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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.

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Movement of a partially filled oil tanker

I came across the following question A partially filled oil tanker is being carried on a truck moving with constant-horizontal acceleration. What will happen to the level of oil? which had the following answer: -The level of oil will rise on the…
Sharmi C
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Solving the 2D Navier-Stokes equation in vorticity form

I am trying to solve the vorticity equation, Eq. 9 in this paper: \begin{aligned} \partial_{t} w(x, t)+u(x, t) \cdot \nabla w(x, t) &=\nu \Delta w(x, t)+f(x), & & x \in(0,1)^{2}, t \in(0, T] \\ \nabla \cdot u(x, t) &=0, & & x \in(0,1)^{2}, t \in[0,…
FM87
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fluid in a vessel

Consider fluid in a cylindrical vessel of radius a which is undergoing solid-body rotation so that its velocity field is given by $v = (−\sigma y, \sigma x, 0)$. (The z-axis is along the axis of the vessel and vertical.) (a) Show that to within an…
questmath
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I need help modeling the velocity profile of a river's current

I am trying to solve Zermelo's Navigation Problem. One of the cases I'm looking at is when the river's current is a function of the $x$-position only. From what I learned in Fluid Mechanics courses, I know that at the two ends when (i.e. the river…
Scotch Jones
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Sphere with constant velocity moving in stationary fluid.

A sphere of radius a moves with constant velocity $U$ in a fluid otherwise at rest. How far ahead of the sphere is there a disturbance of magnitude $1/20.U$? Show that the acceleration of a fluid particle at distance x ahead of the centre of the…
videlity
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Expansion of a liquid in a bottle under atmospheric pressure changes

So my question is relatively simple. First, consider a bottle modeled as a cylinder with length $L$ and cross-section $A$. You fill it to the brim with water on the ground. Take it up on an airplane and open it. The pressure change will cause the…
ViktorV
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Lubrication Theory Cylinder approaching a wall

In my lecture notes, we went through a problem with a cylinder approaching a stationary wall with speed $v$. Since we are interested in the thin layer approximation, we utilised lubrication theory. Approximating the distance between the cylinder and…
MathematicianP
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Fluid Mechanics (compressible flow question)

I am a grader for a fluid mechanics class, and have come across a problem that I don't understand the answer to, and I was hoping someone could explain it to me. I've quoted the question below. Consider compressible flow through the converging…
user177454
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Fluid Dynamics: Understanding check. 2d Eulerian Velocity and Lagrangian Velocity.

I've just started learning Fluids and have been given an assignment of which i want to make sure i'm right before i hand it in. If it's possible, can you fine ladies and gents of math stack exchange please have a tertiary glance over it and if you…
Vaas
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How to prove the Lorenz Equations are in steady state at the origin

The Lorenz equations are described as: $\dfrac{dx}{dt} = -\sigma x + \sigma y$ $\dfrac{dy}{dt} = (r-z)x - y$ $\dfrac{dz}{dt} = xy - bz$ I’m looking to prove that these are in steady state at the origin Any help would be greatly appreciated!
user706888
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Significance of independence of viscosity and viscosity

I have calculated the shear stress at the wall of a circular pipe to be independent of the viscosity, and I am just curious as to the significance of this result. I have assumed constant pressure gradient.
MathematicianP
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Getting the speed of a fluid streamline

I have the following streamline function, $$(r^2 - \frac{a^3}{r})sin^2\theta = b$$ how do I get the speed of this fluid at each point on the streamfunction? Incompressible, this is the streamline for very large r. It is derived from the…
user57142
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Complex Potential of a Vortex in a Horizontal Strip

There is fluid in between two boundaries $\operatorname{Im} z = a$ and $\operatorname{Im} z = -a$, with a vortex of strength $Q$ at the origin. I need to find the complex potential using method of images. Now, when you have this question but with a…
Mt123
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Inviscid Taylor Couette Flow

I'm trying to solve a simple problem where I have an INVISCID fluid between two cylinders and they are rotating with some angular velocity $\Omega_1$ and $\Omega_2.$ The cylinders have radii $R_1$ and $R_2$ where the latter is larger than the…
whiteiverson
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Question on free surface elevation of water wave

A semi-infinite channel of finite depth is occupied by an ideal fluid layer initially at rest . the vertical finite end of the channel is fixed and only a part of the horizontal bottom , with finite support , is set in a bounded motion . Find the…
Mahmoud Hassan
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