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If you look at pictures of the boats in action you'll notice that they have hydrofoils and so the hull shape is only important at slow speed: in maneuvers or very light wind. Having said that I would guess that the hull shape is to help minimise wave drag, which is fairly significant, especially as you approach foiling speeds. Firstly, a more pointed shape ...


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Recall that in two dimensions, vorticity is given by $\omega=\partial_x v_y -\partial_y v_x$. The analogous definition in three dimensions is $\omega=\nabla\times v$, where $\nabla\times$ is the curl operator (these derivative operators can be expressed as differential forms if you prefer). Now a fundamental result of vector calculus is Stokes' theorem, ...


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It's the same definition (effectively). Circulation is the flux of vorticity through a control surface: $$ \Gamma = \iint_S \vec{\omega} \cdot d\vec{S} $$ So in 3D, you define your control surface (which will now be a shell) and you compute the integral of the vorticity dotted with the surface normal at each location.


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I think piercing the waves gives more pitch (backward/frontward) stability. If a big wave hits the bow then you do not want your bow rapidly forced upwards and you really don't want your bow to be forced downwards which can lead to pitch pole capsizing. The most common capsize in sailing is for the boat to be pushed onto its side, but sailing boats can ...


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Although this question might be better addressed in a foods forum, there are some physics going on. The discipline of concocting drinks is known as mixology. The article here gives a mixologist's reason for shaking or stirring, based mainly on what the drink's constituents are and how much dilution you want to take place by the amount of ice added. From a ...


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The purpose of shaking or stirring a drink is to cool it and to distribute the ingredients. Stirring is a much less violent way of achieving this, but it will take a longer time than shaking, if you want to fully distribute all the ingredients. Shaking a drink often allows bubbles of air to enter the mixture. This affects the way the drink tastes and ...


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Acid Jazz is quite right. Generally any instability in air medium can result in sound waves radiation. Vortices causes local pressure instabilities and the medium is "able to propagate the image of it" (well, the Wave equation). Kármán vortex street is nice (and most of all solvable!) example of vortex shedding. But in certain domain of the Reynolds number ...


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Approximation Slightly better and more elegant than the first. Let's make some assumptions. Let's assume that on impact, a fraction $\lambda$ of the ball's Kinetic Energy is transferred to the liquid. Let's also assume that all of the energy transferred will go into shooting water up. This should give the upper bound on how high the water "tower" will be. ...


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The effect of surface tension on bubble size The Young-Laplace law describes the relation of the pressure difference $\Delta p$ on the curvature $C=2/R$ of a spherical bubble: $$\Delta p = 2\frac{\sigma}{R}$$ where proportionality constant is known as the surface tension $\sigma$. Now, if the surface tension were reduced to half its original value ...


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As a simplification, you can consider that you have a 2D viscous flow between two boundaries that approach each other. Assuming that the flow is symmetrical about the line (with the line along the Y direction), you can simplify this further to "no flow at x=0". What you are left with is a pressure distribution $p(x,t)$ whose integral in $x$ should equal the ...


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Assuming the hose length is the same, and ignoring any restrictions caused by bends in the hose, you want as great a gravity and pressure difference as possible to pull the liquid through. If you have the hose end at the top of the destination container, with the liquid falling down to the level of the already-moved liquid, then you aren't getting as much ...


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Solution using Laplace transforms Using the definition of the Laplace transform: $$\tilde{u}\left(y,s\right)=\int_{0}^{\infty}u\left(y,t\right)\exp\left(-st\right)dt$$ we can transform the PDE to an ODE: $$s\tilde{u} - u\left(y,0\right)=\nu \frac{d^2\tilde{u}}{dy^2} \rightarrow \frac{d^2\tilde{u}}{dy^2}-\frac{s}{\nu}\tilde{u}=0$$ with transformed boundary ...


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There are two forces acting on your piece of paper: 1) the force of gravity, pulling both down with the same force $F_g = m\cdot g$ 2) drag force due to the air. In general, drag force is proportional to the projected area of the object. For regularly shaped objects (like a sphere) the drag is usually expressed as $$F_{drag} = \frac12 \rho v^2 A C_D$$ ...


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While falling, both the sheet of paper and the paper ball experience air resistance. But the surface area of the sheet is much more than that of the spherical ball. And air resistance varies directly with surface area. Hence the sheet experiences more air resistance than the ball and it falls more slowly than the paper ball.


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Yep, air resistance is proportional to surface area and the velocity squared of the object moving through the air https://en.wikipedia.org/wiki/Drag_(physics)


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First, remove the flaps and replace them a single flap (or valve) where the balls enter the water on the bottom right which prevents the water to flow out. In order to get the red ball into the water, you'll then have to overcome the excess pressure corresponding to the water column, which will cost an energy exactly equal to the energy gained by the balls ...


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So, why some objects, even if the velocity before and after the collision seems to be the same, are louder than others? I mean, how do the different material properties enter in the phenomenon? As dmckee stated Sound is longitudinal pressure waves in the air... The impact can set up pressure waves and or ringing in the bodies themselves ...


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In my answer, I assume that "scatter" can be generalized to wave motion. In general, we recognize different kinds of surface waves: gravity waves (main driving force is gravity), and capillary waves (surface tension dominates). Now gravity waves have a velocity that is a function of both wavelength and depth: ...


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The short answer is that the hypotheses assumed for the Bernoulli equation are not met for airplanes. (I can't speak for birds since I haven't studied that in detail.) In particular, The air is not incompressible and Energy is not constant - the plane's engines are adding energy to the airflow That said, it's "close enough for the engineers" - ...


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A sloop has two sails, the jib and the main. There's a slot between the trailing edge of the jib and the leading edge of the main. When sailing close-hauled into the wind, you try to get the air flowing off the leeward side of the jib (side away from the wind) to go through the slot and on to the windward side (side toward the wind) of the main, because ...


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Seems to me that you are trying to calculate the lift on an airfoil from first principles using only Newton's laws of motion. Chris Waltham did exactly that in his paper "Flight without Bernoulli". You might want to check it out. http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/fluids/fly_no_bernoulli.pdf Note that this is a non-standard way of ...


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When waves roll in from deeper seas to a shallow shelving shore, they become steeper, pile up and eventually break as the amplitude of the wave increases. This may be caused by a shallow bottom interfering with the circular motion of water molecules as they are displaced by the passing wave energy. If the bow wave of your boat builds higher than it would ...


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As I am not allowed to comment on the above answer I need to add a new one: You do not need to estimate the wavelength of your vessel, you can calculate it: $\lambda = 2 \cdot \pi \cdot Fn^2 \cdot L_{pp}$ where Fn is the Froude number and Lpp is the length of your canoe. $Fn = \frac{v}{\sqrt{g \cdot L_{pp}}}$ where v is the forward speed and g is the ...


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Before everyone freaks out, no, you don't use petroleum oil. You use vegetable, fish or animal oil. In earlier times, whale oil would be used. The OP's picture looks like a fuel oil leak, not an attempt at wave calming. I have seen references of this technique being used since at least the early 1800s, probably much earlier. Ernest Shackleton made use of ...


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They are three dimensional! Two of the dimensions tell us where to locate a point on the surface, and the third tells us how high the wave is above the surface. Or to put it another way, the value of the wave is the "vertical disturbance".


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The waves are of 1D,2D,3D and if their nature is described within those dimensions of space. 1D Waves : The direction of propagation of wave and the oscillation of the particles of wave are in same direction.(Spring Waves) 2D Waves : The direction of propagation of wave and the oscillation of the particles of wave are perpendicular to each other in the same ...


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This is a "good" model from a conceptual standpoint. It's the model Isaac Newton himself used when he tried to model the concept of aerodynamic lift. However, modeling air as a series of little balls bouncing off one side of the sail ignores the contribution of the air on the other side of the sail. Air consists of a bunch of "little balls", not just a ...


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The easiest way to understand how a sail works is to observe that the sail is curved and when air flows parallel to the surface of the sail it will follow that curve and be deflected backwards. Air comes in from the side and exits toward the rear. Air goes backwards, boat goes forward. This is the same physics as the following examples: a canoe paddle ...


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The fastest point of sail depends on the boat (both its hull shape and its sail plan), the wind strength, and the sea state. In general, a beam reach is not the fastest point of sail. For instance, in very light wind some boats will go fastest on a close reach due to the increased apparent wind from going toward the wind. For boats that sail faster than ...


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We (humans) exist in and so perceive our world as one of 3 dimensions in space. Although some physical phenomena we observe may appear to be 2 dimensional in nature, if observed more closely we will see that behavior poking its way into the third dimension somewhere. Strictly speaking 2 dimensional behavior cannot exist in a three dimensional world. While ...


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Yes it works. But let's not use it on a massive scale, lest we damage the ecosystem (tip of the hat to @phi1123). A hint to the mechanism can be found in Behroozi et al (Am J Phys, 2007) They state in the abstract: From the attenuation data at frequencies between 251 and 551Hz, we conclude that the calming effect of oil on surface waves is principally ...


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There are two different kinds of wave here. The ones that you see on the surface are the (IMO) badly named Gravity Wave (not to be confused with a Gravitational Wave), which is the familiar phenomenon of waves on the ocean surface and arise at the interfaces between dissimilar fluids. Their phase velocity is $\sqrt{\frac{g}{k}}$ and the group velocity ...


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Take a 1-cm square tube and place it vertically in the container from top to bottom, touching the bottom so that the bottom of the container is the bottom of the tube. The pressure at the bottom of the tube is nothing but the weight of water it is supporting - the water in the tube. Supporting means to keep from falling. (Forget the air pressure - that's ...


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If you remove the bottom you no longer have a container. The pressure is atmospheric and you just have gravity at work.


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I'm late to the party here and I think the top vote-getters (Skliwiz, niboz) have adequately answered it, but I'll give my two cents anyway: There are several ways to explain how an airplane flies. Some are more detailed than others, and unfortunately most popular explanation get it wrong. Here are some explanations that are useful, depending on the ...


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Sometimes you will see statements like 'some of the lift is caused by Bernoulli's principle and some of it is caused by Newton's laws", but this is the wrong way to think about it. The fact is that 100% of the lift can be explained by Newton's laws and 100% can be explained by Bernoulli's equation. Both approaches explain 100% of the lift. The problem is ...


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The places in physics where commutation of partial derivatives tends to be important are in the identities of vector calculus. The situations where these identities might seem to break down is when there is some kind of topological winding. Then the partial derivatives commute at almost all points except some small set where they are undefined but still can ...


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The air would be creating a high pressure in front of it and low pressure behind it, so the force would be pushing the door closed. If you were driving at highway speed backwards the door could be ripped off. To find out whether or not the force is enough to redirect the car, math is necessary. The drag force depends on surface area, airspeed, air density, ...


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Singularities in functions often lead to non commuting second derivatives. As for a Physical interpretation I think the following exercise may help: The partial derivative can be from First Principles can be written as df(x,y)/dx = (f(x+h,y)-f(x,y))/h i.e the function is incremented by h and then the derivative is found. (x,y+h). .(x+h,y+h) (x,y). ...


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The chemical kinetics of air depend on both how fast you are flying and your altitude. Fortunately, NASA has studied these issues. The figures below are from NASA Report NACA-TN-4359. The predominant chemistry in the stagnation region of an airfoil as a function of flight speed and altitude are shown below: You say $M=7$. If your vehicle is near sea ...


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To work out the force needed to move a ship there are two considerations: the mass of the ship the hydrodynamic drag due to the ship's motion through the water At low velocities the force is likely to be dominated by the mass of the ship because the drag is roughly proportional to velocity. Newton's second law tells us that the acceleration of the ship ...


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If it was just standing with no gravity then round to minimize surface tension. I forget the name of the law but a system will react to minimize external forces. If the drop is falling the drop takes a shape to minimize the external force of the wind resistance. It seeks an aerodynamic shape. The surface comes into play as more surface is more surface ...


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For a given volume (for raindrop - a given amount of water translates to volume with the relevant density value) - the shape with the least surface area is a sphere. This is important because there is an energetic difference between molecules inside the drop and on it's surface - molecules inside the sphere have more connections to other molecules , which ...


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What you're describing is Brownian motion. If there is a force only on the particle, then you should simulate Brownian motion with an additional vector in the direction of the particle force. Obviously the intensity will determine how quickly a particle will move through the fluid. Rather if the velocity is being applied to all particles, then all ...


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Suppose in zero gravity you squirt a smooth stream of water from a nozzle. A cylindrical tube of water with surface tension is not a minimum energy configuration. Spherical drops are minimum energy. The cylindrical tube is a metastable state, like a ball perfectly balanced on a point. Any slight variation from a perfect cylinder will be increasingly ...


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I reckon I'm going to get lit up like RoboCop because of this post but here we go: I think the apparent separation of the water into droplets the higher up you go is caused because of two reasons: gravity and the cohesion/adhesion of water (also see Van der Waal forces). Essentially, the cohesive/adhesive forces are responsible for keeping the water ...


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The Navier-Stokes equations represent the flow of a fluid with friction. They consist of the following conservation equations: Conservation of mass (second line): div u=0 Conservation of momentum (first line) −μΔu+(u⋅∇)u+∇p=f Conservation of energy (probably, in the third line, but I don't know the nomenclature): u∣Γ=0.


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The distinction between body force and surface force on a fluid's control volume (say a cube) is that in the integral form of the momentum equation, the body force is integrated with respect to the volume of the cube, but the surface force is integrated with respect to the surface area. Pressure is a surface force because it acts normal to the unit surface ...


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The term $(u \cdot \nabla)u $ describes non-linear advective acceleration through a fixed point in the stationary frame of reference (Eulerian frame of reference). In your momentum equation, you need to multiply by this term by $\rho$ to have rate of change of momentum per unit volume. If $(u \cdot \nabla)u = 0$ in your momentum equation, then you have ...


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A discontinuity in the flow of water could be a wall, or a clog that water is still getting around, but not flowing directly through. In finite electric current it could be a substance with a different conductivity, notably zero or ∞. In theory, the mixed partial second derivatives would not be generally equal, just on the cusp of a boundary such as these. ...



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