# Tag Info

### analytical solution for navier stokes where non-linear term is important

In cylindrical Couette flow the non-linear term is non-zero: in fact it is the centripetal acceleration $$\mathbf{ u}\cdot\nabla\mathbf{u}= -\frac{u^2}{r}\mathbf{\hat r}.$$
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### Incompressible fluid flow in tilted pipe setup - Continuity Equation, Flow Rate, Mass Conservation

The water does not necessarily accelerate going through a downwards stretch of pipe. It is prevented from doing so by the other water ahead of and behind it, and by the walls of the pipe. Just as you ...
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### Derivation of flow rate and pressure drop

That was my question. Friction losses are usually characterized in terms of dynamic pressure: $$\Delta P = k \frac{1}{2} \rho u^2$$ ($\Delta P$ pressure drop, $\rho$ density, $u$ average flow ...
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### Incompressible fluid flow in tilted pipe setup - Continuity Equation, Flow Rate, Mass Conservation

Very good question! I myself would love to have a good explanation. For now, though, I can give you an explanation which is not good but may satisfy you. To describe fluid motion, we use the field ...

### Why flapping rudder produce net thrust if one half-stroke produce thrust and second half-stroke drag?

The key point may be that stern of the boat moves laterally. During the first half of the stroke, the force exerted on the rudder by the water is forward and to the side. The sideways component causes ...
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### Additional Pressure/Force Impact on a solid body as it moves through a fluid

The amount of force exerted by a fluid on an immersed moving object is just the opposite of the amount of force applied by the object on its surrounding. As far as I know, there is no global formula ...
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### Why is the wake of boats leaving a long lasting print on the sea?

A ship's wake is just very fine air bubbles churned into the water by the propeller. It is not oil because boat engines do not leak that much oil. You'll also find other type of surface watercraft, ...
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### Why flapping rudder produce net thrust if one half-stroke produce thrust and second half-stroke drag?

I guess that during the forward thrust portion of the stroke the skipper pushes harder and faster creating more turbulence and drag and thus more thrust. During the reverse thrust part they slow down ...
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### Can Mach number be greater than 1 if mass flow rate is decreasing?

The vertical axis is labeled Normalised Mass Flow Rate ( and the brackets [-] indicates no units). It is the value calculated on the right side of the equation divided by the value of the right side ...
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### Why flapping rudder produce net thrust if one half-stroke produce thrust and second half-stroke drag?

Below the horizontal line is my original answer, submitted 5 hours ago, but there is a better explanation that I overlooked. In a comment to another answer Gordon McDonald points out that since the ...
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### Why flapping rudder produce net thrust if one half-stroke produce thrust and second half-stroke drag?

I suspect it has nothing to do with regions of higher or lower pressure (if those even exist). When you pump the rudder you are pushing water backward and by Newton's Third Law that water exerts an ...
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### $\Delta P=QR$ in fluids

Its just a matter of convention which direction voltage/pressure difference is calculated. When using Ohms law in a circuit, youre supposed to follow the so called "passive sign convention". ...

### Why does a stream of falling water get narrower at the bottom?

There will be an additional contraction term due to the fact that the water entering the stream sideways carries with it a velocity component in the x and y directions, but I do not know how to ...
Accepted

### Comparison of 2 fans

Poor design of the blade shape will cause more useless churning of the air and greater noise generation. Better design will cause less churn, less noise, and better power transfer from the motor to ...
Accepted

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### Galilei transformation of mass flux

You need five-vectors to take the Galilei limit of special relativity. Check out Davison Soper Classical Field Theory. He uses the Galilei limit of the NS equation as an example if I remember ...
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### Navier-Stokes Equations in Einstein Notation and its relation to Poisson's Equation

You can only repeat an index twice: that means sum over it. Your equation with three js is meaningless. You need to take a curl in order to eliminate the grad p term, not a div. That will involve the ...
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1 vote
Accepted

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### Bernoulli's equations on a falling (not freefall) bucket of water

The air pressure above and external to the spout do not change. But, if the bucket is accelerating downwards, the water in the bucket experiences a (fictitious) upward force that counters gravity and ...
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### Does the Continuity Equation Imply it's Zero for Incompressible Flow?

Since the dot product is commutative, doesn't this imply that $(\mathbf u\cdot\nabla)\mathbf u=0$? No because $\nabla$ is an operator that acts on the object to its right. The term in the parenthesis ...
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1 vote

### Velocity at a place for fluid with a given pressure gradient?

I think the answer should be $$v \propto \frac{1}{\sqrt r}.$$ Indeed, if we assume a purely radial, steady, incompressible, inviscid flow, then the Navier-Stokes equation along the radial coordinate ...
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### If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it?

It can also be viewed in acceleration terms, a sufficiently accelerated water still will pass through a concrete wall, neatly
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### Submerged Landau jet

The same total momentum flux (the "momentum of the jet") must pass through any closed surface surrounding the origin (in particular, through an infinitely distant surface). For this to be so,...
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1 vote

### If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it?

Basically, you do experience an impact when you hit the free surface of a liquid (which could be very substantial), but the water moves out of the way so it's not like hitting concrete. When a solid ...
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### If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it?

As others have pointed out, water isnt very different from solids in terms of its resistance to changes in volume; but the defining difference between a liquid and a solid, lies in its resistance to '...

### If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it?

I don't quite understand the question, but isn't it: Because water is a fluid and ground is not. Falling with 100m/s on water might be much the same as falling on ground, but when diving, then your ...
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### If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it?

Well, depends on the way someone dives in and the altitude. You might have wondered at some point, why does it hurt when you fall into the water with your belly, but when you fall in with your feet ...
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### If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it?

If water is treated as incompressible it has constant volume, but being a fluid it can change shape. The less the viscosity the easier it is to change its shape.
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### If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it?

For very skilled divers, they will also use a technique where they enter the water hands first, with a particular shape that pulls air in with them. They then spread the hands out, creating a 'hole' ...
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### If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it?

Concrete is rigid to a good approximation: it will keep its shape and its volume. Water is just incompressible: it will keep its volume but not its shape. Water will move out of your way on impact.
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Accepted

### If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it?

Adding another perspective to the existing answers: In your usual diving scenario, water is not confined to the points in space it occupied before, while a slab of ground is – on account of water ...
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