# Tag Info

9

It is an interplay between the wind and the shoreline, and basic laws of reflection. As you can see in your photo, where the water surface is still, you see a reflected image of the skyline - lighter for the sky, darker for the buildings. Where the water surface ripples, you get reflections "from everywhere" - some from the sky, some from buildings, etc. ...

7

It depends. It could be wind, simply the lighter section is rougher and the waves scatter light back to you while the flatter section appears darker because the light is scattered in a different direction. It can also happen where waters mix. A fresh water stream merges into an ocean, a flowing river meets a shallow stagnant area or (as below) river water ...

7

Yes, the exact solution is known. The general spherically symmetric metric is $$g=-B(r)\mathrm{d}t^2+A(r)\mathrm{d}r^2+r^2\mathrm{d}\Omega^2.$$ The solution for $A(r)$ is $$A(r)=\left[1-\frac{2G\mathcal{M}(r)}{r}\right]^{-1},\quad\mathcal{M}(r)=\int^r \rho \,\mathrm{d}V=\int_0^r 4\pi r'^2\rho(r')\,\mathrm{d}r.$$ The solution for $B(r)$ is ...

4

There are two primary factors that allow the cochlea to isolate frequencies. These are generally referred to as passive and active properties: tl;dr version: The passive properties are due to the mechnical properties of one of the membranes in the cochlea, the basilar membrane, primarily the width and stiffness at a given point. The active properties are ...

3

Imagine your object to be made up of a lot of infinitesimally small "straws" - little cylinders. Each cylinder has an area $dA$ and a length $\ell$. You know that the volume of such a cylinder is $\ell dA$. Now look at the pressure difference between the top and bottom of that cylinder: at the bottom, the pressure will be greater by $\rho \ell g$ (where ...

2

Altitude can indeed have such an effect. As your linked article explains, one can get a rough sense of the aerodynamic force on a spherical ball by neglecting viscosity (i.e., model air as a bunch of ballistic particles that do not drag on one another), in which case the formula is1 $$F = \frac{16\pi^2}{3} C_l \rho \omega v r^3.$$ The important point is ...

2

You are confusing yourself. The statement $P - P_0$ would remain the same is false. Why would it remain the same? There is a certain amount of compressed gas inside the bubble, and there is a force that maintains it compressed. In the first case, this force is just the surface tension. In the second case, it is the surface tension reduced by the ...

2

Both are of course connected, but denote very different concepts. Your definition of variance is fine with me. It tells us, on average, how much the flow deviates from its average. Intermittency is much harder to explain. I'll do my best here: In a scale invariant flow, the $n$'th order correlation function will take a scaling form, $$\Delta\Psi(n,r) = ... 2 Inviscid flow doesn't exist. That's so important to understand, I'll say it again: Inviscid flow doesn't exist! However, we use it all the time. So what gives? It turns out that many of the effects we are interested in are viscous, but the viscous effects can be modeled various other ways. This is effectively the same type of question as Does a wing in a ... 2 Since the force is based on the wetted perimeter, any configuration that would make the perimeter very large in a very small area would be overwhelmed by the surface tension of the water droplets connecting nearby perimeters. So the effective perimeter would be much lower. So you are sunk! 2 You are referring to the equation:$$\frac{\partial \rho}{\partial t} + \frac{\partial \rho u_i}{\partial x_i} = 0$$which is the conservative form of the continuity equation in Eulerian form (fixed domain, fluid moving through it). This can also be written as:$$\frac{D \rho}{D t} = 0$$which is the Lagrangian form (the density of a moving region of ... 2 First up thanks to all who took an interest especially @irishphysics who stuck with the question for some time. It turns out that the phenomena was analysed and solved by Lord Kelvin and is known as the Kelvin wave pattern. The pattern itself is the result of a spreading pressure wave which manifests itself as the curved diverging wave crests (the ones I ... 2 Consider a control volume \Sigma(t) of a fluid with density \rho(\mathbf x,t). The mass inside \Sigma(t) is clearly given by$$M(t):=\int_{\Sigma(t)}\rho(\mathbf x,t)\text d^3\mathbf x.$$The way \Sigma(t) is defined is that its mass content doesn't change with time, that is, a control volume is representing the time evolution of a certain amount of ... 2 Flutter is only possible if you have similar structural and aerodynamic frequencies. One without the other would produce much lower amplitudes. Look at a mass-spring system suspended on an eccentric tappet which sits on the edge of a small rotating wheel. When the wheel turns, it raises and lowers the top of the spring, and the mass on the bottom will ... 2 Obviously darkness of lake water depends on depth of lake, impurity in water and many other things. But my answer to the question What causes the surface of lake to appear darker in some places? is Its depends on two things, [1] Position of observer [2] Position of sun in the sky. If sun is nearer to horizon then the amount of light, reflected from ... 2 I don't think creating a vortex effect will increase the velocity of flow, because it would direct movement in a direction other than forward. Smooth bore gunbarrels, for example, have greater muzzle velocity than rifled gunbarrels (assuming all other variables are equal). You might want to maximize laminar flow and to minimize turbulence inside the tube. ... 1 The key to flow of macroscopic particles is to make sure they don't "clump" or jam. I don't know what is propelling them down your pipe (gravity? Air flow?) but that will affect the answer. In general, adding some vibration keeps particles flowing freely; a larger pipe diameter with minimal obstructions / bends is the other thing. Making the pipe diameter ... 1 Water forms close to perfect spheres in zero gravity due to it's surface tension. There's a variety of videos of water in the space station. Ice, assuming you start with one of those balls of water, you have to ask first, would it freeze outside in (say, the temperature of the station is dropped below 0 C), or would it freeze inside-out, say you stick a ... 1 Let's review the linearisation and go to the further details. Just the pressure might be not enough. Take the momentum equation:$$ -\frac{1}{\rho}\nabla p = \frac{\partial \vec{v}}{\partial t}+\vec{v}\cdot\nabla\vec{v} $$Here we have to eliminate the convective part \vec{v}\cdot\nabla\vec{v}. Usually the argumentation is that changes of the velocity ... 1 If we can assume the flow rate is low, so the flow is laminar, then the rate of water flow is given by the Hagen-Poiseuille equation:$$ V = \frac{\pi r^4}{8\mu\ell} \Delta P $$where r is the radius of the neck, \ell is the length of the neck and \mu is the viscosity. The pressure different, \Delta P, is given by:$$ \Delta P = \rho g h $$where ... 1 One-dimensional shocks are modeled using the Rankine-Hugoniot relations. These give the jump in density, pressure, and temperature across an infinitely thin shock and are found by conducting a control-volume analysis of the region around the shock (conservation of mass, energy and momentum). The relations are:$$\frac{p_2}{p_1} = 1 + \frac{2 ...

1

Your assertion that spinning the glass causes the liquid in it to also spin may contain only a grain of truth and a lot of optical illusion. It is extremely difficult to see the motion of water or even just the exact position of its surface; especially with calm water, this is a frequent cause of misjudged landings for pilots of sea or amphibious planes. ...

1

i searched for the exact same problem recently after a debate with one of my colleagues. In my opinion, you already gave the answer to your question yourself. A source dipole is the flow field resulting from a sink and a source brought together. In a sink, all streamlines point radially inward to the singularity at the origin, in a source, all point ...

1

UPDATE - With a reference to: http://www.researchgate.net/publication/48323925_Applying_physics_makes_auditory_sense__a_new_paradigm_in_hearing OP, user263399, COMMENT: Can you explain the phase wave and its cause? On reading the linked paper I'm confused on how ther explanation involving the change in liquid volume velocity would create a ...

1

The full Euler equations (so assuming inviscid) are: $$\frac{\partial }{\partial t} \iiint \rho \vec{u} dV + \iint_{CS} \left[\rho \vec{u} \left(\vec{u}\cdot \hat{n}\right) + P \hat{n}\right] dA = 0$$ or in differential form if you prefer: $$\frac{\partial \vec{u}}{\partial t} + \vec{u}\cdot\nabla\vec{u} + \frac{1}{\rho} \nabla P = 0$$ So your force ...

1

I don't really conceptually understand why the mass flux/mass flow rate into the arbitrary volume BCDE is given by [...] $u$ is speed. This is a distance per second. Multiply a distance (per second) with a cross-section area, and you get volume (per second). So $$\dot V=Au$$ where the dot in $\dot V$ simply means per second. If some particles of water ...

1

The continuum hypothesis means the following: at each point of the region of the fluid it is possible to construct one volume small enough compared to the region of the fluid and still big enough compared to the molecular mean free path. Why is that important? Because of two things. First, since the volume you can build at each point is very small compared ...

1

You're calculating the rate of liquid flow through a tube under a specified pressure gradient. The rate of flow changes depending on whether the flow is laminar or turbulent. Laminar flow is described by the Hagen-Poiseuille equation: $$\Delta P = \frac{8\mu\ell V}{\pi r^4}$$ where $\Delta P$ is the pressure drop, $\mu$ is the viscosity of your saline ...

1

You are missing the bit under-braced here: $$\dot{m}=\rho\underbrace{\mathbf A\cdot\mathbf v}$$ This is a dot product, which takes two vectors and returns a scalar: $$c=\mathbf a\cdot\mathbf b=a_xb_y+a_yb_y+a_zb_z$$ So the mass flow rate is indeed a scalar value.

1

Your fractal pattern will fail for reasons already given. However, given a large enough lake, you should be able to stand on a frame which is supported by a very long (perhaps circular) wire. All you need is for the force per meter (assuming uniformly applied) caused by your body weight and the structure itself to be less than the surface tension force ...

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