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7

Note that this is almost identical to this previous SE question; the answers on that question however, including the favourite answer with 13 upvotes, are somewhat erroneous (or rather oversimplified). This is a good question: the exact details of how such elevations, called 'central uplifts', form are not well known. What follows is a brief summary of ...


5

The heat flow (per unit area) through some thin layer, e.g. a boundary layer of water, is given by: $$ \frac{dQ}{dt} = \frac{K\Delta T}{d} $$ where $K$ is the thermal conductivity, $d$ is the thickness of the layer and $\Delta T$ is the temperature difference between the two sides of the layer. So a high thermal conductivity does indeed mean a high heat ...


5

The cochlea has a complex physical structure, with multiple membranes and fluid-filled chambers. Therefore to explain the separation of frequencies along the basilar membrane of the cochlea is complex to. Sure, there are a lot of very general descriptions (even the answer of theblackcat) and a lot never go into the actual physics of the system. This ...


3

The argument is that the air was flowing through the hole at around 700 mph, so the air inside the aircraft had a substantial velocity in the direction of the hole. The air velocity inside the plane would have been less than 700 mph because the flow was converging on the hole, but the speed of the air would still have been hundreds of mph. When the hole was ...


3

The idea (theory) behind the selfsimilarity Parameters like Reynolds- or Machnumber is: that fundamental flow features of a specific flow have a dimensionless number connected to it (Dimensional homogeneity). This means: not the dimensional units (like inch, meters, tons, horsepower) should be used to describe (in this case) flow but dimensionless numbers. ...


3

I think you are right. (Involute spiral: Wikipedia) If you take a string wound around a stationary ball and unwind it, its end traces an involute spiral. Similarly, if the ball is rotating and the string runs out in one direction, it is the same curve with respect to the ball. A drop of water leaving the surface of the ball should travel in a straight line ...


3

Don't do it that way. You have what is called a "Change Point". Run it up until the time when the change should occur. Then stop the solver. Perform the instantaneous state change. Then restart the solver. So much silliness happens when people try to run ODE solvers over discontinuities.


2

I don't think this is as large of a problem as it seems. Consider the steady state assumption in more detail. $v_2$ is the final velocity going through the hole after sufficient time has passed for the acceleration to occur. Right after you open the hole everything is stationary. There is an acceleration phase which is normally assumed to take a short ...


2

If you assume that the water leaves the ball tangentially and ignore the effects of gravity you get exactly those equations. To see it look at the trajectory of a drop released from a given point at time t (ball rotating clockwise): $x=x_0+v_{0x}t=r \cos\omega t+ r\omega t \sin(\omega t) $ $y=y_0+v_{0y}t=r \sin\omega t- r\omega t \cos(\omega t)$ The ...


2

For the modeling of surface wave motion there are only two restoring forces to consider: surface tension and gravity. Compared to gravity, surface tension forces are very weak and therefore have a greater influence on the regime of the smaller, capillary waves. Waves in deep water carry away the energy dissipated by shear wind forces - perhaps from a storm ...


2

Azad provides a link to one of the many empirical models that can predict pressure drop, but if you are seriously planning and investing in plumbing a new home - take caution. A general comment to begin is that tubing or pipe in general will create a resistance to the flow of fluid going through the pipe for any given pressure, so the bigger the pipe, the ...


1

1/f spectra have the unique distinction of being "scale invariant" in the sense that the energy in an interval df is proportional to df. The 1/f spectra in fact have the property that the in an interval with width df available energy is proportional to df but not with f. There, namely "scale invariant" attribute for. It is not the energy, but the signal ...


1

Probably you have your question answered already, however, let me point out that: You are incorrect. You can't think of a hydrostatic system as it was an electric circuit. In an electric circuit what you (or the source) supply(ies) is the voltage and the result of that voltage acting upon the resistor of given resistance is the current. In hydrostatic ...


1

How would you solve this for a single small hole? What happens if you now move that hole down by a small amount? What if you add up the contributions of all these holes? Congratulations, you just integrated the expression for the flow rate over the aperture.


1

Perhaps I could share some idea for further research. If we could make actual and correct pressure measurements in the cochlea to reveal wether the non-stationary Bernoulli effect is a good description of the actual physics-of-how-the-cochlea-isolates-frequencies-along-its-length? I would consider: I would propose to use a pitot tube, with sensor in the ...


1

First, it's not only drag that slows down the air, every force has to be matched by an equal and opposite force including lift. Second, friction is not the sole cause of drag, indeed there's drag on an airfoil in an inviscid fluid due to pressure. So why we need sophisticated airfoil design when traditional windmills can work and how modern wind turbines ...


1

A fluid in motion possesses momentum, just like any massive body in motion. And if the momentum changes, for example if the fluid hits a plate as you suggest, then there will be a force defined by: $$ F = \frac{d\vec{p}}{dt} $$ And remember that momentum is a vector, so the force we get by differentiating it is also a vector (obviously) and is dependant on ...


1

Initially, I agreed with Olaf Chujko's answer to this question; however, on further reflection, I think the most accurate answer is 'it depends': Firstly, from the schematic that is given, when switch A is pressed, the cylinder volumes above the two cylinders will be vented to a reservoir at ambient pressure (trust me, I work in Oil & Gas and I look at ...


1

As a planetary science and aviation enthusiast I can offer these tidbits, although a bit late for the 2013 posted question.... http://www.wired.com/2010/05/gallery-clouds/ This shows mountain-induced Van Karman vortex street (Strouhal instability) in a cloud layer as viewed from space. and so does this: ...


1

Joule heating is typically associated with increases in random kinetic energy (i.e., heat) due to $\mathbf{j} \cdot \mathbf{E}$. Ohmic dissipation and resistive heating are similar in a sense to Joule heating, as all three result from fluctuating electric fields acting as an effective drag force on an otherwise free flowing charged particle. Ion drag is ...


1

Here is a sketch of where it comes from. First just consider the perfect fluid terms and note the thermodynamic relation $$ \rho + p = \mu n + T s, $$ where $T$ and $s$ are temperature and entropy, $\mu$ and $n$ are a chemical potential and number density. We also have a relation for derivatives of $p$ $$ dp = n d\mu + s dT. $$ Now if you take the ...


1

The Navier-Stokes equations assume (assuming we are looking at a vector conservative form): The continuum hypothesis, which is applicable for Knudsen numbers of much less than unity. The Navier-Stokes equations must specify a form for the diffusive fluxes (e.g. otherwise you would have the Cauchy momentum equation not the Navier-Stokes momentum ...


1

For our three compartment hearing sense, from a physics point of view, there is a basilar membrane stimulation, from base to apex, in its pathway in the cochlea, to a place on the basilar membrane. By periodic movement of perilymph, non viscous fluid, backwards and forewards, in the cochlear duct meet the conditions of a potential flow. The basilar ...


1

Pretty often I notice that a small rain system or even a large one will congregate or follow a large interstate highway It is like urban pollution. A storm releases rain over cities: City pollution may also impact cloud formation and rainfall. “Water vapor doesn’t ordinarily spontaneously condense into drops to form clouds,” says climate scientist ...


1

I'd say option 1. Doubling the diameter would reduce the pressure loss in that pipe by 32 times in a constant flow rate scenario. Overall pressure loss will also decrease but not that much. Surface area increases 4 times then if the flow rate is constant the flow velocity will decrease by 4 times according to continuity equation. Then we have this ...


1

Bernoulli's principle is a simplification of the Navier–Stokes equations, namely it assumes constant density and steady state. In the situation where $A_2$ has almost the same surface area as $A_1$ it will be hard to satisfy the assumption that the system is steady state. In real life there will also be some frictional losses, but if you neglect those then ...


1

Static pressure in a compressible flow depends on the density but not the speed (not directly). Speed and geometry may affect the density. For isentropic flow (neglecting gravitational potential): $$ {p \over \rho^\gamma} = constant, \gamma = {c_p \over c_v} $$ which could be turned into this: $$ {p \over p_0} = ({1 \over 1+{(\gamma-1) \over ...


1

Yes, the flow rate is related to the pump pressure by the Darcy-Weisbach equation: $$ \Delta P = f_d \frac{L}{D} \frac{\rho v^2}{2} $$ where $L$ is the length of the pipe, $D$ is the diameter, $\rho$ is the water density, $v$ is the flow velocity and $f_D$ is a fudge factor called the Darcy friction factor. $f_D$ varies with the pipe diameter, density and ...



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