Mathematics Stack Exchange
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
1
vote
1 answer

In 3D printing does the Bernouilli Equation mean that 1.75mm filament drive has less force on the extruder gear than 3.0mm?

There is a lot of misunderstanding about 3D printer filament drives so I thought it might be a good idea to ask here :) A FDM 3D printer basically has a drive gear pushing the filament (1.75mm or 3.0mm) down into a heater block where it becomes…
lkcl
  • 39
1
vote
0 answers

How to write equation of continuity and equation of motion in arbitary co-ordinates?

Problem In the above problem: I am unable to figure out how the equation of continuity and equation of motion could directly be written in terms of the variable s. s is not the usual cartesian co-ordinate but the distance along the curved tube which…
AJ_
  • 273
1
vote
0 answers

Timescale for fluid to reach maximum velocity

Suppose there is a large reservoir of water, and a small horizontal pipe at one of the walls of the pipe. I have done some calculations using Bernoulli's theorem to show that the velocity in the pipe when the end is opened is approximately…
John Doe
  • 14,545
1
vote
1 answer

Intuition for Material Derivative

I am studying fluid mechanics and am trying to gain a finer intuition for the meaning behind the material derivative. So, firstly this is defined as $ (\partial_t + \mathbf{u}\cdot\nabla )f$ where $f$ is some multivariable function and $\mathbf{u}$…
Max Sykes
  • 61
1
vote
1 answer

Pressure at the outlet of a pipe

I am revising for a fluid dynamics exams and I am struggling with the following question: Consider a pipe that consists of a horizontal segment with a varying cross-sectional area that is aligned along the $x-axis$ and a downward segment of height,…
juper
  • 267
  • 1
  • 10
1
vote
1 answer

Axisymmetric vortex

An axisymmetric vortex, for which the azimuthal velocity $u_\theta$ is proportional to $r^{-\beta}$. What are the values for $\beta$ so that the circulation ($\Gamma(r))$ is finite
Abigail
  • 73
1
vote
1 answer

Showing Bernoulli function is constant on streamlines

An incompressible inviscid fluid, under the influence of gravity, has the velocity field $$\textbf u = (− \cos(x)\sin(y), \, \, \sin(x)\cos(y), \, \, 0)$$ with the $z$-axis vertically upwards, where $g$ is the acceleration due to gravity. Show that the…
snowman
  • 3,733
  • 8
  • 42
  • 73
1
vote
0 answers

Details of Shouryya Ray's Solution

Possible Duplicate: Teenager solves Newton dynamics problem - where is the paper? Duplicate question. Please answer here instead: Teenager solves Newton dynamics problem - where is the paper? I came across some news stories regarding Shouryya…
Sharanjit
  • 63
1
vote
0 answers

Presentation of Navier-Stokes eqns

This may be a trivial point, perhaps it's a lack of understanding on my part? When I was first introduced to fluid mechanics I was instructed to write the continuity and (generalized) Navier-Stokes equations as…
Juggler
  • 465
1
vote
1 answer

fluid dynamics Bernoulli's equation

I really can't seem to prove this. Using $A_1u_1 = A_2u_2 $ I get: $$\frac{r_a^2}{r_b^2} = 1.$$ Using Bernoulli's equation, I can't figure out what the other terms should be? $$\frac{1}{2}\rho u_a^{2} + \rho g z_1 + pa = \frac{1}{2} \rho u_2^{2}…
italy
  • 1,001
1
vote
2 answers

Is a 3D or 2D Poisson's equation separable or non sperable?

Can someone please explain to me if a 2/3D Poisson's equation is separable or non separable? Thank you
Amani Lama
  • 143
1
vote
1 answer

Horizontal Pressure gradient.

The dynamics in the ocean can be described by the equation of motion $\frac{Du}{Dt}=-{\nabla}{\Phi}- \frac{1}{p}{\nabla}p- f\cdot u$ . Consider the motion of water in a full kitchen sink, with the water slowly draining out the bottom. The height…
Massin
  • 314
  • 1
  • 3
  • 20
1
vote
1 answer

How do i correctly go from a two variable function to a function of difference?

I would like to know how I can go from a two argument function $g(x_1,x_2)$ formally correct to a function of the difference of the parameters $g(x_1-x_2)=g(x)$ this seems to involve integration over $x_2$ but I have no idea what to look for to find…
Kuhlambo
  • 207
1
vote
1 answer

Finding the centre of two vortices rotating around each other of different strengths

Two vortices, of strengths $\Gamma_1$ and $\Gamma_2$, are at the points $z = z_1$ and $z = z_2$ respectively in the complex plane, where they are free to move. So I have the complex…
Freeman
  • 5,399
1
vote
1 answer

Fluid Mechanics for Low Reynolds Number

I've tried to answer this question but I seem to get a really weird (and suggestively incorrect) answer. The question is: "Fluid is injected radially and slowly into a circle, radius R, with the velocity on the surface of the circle being $u_{\rho}…
ZahaMan
  • 31
1 2 3
…
8 9