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21

What you need to compare when looking at bodies of different sizes and asking how the forces relate, is in general, the Reynolds Number as you included in your question. This is defined as: $$ Re = \frac{u L}{\nu} $$ where $u$ is the fluid velocity, $L$ is a representative length scale and $\nu$ is the kinematic viscosity of the fluid. This can also be ...


16

One's naive expectation would be that as the object moves through the medium, it collides with molecules at a rate proportional to $v$. The volume swept out in time $t$ is $A v t$, where $A$ is the cross-sectional area, so the mass with which it collides is $\rho A v t$. The impulse in each collision is proportional to $v$, and therefore the drag force ...


10

Actually, there are two different viscosity coefficients. You can see this from the stress tensor $$ \sigma_{ij} = -p_0 \delta_{ij} + \eta \left( \frac{\partial v_i}{\partial x_j} + \frac{\partial v_j}{\partial x_i} - \frac{2}{3} \delta_{ij} \frac{\partial v_k}{\partial x_k} \right) + \zeta \delta_{ij} \frac{\partial v_k}{\partial x_k} $$ which has the two ...


10

The Kutta condition is completely artificial. The potential equations are completely artificial. The potential equations are a mathematical construct we use because it's much simpler than the full Navier-Stokes set of equations. We know the Kutta condition is never actually upheld in any real flow ever. However, when we perform all of our mathematical ...


9

This is what's happening in the video. I've drawn just a single drop, and for convenience I've ignored the curvature of the plates (it's harder to draw curves!): It looks as if the (red in this example) ink drop is being mixed with the fluid, but actually it's just being stretched out into a thin sheet. When you turn the cylinder back again the sheet is ...


7

I don't know if there is a formal name for it, but my favorite search engine likes to call it a Reverse Entropy Machine. The main fluid is glycerin and the dye is food coloring. You can see an example of the setup here. You can also watch a video that describes it along with some lecture notes where it is called Kinematic Reversibility. It works because ...


7

A version of your proof without a stream function: The Laplace acting on the velocity may be expressed via the curl of the curl identity and aside from the $\nabla\times (\nabla\times \vec u)$ which vanishes, you also get another term $\nabla\cdot (\nabla\cdot \vec u)$ which vanishes (only) if one assumes incompressibility (it's the conservation of the ...


7

Imagine two two trains side by side - one going faster than the other. Frictionless rails. Start shoveling coal from the slow train to the fast one, and from the fast to the slow one. Every shovel of coal results in a transfer of momentum - until the two trains move at the same speed. In the same way, when layers of liquid move past one another at different ...


6

The article's preprint Mayer H. C., Krechetnikov R. "Walking with coffee: why does it spill?," Phys. Rev. E 85, 046117 (2012). is available from the UCSB site. From a glance of the article the phenomenon is not specific only to coffee. The authors make use of the next formula: The natural frequencies of oscillations of a frictionless, vorticity-...


6

When a viscous liquid flows through a tube in a laminar flow,why is its velocity highest at the center? Because the boundary condition is that it's zero at the walls? Does that answer your confusion? It shouldn't seem surprising that the point furthest from the walls (the center) is the highest velocity, considering that the fluid exactly at the wall is ...


6

Both viscosity and surface tension are connected theoretically to inter-molecular forces, but they are still very different concepts. Viscosity force is a force that acts only when the fluid is moving and acts to decrease the gradient of velocity in it. Viscosity is a characterization of the fluid itself. Roughly speaking, it says how fast momentum of ...


6

Not necessarily, it depends on how different the viscosities are. @MonkeysUncle got it right. If the Reynolds number is < 2,000 the flow is laminar; if it's > 4,000 the flow is turbulent. Since the Reynolds number depends on viscosity, if the viscosity of the two fluids is different enough that it changes the flow from laminar to turbulent, then you ...


6

Viscosity of air will be same for both fly and human. In the case of flies, from the point of view of the fly, it would seem to it that the viscous force is very high as it keeps the fly afloat. In case of humans, such viscous forces are negligible. So we don't notice it. If you want to scale up the insect flying "experience" to the human level, think about ...


6

Two typical quantities which characterize these systems are the Reynolds and Schmidt number: $$\mathrm{Re}=\frac{vL}{\nu} \qquad \mathrm{Sc}=\frac{\nu}{\mathcal{D}}$$ where $v$ and $L$ are characteristic velocity and length scales and $\nu$ and $\mathcal{D}$ are the kinematic viscosity and the diffusion coefficient (both material properties). These ...


5

Do we have viscous force acting between two layers even if there is no relative motion? No. From the Wikipedia article on viscosity: In general, in any flow, layers move at different velocities and the fluid's viscosity arises from the shear stress between the layers that ultimately opposes any applied force When the fluid is stationary, there's no ...


5

The high speed expression, proportional to $v^2$ is the ram pressure, which is wholly a momentum transfer effect and has nothing to do with viscosity - in contrast with the low flow speed Stokes law you cite above. To understand the ram pressure, which arises particularly for supersonic objects, witness the object is just shoving fluid out of its way, and ...


5

Yoghurt is a flocculated suspension of casein micelles. The acid secreted by the bacteria growing in the milk destabilises the casein particles and they aggregate together. Because the volume fraction of the casein particles is high in milk the aggregated particles form a gel. This image shamelessly stolen from Wikipedia gives a schematic illustration of how ...


5

Yes there is. Let's focus on the kinematic viscosity ($\nu$), which is defined as the diffusion constant for momentum in the fluid. That is, it tells us how quickly a momentum disturbance would diffuse through the rest of the fluid. Or, in particular, it gives us the linear dependence on the mean square propagation of the momentum as a function of time, ...


5

For the most part, temperature is the dominant factor in viscosity, not density. Unless you are also considering multi-component fluids, in which case the components of the fluid are the biggest factor. At any rate, the typical rule of thumb is that for liquids, the viscosity decreases as temperature increases. For gases, the viscosity increases as ...


5

It is due to the viscous nature of any liquid. When you stir, the liquid starts spinning and this causes the liquid (the part which is in contact with the pot) to "drag" the pot(due to friction) along with it in the path of its motion.Hope this answers your question.


4

If "not much less than water" means "not an order of magnitude lower than water at room temperature" this is probably correct. However there are substances like http://en.wikipedia.org/wiki/Pentane with a viscosity 4 times less than that of water or http://en.wikipedia.org/wiki/Acetone with a viscosity 3 times less than water (at 20 degrees celcius). At ...


4

Friction is caused by two physical processes, both of which dissipate energy. It's the dissipation of energy that means work is required to slide over the surface, and this work is why we feel a frictional force. Anyhow, the first factor is the surface energy of the material because this affects the adhesion between the sliding object and the substrate. A ...


4

This is an excellent question and requires more discussion. Therefore, my answer will also have questions in it for others to weigh in. Bird and Stewart explain this very well in their Transport Phenomena book. In its general form, the viscous stresses may be linear combinations of all the velocity gradients in the fluid: $$\tau_{ij} = \sum_k \sum_l \mu_{...


4

Ultimately, the Navier-Stokes equations explain this :) OK, that's not a useful answer: here's how they explain the phenomenon in some cases. Under steady state conditions for a fluid (inviscid, incompressible) that doesn't differ too much from a cup of tea, the Vorticity Transport Equation shows that the vorticity $\omega = \nabla \times \vec{v}$ (the curl ...


4

1D Burger's equation is not meant to model a physical phenomenon. Rather, it is a simplification of homogeneous incompressible Navier-Stokes equations that preserves (some of) its mathematical structure: the non-linear convection term and the second order derivative of viscous forces. It was initially intended as a useful simplification to try to ...


4

As @JánLalinský nicely explains, surface tension is measured between two fluids, while viscosity is measured within one. Say that you have a droplet of some liquid this means that if you change the surrounding medium the liquid-surrounding surface tension changes, while the viscosity of the droplet will not. That said, if you keep the surrounding medium ...


4

In mechanics, "kinematics" means describing the motion mathematically, so, for example, if the acceleration is known I can integrate to find the velocity and position. "Dynamics" means analyzing motion due to the influence of forces. The two are related through Newton's second law: F = ma (dynamics version) is the same as a = F/m (useful for kinematics). ...


4

Physics should not be different on other planets, so the same laws apply as on earth. Only the results of an optimization might look unfamiliar. See here for an answer on Aviation SE on a Mars solar aircraft. The lift slope equation you found is only valid for slender bodies, like fuselages and fuel tanks, and once wing span becomes a sizable fraction of ...



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