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Mathematics Stack Exchange

Questions tagged [fluid-dynamics]

For questions about fluid dynamics which studies the flows of fluids and involves analysis and solution of partial differential equations like Euler equations, Navier-Stokes equations, etc. Tag with [tag:mathematical-physics] if necessary.

Fluid dynamics is a branch of physics that studies the the flows of fluids-liquids and gases, which involves analysis and solution of partial differential equations like Euler equations, Navier-Stokes equations, etc.

1103 questions
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Euler's equation for an incompressible fluid

I am trying to solve the following problem: I rearranged the Euler equation to find grad(p) and then I did -u.grad(p) to see if i could simplify this to get the LHS However i am very stuck on what happens when i apply -u.grad(p) i would appreciate…
Robert Thompson
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Substantial derivative of density in the derivation of mass conservation equation.

We are all taught the derivation of the mass conservation using a fixed Eulerian control volume in a typical fluid dynamics course. That is, first we think about the total rate of change of mass in that control volume. $$ \frac{d}{dt}\int_V\rho…
Abhinav Rajagopalan
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How to calculate blood viscosity formula using $cm^3$ (lt) and $cm^2$ (area) units

I'm reading a blood viscosity related theory and I have an example formula which I don't understand. It turns lt (fluid liters) or $cm^3$ into $cm^2$ and comes out with a number. I don't understand how the conversion is made from area to volume and…
atmosx
  • 103
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Velocity profile for a fluid with no net volume flux

I've established a relationship between the upper horizontal boundary layer $U$ and pressure gradient $G$ where $\mu$ is dynamic viscosity and h is the height of the pipe the fluid is travelling through $$U=\frac {Gh^2} {6\mu}$$ And I'm now asked to…
Doug
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Fluids contained in a closed cylinder

While reading a fluids book for my course and doing some problems I came across this question that the book didn't provide an answer for and was wondering if one of you kind folks could help me out because i haven't the foggiest. Question: If a…
WillBee
  • 43
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Why is the stream function $\psi$ in fluid dynamics constant on streamlines?

Incompressibility of fluid $\Rightarrow \exists\psi: \mathbf{u}=(u,v)=(\psi_y,-\psi_x)$ Where $\mathbf{u}$ is the velocity of the fluid Could someone explain why $\mathbf{u} \cdot \nabla \psi=0 \Rightarrow \psi$ is constant on streamlines Many…
Freeman
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Particle paths and standing waves

Here $x_0$ is the $x$ coordinate of a point in $x-y$ space Here $x_0$ is the $x$ coordinate of a point in $x-y$ space. I understand where the nodes and crests are on the figure. However, I don't understand why under the crests $cos(k x_0)=0$ . I…
user229011
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Wall boundary condition

Why is it that at $y=0$ (at the wall), we have $v=0$ (vertical component of velocity)? Obviously $v$ cannot be negative there as there is no flow through the wall, however how do fluid particles move off the wall if they don't have positive…
user229011
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Continuum hypothesis confusion (fluid dynamics)

For the quantity $\rho(x,t)$ with the continuum hypothesis am I taking the average value of the density at each point in the small volume surrounding the point $x$ or am I taking the average density of each molecule in the small volume. If it's the…
usainlightning
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Fluid Dynamical problems

I'm just going through Batchelor's book on Fluid Dynamics, and I'm not too sure about a couple of questions in "Exercises for Chapter 4", which are the following: Exercise 3 for Chapter 4 "A long circular tube has a cylindrical layer of liquid of…
ZahaMan
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Fluid Dynamics Problem

A vertical circular stack 100 ft high converges uniformly from a diameter of 20 ft at the bottom to 16 ft at the top. Coal gas with a unit weight of 0.030 pcf enters the bottom of the stack with a velocity of 10 fps. The unit weight of the gas…
Edison Ulanday
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Doubt about 0-norm in Majda Bertozzi

I'm studyind Majda Bertozzi book about vorticity and incompressible flow, and I don't know what's the 0 norm which appears in it. Thanks a lot!
Alex
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Problem with the 2nd part of the exam, please help me get to the bottom of this!

Some parts of this exam are skipped and I need step by step explanation after the 1st line. And confirmation if result is really correct? It's from the workbook of some student and our professor gave it to us for practice and I keep getting some…
John Doe_2017
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