New answers tagged

0 votes

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 $$\mathbf{ u}\cdot\nabla\mathbf{u}= -\frac{u^2}{r}\mathbf{\hat r}.$$
user avatar
  • 947
2 votes

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 ...
user avatar
  • 2,818
0 votes

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 ...
user avatar
  • 2,818
0 votes

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 ...
user avatar
0 votes

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 ...
user avatar
  • 9,211
0 votes

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 ...
user avatar
  • 697
0 votes

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, ...
user avatar
  • 7,720
0 votes

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 ...
user avatar
  • 9,458
0 votes

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 ...
user avatar
  • 201
2 votes

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 ...
user avatar
  • 15.8k
2 votes

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 ...
user avatar
  • 826
0 votes

$\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". ...
user avatar
3 votes

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 ...
user avatar
0 votes
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 ...
user avatar
8 votes
Accepted

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

Is my line of reasoning correct? Is there any incorrect assumptions that I made? Is this resoult coherent or even correct? Seems reasonable to me, at least to zeroth order. You are basically using: $$...
user avatar
  • 8,571
0 votes

What is the $P_o$ or $P_i$ in Bernouilli's equation?

Here is the hyper-physics link for Bernoulli's principle The Bernoulli Equation can be considered to be a statement of the conservation of energy principle appropriate for flowing fluids. You ask ...
user avatar
  • 31
0 votes

What is the $P_o$ or $P_i$ in Bernouilli's equation?

In a static situation, each volume element has its weight balanced by the forces of the surroundings. The sideways pressure (say directions x and y) is equal at both sides of the element by symmetry. ...
user avatar
0 votes

What is the $P_o$ or $P_i$ in Bernouilli's equation?

$P_i$ can be thought of as an initial pressure measurement at some point in a system that contains a flowing fluid. $P_0$ can be thought of as another pressure measurement somewhat downstream of the ...
user avatar
  • 11.5k
0 votes

Propagation velocity of circular gravity-capillary surface waves in shallow water

The first answer is the dispersion relation for plane or one dimensional surface waves in shallow water; $h$ is the depth. If the surface tension term is negligible (low-$k$ regime) it also applies to ...
user avatar
  • 947
2 votes
Accepted

What is the speed of the information transmission between water molecules?

Water molecules in liquid form "communicate" between their nearest neighbors via electrostatic forces, which propagate at the speed of light. But because each water molecule is electrically ...
user avatar
4 votes

Conflicting result for velocity and radius in physiology

When you conclude from $V=Q / A$ that $V$ is proportional to $r^{-2}$ you are implicitly assuming that $Q$ is independent of $A$ and $r$, which is incorrect. Poiseuille’s law tells us that $Q$ is ...
user avatar
  • 35.5k
0 votes

Would water flow from the higher container to the lower one?

Shouldn't the pressure be the same in both buckets, meaning that the water does not flow? This is from a comment, and is the crux of the reasoning for the question. The answer below explains why ...
user avatar
  • 2,829
2 votes

Would water flow from the higher container to the lower one?

I like the willingness to experiment! The result of the experiment is indeed expected. Basically, because there is a connection this is all one body of water. If the surface of a body of water is ...
user avatar
  • 68.9k
3 votes

How far should I spread my fingers when swimming?

fitness.stackexchange link Scholarly literature quotes: The optimum finger spacing in human swimming (2009) by Minettia / Machtsiras / Masters, 10.1016/j.jbiomech.2009.06.012 optimal finger spacing (...
user avatar
  • 628
13 votes

How far should I spread my fingers when swimming?

For swimming, your goal is to maximize the surface area of your hand to allow for more pulling. So you don't want to "shrink" the area by squeezing your hand into a smaller cup shape. But at ...
user avatar
  • 24.7k
1 vote
Accepted

Navier-Stokes Equations in Einstein Notation and its relation to Poisson's Equation

You are taking the inner product of $\nabla$ and $\mathbf v$, so you need to make sure they both have the same index: $$\partial_i\left[\partial_tv_i+v_j\partial_jv_i\right]=\partial_i\left[-\...
user avatar
  • 24.7k
0 votes

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 ...
user avatar
  • 947
-1 votes

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 ...
user avatar
  • 947
1 vote
Accepted

Mass flux in a multicomponent mixture with a concentration-dependent density

First, recognize that because the densities are always uniform, the diffusive mass fluxes are always zero. Therefore, the continuity equation for species $j$ in this special case is: $$ \frac{\partial ...
user avatar
0 votes

Change in appearance of liquid drop due to gravity

It is not an answer but an unfinished draft of how to get the shape : Let $y(x)$ be the profile function of this axisymmetric shape. Supposing a laminar regime friction implies the total counterforce ...
user avatar
  • 165
0 votes

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

Try this in a pool or bucket of water or whatever: Slap the water with your open palm. OUCH ! BELLY FLOP Stab the water with your outstretched fingers, blade-like they go right in like an Acapulco ...
user avatar
  • 1
1 vote

Reducing yawing in a kayak with a rudder

I want to know how much the kayak will yaw $~\psi(t)~$ and where the center of rotation is. I) the equation of motion $${\frac {d}{d\tau}}\beta \left( \tau \right) -{\frac {{}{\it Fy }-m \left( {\...
user avatar
  • 8,756
0 votes

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 ...
user avatar
  • 6,736
2 votes

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 ...
user avatar
  • 24.7k
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 ...
user avatar
  • 2,341
-1 votes

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
user avatar
  • 1
0 votes

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,...
user avatar
  • 8,571
-1 votes

Submerged Landau jet

Since the problem has an axial symmetry then he rid off the $\phi$ angle, i.e. no dependence on the azimuthal angle $\phi$ hints to the absence of this variable in the solution in the function $F$ or $...
user avatar
  • 69
1 vote

Navier-Stokes Equation Derivation in "A Mathematical Introduction to Fluid Mechanics" (Stress Tensor)

Assumption 1) in the book means that each component $\sigma_{ij}$ is a linear and homogeneous function of each $\frac{\partial u_k}{\partial x_l}$. To express that mathematically you need $3^4$ ...
user avatar
  • 228
1 vote

Navier-Stokes Equation Derivation in "A Mathematical Introduction to Fluid Mechanics" (Stress Tensor)

No, not a matrix, but a rank 4 tensor. In index notation it means: $\sigma_{ij}=A_{ijkl}(\nabla u)_{kl}$ You can think of it this way: A linear transformation taking one vector (1-index object) to ...
user avatar
  • 365
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 ...
user avatar
  • 812
2 votes

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 '...
user avatar
0 votes

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 ...
user avatar
  • 101
2 votes

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 ...
user avatar
0 votes

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.
user avatar
  • 6,736
8 votes

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' ...
user avatar
8 votes

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.
user avatar
  • 732
108 votes
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 ...
user avatar
  • 5,005
74 votes

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

In simple terms, water (or any fluid) will move out of the way; concrete won’t (unless it is hit very hard). The important properties are viscosity and elasticity rather than compressibility.
user avatar
  • 35.5k
13 votes

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

Incompressible doesn't mean that it has to keep the same shape. But, due to viscosity, water can be "slow" to change its shape under external influence. So when a diver arrives too fast, ...
user avatar
  • 4,323

Top 50 recent answers are included