where the coordinate system is fixed. In that case, the partial time derivative and volume integral operators ...
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Forces On Toroidal Wind Tunnel wihen Wing is attached inside? [closed]
Consider the attached Toroidal wind Tunnel.
The Wind tunnel is in Vacuum and the moving air and the attached wing are only inside the toroidal tunnel.
Will the mounted wing on the walls of the tunnel ...
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Airflow between two rooms (one hot, one cold) [closed]
Scenario —
It is night time and somewhat cold outside.
Room 1 (Bedroom): The window is slightly creaked open. I have a space heater going on continually heating room 1. One door is closed to the ...
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Can irreversibility arise from systems that are microscopically reversible? [duplicate]
I was reading about Feynman's sprinkler problem, and came across a paper that discussed irreversibility in ideal fluids. It quoted the fact that
When a real fluid is expelled quickly from a tube, it ...
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Time dependence in Eulerian description of fluid flow
In the Eulerian description of velocity field, suppose $x,y,z$ are fixed coordinates, the velocity at that point at time $t$ is $\mathbf{u}(x,y,z,t)$.
I am confused whether $x,y,z$ depend on time or ...
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Fluid compression against wall
A compressible fluid within a fixed cubic container is compressed at time $t=0$ by a spatially homogeneous force against one face of the cube. After a long time the mass distribution of the fluid ...
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Flow down an incline - Understanding boundary conditions
After working with some problems regarding flow, I came up to a similiar problem as the one presented here:
In solving the problem, we assume a laminar flow in steady state.
When using Navier-Stokes ...
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Potential energy density of a fluid in motion
If I have a fluid in motion at a given time and I know its pressure $p$ everywhere, I know its dynamic viscosity $\mu$ and I know its velocity field $\vec V$.
This system must hold some intrinsic ...
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