Questions tagged [potential-flow]
In fluid dynamics, potential flow describes the velocity field as the gradient of a scalar function: the velocity potential.
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Trouble understanding the boundary conditions for the Blasius boundary layer equation
In Section 7.2.1 of Bergman's Fundamentals of Heat and Mass Transfer, there is a derivation of the Blasius equation
$$ 2 \frac{\mathrm d^3 f}{\mathrm d \eta^3} + f \frac{\mathrm d^2 f}{\mathrm d \eta^...
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The validity of "added mass" calculations for real fluid
When a body moves with a constant speed $U$ through a fluid, it experiences constant drag due to the fluid viscosity $\mu$, and dynamic pressure $\frac{\rho_f U^2}{2}$. The question which type of drag ...
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What is the Pressure Across Streamlines?
If you have a flow with uniform streamline entering a bend in a pipe, is the pressure on a streamline near the outside of the bend larger than the interior of the bend if the flow is irrotational? I'...
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Doubt regarding seepage pressure in flow net
The seepage pressure at an intermediate point of a flow net in many books, is given by the formula
$$p=(H-nh)Y.$$
Here, $H$ is the total head at the upstream side of the flow net, $n$ is the number of ...
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Can the irrotational vortex be described using spherical harmonics?
THE BACKGROUND:
The irrotational vortex is an ideal fluid flow that can be represented via the following expressions in cylindrical $\{R,\psi,z\}$ and spherical $\{r,\theta,\varphi\}$ coordinates:
$$\...
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Potential flow over a sphere in circular motion
The potential for a sphere moving in a straight line with a constant velocity U in an incompressible, inviscid and irrotational fluid is given by the following potential:
$$
\phi =−U \left(r+\frac{a^3}...
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Differential equation of a streamfunction
I am studying 2D incompressible potential flow, and there we are usually given the velocity potential $\varphi$.
From there, we then use the Cauchy–Riemann equations
$${\displaystyle {\begin{aligned} ...
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What is smallest hole water will flow through a rain gutter cover?
Consider cover installation over rain gutters on a home.
Reading this question and answer, referenced in link on this site, is very interesting:
Maximum hole size to stop a fluid passing through a ...
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Potential function of a flow around a stagnation point
Following the Steve Brunton lecture about the potential flow. It is possible de find the potential function by solving the Laplace's equation. In his first example (the same as the following picture) ...
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Azimuthal symmetry in the flow past a spherical obstacle
For a flow passing a spherical obstacle, I don't really understand why the azimuthal term
$$\dfrac{1}{r^2 \sin^2 \theta} \dfrac{\partial^2 \phi}{\partial \varphi^2}$$
of $\vec{v} = - \nabla \phi$ is $...
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Stokes stream function derivation
I want to know a concrete derivation of 3D Stokes stream function.
The statement is, for example in 3D spherical coordinates (with symmetry in rotation about the $z$-axis), if
$$\nabla \cdot u=0\tag{...
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How can the vortex be an elemental potential flow if there is a point of curl?
Aero is not my speciality at all so apologies if missed anything. But when looking at potential flows, i thought the whole point is for there to be no rotation at any point and its that reason the ...
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No-slip condition tangential and normal component decomposition
No-slip condition on a corrugated surface (modelled by a sinusoidal function $b(x)$))
$\vec{ u} (x,b(x)) =u \vec{i}+ w \vec{k} = 0 \vec{i} + 0 \vec{k}$
expressing in terms of the stream function :
$$\...
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Which are the incompressible flows around a sphere with no azimuthal vorticity?
Assume fluid velocity $\vec{u}(r, θ, φ)$
radial distance: r ≥ 0,
polar angle: 0° ≤ θ ≤ 180° (π rad),
azimuth : 0° ≤ φ < 360° (2π rad).
At r much larger than sphere radius the flow is $\vec{u}_{r\...
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Fluid-mechanics: Scalar field associated with velocity field
I have just started studying fluid mechanics (without a proper physics education :) and came across the following equation for incompressible steady-state fluids.
$$
\nabla\cdot \mathbf{u} = 0
$$
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