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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.

1103 questions
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Calculating particle paths for a two-dimensional flow

I'm having trouble considering the velocity field $\mathbf{u}=(u,v)=(y,-x)$. I have been asked (as part of a homework assignment) to determine the time-dependent position of a particle in this field that is initially at $\mathbf{x}=(x_0,y_0)$. I…
dplanet
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Question about cross multiplication in fluid dynamics

While finding out stream lines in a problem of fluid dynamics, the text-book wrote at one stage something similar to this: $$\frac{dx}{a}=\frac{dy}{b}=\frac{dz}{0}$$ The next step is to equate two pairs and then…
Kawrno
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Velocity of an axisymmetric, steady, irrotational flow

The Question: Suppose we have an axisymmetric, steady, incompressible flow whose velocity $$\vec u (r,\theta ,z)=u_r(r,\theta ,z)\vec e_r+u_\theta(r,\theta ,z) \vec e_\theta+u_z(r,\theta ,z) \vec e_z$$ in cylindrical coordinates only has $\vec…
glowstonetrees
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Hydrostatic Pressure in Feet, Inches and PSI.

I am looking at this example from my engineering manual. Is there anyone that understands each step of the math so that the answer 0.866 can be reached. It would help me to understand if the steps could be shewn. The unit conversion is a bit…
Eae
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Finding Bernoulli's Equation for a Gas Flow

For inviscid, compressible, but isentropic ($s=$ constant) flow of a diatomic gas, the relationship between the pressure and density is $$p = A(s)\rho^{\gamma}\quad\text{where}\quad \gamma = \frac{c_p}{c_v} = \frac{7}{5}$$ Give Bernoulli's…
MRT
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Finding The Total Surface Force of a Fluid

The question is as follows: The curved surface of a circular cone of radius 2 sitting on the plane $z=0$ is defined vectorially as $$\underline{r}(R,\phi) = R\cos\phi\underline{\hat{\imath}} + R\sin\phi\underline{\hat{\jmath}} +…
MRT
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Differential form of continuity

I hope my question is not too ridiculous, but why can differentiate a physical equation in the following manner: $$\rho VA=\textrm{constant}$$ $$\frac{d\rho}{\rho}+\frac{dA}{A}+\frac{dV}{V}=0$$ It is the equation of continuity at steady state, and I…
George Sailor
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Drawing streamlines of 2D water flow

The $u$-component of a $2D$ water flow is given by $u=7x^2+2y^2$. Is it possible to draw streamlines based on only this?
Bernhard Listing
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Vorticity and circulation of fluid

Does a fluid with velocity $q =\left (z-\frac{2x}{r},2y-3z-\frac{2y}{r},x-3y-\frac{2z}{r}\right)$ posses vorticity? What is the circulation in the circle $x^2+y^2 = 9$, $z =0$ ? where $r^2=(x^2 + y^2 + z^2)$ PS: This question has been asked already…
user1611542
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Basic fluid flow question

I have a question and I'm not sure which equation to apply to it: A fluid is at rest in a gravitational field of strength $\mathbf g = −g \underline k$, where $g$ is a positive constant, and both the unit vector $\underline k$ and the $z -axis$…
juper
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Conformal Mappings (transformation)

I'm looking to show that the transformation $z=Z^3$ maps the region $00$ I'm trying to define the boundaries in the form $Z=s$, $Z=se^{i(pi/n)}$ where, in my case $n$ is $3$ and $0
juper
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flow dilution problem

I have a known flow of Brine (Liter/h) with known concentration (gram/Liter), need to be diluted to defined concentration (gram/Liter), with demineralized water. What Equation should be used to determine flow of water by (Liter/h).
Mahmoud
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find the distance between $P_1$ and $P_2$ as a function of time

An unsteady fluid flow has velocity field $$\mathbf{u} = (u,v) = t^2(x^2y, -y^2x).$$ Find the limit as $t \to \infty$ of $\displaystyle \frac{1}{t^3} \ln D(t)$, where $D(t)$ is the distance between $P_1,P_2$ as a function of time. I have that…
Robert Thompson
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Speed of a jet of water draining a tank

If I have a tank of water filled to depth H and if I let $z$ measure the distance from the bottom of the tank at $z=0$. The fluid has density $ρ$ and the tank has a small hole of area $a$ in the base of which water jets out of. If we now assume…
mathsguy123
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preserving diagonality of a tensor

Under what conditions does a diagonal tensor remain diagonal after a coordinate rotation C. If $ A_{11}=A_{22}=A_{33}$. what has to be true about C for A' to be diagonal
Abigail
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