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The sand particles interact on a macroscopic level different from water. The edges can lock together and more efficiently distribute force. Water molecules, being part of a liquid, do not distribute force this way. They tend to move out of the way instead.
Mr Wizard has a great demonstration of this, using a plunger and salt rather than bullets and sand. ...
4
I think the main difference is that the molecules of water moves a lot at room temperature, while the grains of sand are static.
This also explains why sand poured over one side of an U-tube doesn't climb to the other side. Even if instead of common grains, they were lubricated spheres, they have no reason (no force) to climb.
In the case of a bullet, the ...
3
You have the correct understanding about the functioning of the refrigerator. The phenomenon you have stated is known as the Joule - Thomson effect. This effect cannot be observed in all fluids. Also different fluids have different change in temperature for the same pressure drop. This is the main reason why we choose a particular refrigerant which will give ...
2
Moving air can have any pressure. However if air is moving away from a surface without enough new air flowing in to replace it, then the pressure at that surface drops. For a wing with lift the cause is inertia / momentum conservation. Since the air collides at higher rate with other parts of the wing there is a net force, hopefully up.
2
I specialize in acoustics, and so I will discuss shock formation in that context. There are other ways shocks can form (e.g., super-sonic flow over a rigid barrier), but as they may be different (I don't know), I will exclude them from my discussion.
Linear acoustics is, as you say, a perturbation of the fluid mechanics equations. If the small perturbation ...
2
Usually people who open a window are interested in replacing their inside air with outside air. If you only open one window, all of the exchange between inside and outside is happening thanks to turbulent mixing near the window. But if you open two windows, you may be able to arrange them so that air is mostly entering at one window and mostly exiting at the ...
2
Pressure has the ability to do work and change the energy of a system. From thermodynamics:
\begin{equation}\tag{1}
dE = T \, dS - p\, dV.
\end{equation}
You could also define an energy density associated to pressure (at constant entropy):
\begin{equation}\tag{2}
\frac{\partial E}{\partial V} = -\, p.
\end{equation}
Since from special relativity energy is ...
2
They are crystals of ice which grow outward from nucleation sites, where the freezing process prefers to start. Those crystals expand until they hit an edge of the container, or another crystal as it grows.
This effect is exploited in a process called directional casting, in which a gas turbine blade can be grown as a single crystal from molten superalloy by ...
2
Big-O notation, while it is very popular in computer science, is about the growth of functions. In computer science, the functions they are worried about happen to be measuring system resources like number of operations required (and hence the time it takes to run) and space in memory. The basic idea, though, is just functions.
The context in which this ...
2
The shape
The mechanical displacement of water in water requires less energy than the displacement of sand in sand. This is because the movement of a water molecule through the conglomeration of water molecules requires less energy for the displacement and rotation of each molecule than the displacement of grains of sand.
https://de.wikipedia.org/wiki/Sand
...
1
I regard this more as a combined flow and chemical reaction analogy. $\beta s_ix_i$ is analogous to the rate of a 2nd order chemical reaction, representing the rate at which susceptible people become infected. The summation terms represent the flow (interchange) of $s_i$ susceptible people between nodes i and j, and the flow (interchange) of infected ...
1
It's not exactly like a fluid.
We have three possible states.
A fluid can be seen as taking values, at each point in space, on a continuum between two possible states: high density / a location has the maximum number of particles, and empty space.
Here we have similarly let the implicit third state, "recovered", correspond to the "rest" ...
1
It is a basic result from calculus. The derivative of a function $f(t)$ is defined as
\begin{equation}
\frac{df(t)}{dt}=f'(t)=\lim_{\Delta t\to 0}\frac{f(t+\Delta t)-f(t)}{\Delta t}
\end{equation}
Now you can Taylor expand:
\begin{equation}
f(t+\Delta t)=f(t)+f'(t)\Delta t +O(\Delta t^2)
\end{equation}
It means
\begin{equation}
\frac{df(t)}{dt}=f'(t)=\lim_{\...
1
Imagine integrating the equation over a volume. The first term gives the rate of change of the mass inside the volume. By the divergence theorem (see the nice wikipedia article), the second term gives the rate at which mass is flowing out of the volume. Any time mass is conserved in a region, the sum of these two terms has to be equal to zero. The equation ...
1
A stream function is just a scalar function whose gradient is perpendicular to the flow, and the magnitude of whose gradient is the speed. If you define $x’$ to be a coordinate locally perpendicular to the flow, the average speed over a small interval $\Delta x’$ is $v\approx\frac{\Delta \psi}{\Delta x’}$. The flux between two points is $F=v\Delta x’\approx\...
1
Wind blowing against one side of the house will create higher air pressure on that side and relatively lower air pressure on the opposite side. so opening windows on those opposite sides will maximize internal air flow. Even opening a side window that is parallel to the wind can create some air flow from the lower air pressure due to Bernoulli's principle. ...
1
In particular I would like to understand the wave steepening process.
Nonlinear wave steepening can be thought of conceptually as the wave phase speed depending on the wave amplitude. That is, larger amplitude waves will propagate faster than lower amplitude waves. If there is nothing to limit this steepening process, the wave will undergo wave breaking. ...
1
Since I have made several programs for lift and drug force acting on airfoil computation, I can explain my suggestion about how lift force generates. First of all, there is wrong explanation in Wikipedia about it. When we compute force we put some boundary condition for air on the top and bottom surface of airfoil. This condition is very simple and it turns ...
1
Here is something to help us imagine the reason from first principles. We can assume that the air above the paper and the air below have equal temperatures. This can happen if the velocity of the 'blow' isn't too high. Then by the time the moving air reaches the area above the paper, its temperature has equalized with the surroundings.
The kinetic energy ...
1
There are two different issues here:
(1) how do wings generate lift?
(2) what is the physics underlying a connection between flow velocity and pressure in a fluid?
I will answer just (2). The connection is conservation of energy.
To state the connection correctly, you must not look at different places across the fluid; you must pick a flow line and follow it ...
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