# Tag Info

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I learnt now this is what called induced drag. more information are here:https://en.wikipedia.org/wiki/Lift-induced_drag

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The difficulty with Reynolds number is that the length scale (and often times the velocity scale) are both completely subjective, as you have identified. In standard nomenclature, an airfoil (or in your case, an ellipse) would use the freestream velocity as the velocity scale and the chord (semi-major axis) as the length scale. This is the assumed standard ...

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The explanation that the measured pressure is the force on external walls of a reservoir under pressure doesn't quite make sense to me, in that in order for a High-Pressure fuel reservoir to be under greater than atmospheric (30,000 psi) pressure, the fluid within must also be pressurized. The measured pressure is not a force but it is related to force. ...

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In the time $dt$ your diagram shows the infinitesimal transformation M was done to the box (eg: the corners of the box): $$M=I+\begin{bmatrix} 0 & d\beta \\ d\alpha & 0 \end{bmatrix}$$ $$=I+\begin{bmatrix} 0 & {1 \over 2}(d\beta + d\alpha) \\ {1 \over 2}(d\beta + d\alpha) & 0 \end{bmatrix} + \begin{bmatrix} 0 & {1 \over 2}(d\beta - ... 1 Once you have an understanding of fluid mechanics, the two best books for CFD specifically that I have used are: Computational Fluid Dynamics by John Anderson. I don't know if you have ever used any of Anderson's fluid dynamics books, but I highly recommend all of them. His books are all very readable and spend most of the text describing what to do rather ... 0 The book I learned from decades ago was Sabersky and Acosta "Fluid Flow: a First Course in Fluid Mechanics". There are a number of basic concepts: Continuity: mass within a bounding volume, as a function of mass flows across the boundaries. Streamlines and the stream function. Equations of motion with and without viscosity. The Bernoulli equation relating ... 1 I noticed today that the water warmed up in pressure cooker (1.5 ATM) dissolves sugar much faster and much more than water cooked in 1 ATM. The effect you observe is one of temperature, not pressure. Water soluble substances dissolve quicker when the temperature is higher because the water molecules of hotter water have a higher average kinetic energy ... 3 It's important to note that these displacements are all infinitesimal, so while one may be thousands of times the other, during an infinitesimal time slice the displacement is still infinitesimal. If one displacement is much much greater than the other, then that displacement will effectively be half rotation and half distortion, if you rotated the fluid ... 1 The transition from Hagen-Poiseuille to Darcy-Weisbach behaviour happens when the flow regime switches from laminar to turbulent. Note that the DW equation has a fudge factor that describes the energy loss due to turbulence. This friction factor varies with flow rate. For an increase in pressure to produce no increase in flow the friction factor would have ... 2 Here is an alternative way to relate the vorticity (denoted as \vec{\omega}) and the average angular velocity that I think is more transparent. Consider the average angular velocity around an infinitesimal loop of radius l:$$ \frac{1}{2\pi l}\oint_{\partial A} \frac{\vec{u}}{l} \cdot d\vec{s}$$By Stokes's theorem, we find$$ \frac{1}{2\pi ...

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.052 x 8.34 x height above pump. Will provide you with number of pounds of pressure that your pump must provide to push water to your tank. Of course I can give you the formula for diameter of pipe/ and distance; however I'm not sure that anyone wants to begin calculated process factors for the bends, and turns in a friction on water inside a pipe. I'll just ...

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First of all, both pressure and temperature are quantities statistically connected to averages (average force on the wall exerted by the particles and their average energy). So using them in cases, when the system is not homogeneous is not too appropriate. If we want to look at, let's say, gas in the box receiving heat from one side, and see how the ...

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The dynamic version of equilibrium thermodynamic is fluid dynamics, and the dynamic version of equilibrium statistical mechanics is kinetic theory. In fluid dynamics the stress (pressure) tensor of the gas is expanded in time and space derivatives of the thermodynamic variables. This expansion converges if the state variables vary sufficiently slowly. In ...

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A Little History You ask a very good and relevant question. In fact, back in 1958 H.E. Petschek wrote an interesting paper on "Aerodynamic Dissipation". In that paper, he hypothesized that one could, in theory, produce a shock wave in a collisionless medium (like most plasmas in space). This was highly controversial, since the very concept of a shock ...

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The ideal gas law can be derived from the fundamental differential equation of thermodynamics: First, consider a lattice model with M sites and N particles. Then the multiplicity of the system is: $W = \frac{M!}{N!(M-N)!}$ Thus the entropy of the system $S = klnW = kln(\frac{M!}{N!(M-N)!}).$ Using Stirling's approximation: $n! \approx (\frac{n}{e})^n$ ...

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Space isn't empty, as I'm sure you've heard before. There's always something between different bodies, such as the interstellar medium. There are also denser regions of space, including molecular clouds and H I/H II regions. Shockwaves can form in any of these places, and propagate through them. There are several different common sources of these shock waves ...

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In your thought experiment, throughput is the volume of water per second passing a given point, but latency is the time elapsing between a drop of water entering one end of the pipe and its exiting the other end. For a given pressure drop, a fatter pipe will allow more water per second through the pipe. However, (ignoring friction) the longer the pipe the ...

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Physics of siphons You're going to be about at the critical limit for your plans. There may be problems if the heater heats the water nearer to boiling, for example, or if the 500L holding tank is not airtight, or if atmospheric pressure crushes your tank. (You should make sure that it can withstand 10-15 psi just to be safe.) To have a siphon effect you ...

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Yes, dark matter should be considered to be a fluid which fills the space unoccupied by particles of matter. 'Cosmologists at Penn Weigh Cosmic Filaments and Voids' upenn [dot] edu/pennnews/news/cosmologists-penn-weigh-cosmic-filaments-and-voids "Dark matter ... permeate[s] all the way to the center of the voids." 'No Empty Space in the Universe --Dark ...

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Have you ever blown out a candle, from a few inches away? Have you ever wondered why you can't suck out a candle from the same distance? The motion of fluids like air, through an orifice, is not reversible. On the side where it is leaving the orifice it forms a localized stream, which you feel. On the side where it is entering the orifice it comes from ...

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Considering dark matter as a perfect fluid is useful for understanding cosmological evolution via the Friedmann acceleration equation $$3\frac{\ddot{a}}{a}=\Lambda - 4\pi G(\rho + 3p).$$ (note that this is a general relativistic equation, so not strictly Newtonian). Cosmologists use the equation of state parameter $w$ to relate ...

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In order to understand this, you need to understand to concept of shear stress. Consider the diagram below: In this diagram a bloc of viscous fluid is held between two parallel plates of surface area $A$ and with distance between the plates of $h$. We now cause the upper plate to move at a constant speed $v$, while keeping the bottom plate perfectly ...

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If air comes into the vehicle then it must effectively also be leaving it, otherwise pressure would be building up, in accordance with the Ideal Gas Law. Trains and buses are hardly hermetically sealed containers. The reason why you may not notice the air leaving is that it will flow through many orifices like imperfect seals, a slightly open window further ...

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It is by no means certain that when you open the tap the flow is automatically turbulent (although going by your top picture it appears to be). Open the tap just a little to allow a continuous stream of water to exit and you'll see the flow is not turbulent but so-called laminar. Whether flow through a pipe (and by extension when it leaves that pipe) is ...

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Let me arrange some information briefly. Cohesion-tension theory : phenomena that pulls water molecules at leaves producing tension + cohesion along entire stream of water molecules. Cohesion of water molecules mainly arises from high-strength hydrogen bond and the tension that presses the stream is generated from various mechanisms. On the other hand ...

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The xylem actually creates a long thin string of water from the roots to the leaves of a tree. This string remains continuous by two forces. One is the cohesion of water molecules and the other is adhesion of water with xylem walls. Now in leaves water is evaporated. That decreases the pressure of water there. Because the protoplasm of those cells on leaves ...

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A perpetual motion machine is out of the question. You can't get something for nothing, but if you have a flowing stream of water coming down a hill in say a steel pipe, by use of a "Hydraulic ram pump" you can pump some water higher in altitude than where the water is entering the steel pipe. Look it up in google, see videos in youtube.com of this. Boy ...

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If my understanding is correct, you are hoping to design a tubing configuration that, once started (by a temporary boost from an electric pump), will pump water uphill without additional power input. Unfortunately, that would never work, as it would be a perpetual motion machine of the first kind, and would violate the first law of thermodynamics. Were it to ...

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Water in its liquid form is almost incompressible because of the tendency of H- bond not to reduce in length after a certain limit. This can be said in accordance to Hydrogen atom as well. For example,no matter how much you compress the atom, its size will never reduce.

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These have been in use for a long time in commercial woodworking, and agricultural tractor engine air cleaner pre-filters. John Deer released a video thirty years ago with excellent images of their operation. The same principle is used in automotive fuel tank swirl chambers surrounding fuel pumps and pump inlets. In my VERY SIMPLYFIED LAYPERSON'S ...

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Cyclonic separators work through airflow management and centrifugal force. In the video, you see the air enter tangentially at the top of the separator, which makes the air spin around the axis of the separator. In addition, the suction at the top center makes a secondary air flow up the axis and down the walls of the separator. Since dust is heavier than ...

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This is a well known effect, and most clearly happens with hot instant cocoa which has just been mixed. Stir the cocoa while tapping the spoon on the mug, and you'll hear the pitch of the tapped spoon go down. Now start tapping while not stirring; the pitch will gradually go up by an octave or more. But, if you stir again, the pitch will go back down again. ...

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A couple of comments on your implementation: You initialize your distribution functions in an unconventional way; usually, we want to convert known macroscopic 'lattice' quantities like $\rho$ and $\vec{u}$ into $f_i$. An easy way to do this is using the equilibrium distribution you define above: ...

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I enjoy listening to this phenomenon as I wait for my teabag to brew. What is happening is that parts of the the ceramic cup heat up and expand. Because its shape is constrained (assuming it doesn't break), this produces a stress in the material that increases its resonant frequency (like tightening a guitar string). When it gets to Middle C, my tea's ...

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Making conclusion based on dimensional analysis without testing the underlying assumptions is dangerous. The paradox occurs because the validity of the Stokes' equations rely on the Reynolds number being small. This is not the case in 2D as inertia cannot be disregarded in the far-field and therefore a solely viscous dependent force is not possible. Instead ...

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You can try using a modified form of the Poiseuille equation. $$u_2 = \frac{q_2}{A} = \frac{(p_1 - p_2)R^2}{8 \mu_{av} L} \frac{z_2(p_1+p_2)}{2z_{av}p_2}$$ where $\frac{z_2(p_1+p_2)}{2z_{av}p_2}$ is a correction factor that accounts for the gradual expansion of the gas when going from the high pressure inlet to the low pressure outlet. See this link for ...

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As long as the weight is placed slowly, the bowl will remain balanced. The forces on the bowl are Gravity The pole The pressure from the water Note the lack of anything about the added weight. That's because it can only effect the bowl by raising the water level. All three of these will remain centered on the pole as the water level rises, as long as ...

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You certainly can accomplish what you want. Whether you can calculate it with sufficient accuracy is largely a function of need, and access to CFD codes and resources. The shape of the crack certainly has a reasonable influence on what you want to engineer. You cannot reasonably consider the fluid inside the bucket to be a purely turbulent regime. The ...

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(Aero-)Acoustics (among other parts of fluid-dynamics) loves the velocity potential It is something that has nothing to do with Acoustic or any other area where potentials come into play. Rather, it is a general property of fields provided certain assumptions hold. For (usually) simply connected regions whenever you have an irrotational field, that is ...

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Another way of seeing this has recently come out of the Functional Renormalisation Group (FRG) method. Usually Renormalisation Group (RG) flow equations are local in momentum. This means that the correlation functions of two theories that are coarse grained at two neighbouring (momentum) scales $k$ and $k+dk$ only differ for momenta close to $k$. It was ...

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I got the same answer using momentum considerations. In time $dt$ the amount of mass hitting the side of the pipe is: $$dm=\rho A v dt$$ Now, we know that the force must satisfy: $$F_{x}dt=dp=0-vdm=-\rho A v^2 dt$$ Dividing both sides by $dt$ gives: $$F_{x}=-\rho A v^2$$ The force in the $y$ direction is the same as here.

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This phenomena appears tp be related to the Saturn's hexagonal aurora (storm, ?) nytimes video , youtube As the sphere approaches the surface the air is compressed and it happens a speedy radial exit , that's why with no atmosphere the effect is not present (as seen on the video of the answer of Bardamu). explanation on nytimes In laboratory ...

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That's what the muffler does, as you learn the first time you have a car with a muffler that gets damaged. The essential difference between gas and electric cars is that the gasoline power is derived from a carefully timed sequence of small explosions, in the pistons; the electric car does not have this phenomenon and will always be quieter for the same ...

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Going by this theoretical treatment which I believe is valid, it appears engineeringtoolbox is correct. The formulas you linked to assume pressure $p$ to be the same at entry and outlet (an acceptable approximation in most cases). In the page I linked too, set $p_1A_1=p_2A_2$ (which applies to your problem) and thus also $V_1=V_2$ and the conclusions are ...

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The equation $$\partial_tu=\nu\partial^2_yu$$ is a diffusion equation in one dimension. Its Green's function in infinite space is $$G(y,t)=\frac{\mathrm e^{-y^2/4\nu t}}{\sqrt{4\pi\nu t}}.$$ For $t=0$, we have $G(y,0)=\delta(y)$. Note that any solution of your equation depends linearly on $G$. Notice also that the constant function is also a solution of the ...

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As was mentioned in some comments, water is a mostly incompressible liquid - that is, if you want to make the volume of water smaller, you need to apply a LOT of pressure. How much pressure is given by the bulk modulus, which for water at room temperature is about 2.2 GPa. Comparing with the bulk modulus for air at 1 atm, it is about 100 kPa - 2200 times ...

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The ideal gas law isn't a good model to describe a fluid like water, because the ideal gas law predicts that the number density of a fluid, $$\frac nV = \frac P{RT},$$ depends linearly on the pressure and the temperature. Were that the case, ice water at 273 K would have only about 73% the volume of boiling water at 373 K. You are invited to verify this is ...

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High speed winds are accompanied by reduced air pressure So high pressure from inside the house pushes roof to low pressure and gets blown away.

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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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In order for two fluid to coexist in anything close to an equilibrium, they must be at the same pressure. After they have been together for a short period of time, they will ultimately come to the same temperature. If both steam and liquid water exist after equilibrium is achieved, then they must be at what is known as Psat, Tsat. For atmospheric pressure, ...

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