All Questions
Tagged with dimensional-analysis fluid-dynamics
7
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33
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Solving for a linear equation from a nondimensionalisation
Whilst doing my homework I came across the following question and got particularly stumped at question c). I do not know how I could possibly derive a precise linear relationship. Any help?
When a ...
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1
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487
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Deriving the Thin-Film Equation from Navier-Stokes Equations
I want to start with the general Navier-Stokes equation in 3-D:
$$ \frac{\partial \vec{u}}{\partial t} + (\vec{u}\cdot\nabla)\vec{u}=-\frac{1}{\rho}\nabla p+\frac{\mu}{\rho}\nabla^2\vec{u}+g\sin{\...
- 1,019
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Fluid Mechanics. How to nondimensionalize a variable with a power law index.
can anyone help me in nondimensionalizing these equation? I start from the equation in the first line. Using the nondimensional variable from the third line, I get the half-completed equation in the ...
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Problem with Dimensional Analysis - Darcy's velocity
Once, by the Darcy law, the flux of a fluid with viscosity $\mu$ in a porous media with permeability $K$ between the points $a,b$ (with distance $L$) is given by
$$Q=-\dfrac{K}{\mu}(p_b-p_a)\dfrac{...
- 1,525
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What are the units of every vector in the codomain of the vector field $\textbf{F}$?
I don't understand how the rate at which a fluid flows along the bottom edge of a rectangular region A in the direction of i is approximately $\textbf{F}(x,y)\dot{i} \Delta x$. In physics, the rate as ...
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2
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492
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Green's Theorem Derivation and Explanation on the dot product with $\mathbf{\vec F}(x,y+\Delta y) \cdot \mathbf{\vec j}\,\Delta x$
Green's Theorem gives that the flux on a vector field $\mathbf{\vec F}$ over a closed curve C is equal to the double integral over the enclosed region of C of the divergence of $\mathbf{\vec F}$ (...
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253
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Normalizing (Non-Dimensionalising) the Young-Laplace equation
I have a simple fluid statics problem of a liquid drop, resting on a stationary flat solid surface with a static gas of constant pressure above. The density in both the gas and liquid are constant. To ...
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