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Suppose we have a pump submerged in a liquid of density $\rho$ at a depth $d$ which we want to use to raise the liquid to a height $h$. The pump has to do work to overcome the potential energy difference between the two heights of liquid. That is: $$W(t)=\rho Qg (h-d)t$$ Where $g$ is the acceleration due to gravity (taken as $9.81m/s^2$). $Q$ is the ...


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The "far away" phrase indicates that the airfoil does not disturb the velocity flow. In the image below (source), you can see how the airfoil affects the flow near the airfoil itself. But "far" above and below the airfoil, the flow isn't affected. This is your $v_\infty$ and, as WolphramJonny points out in the comments, this is equal to your $v_{in}=30$ m/s. ...


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Water has its highest density at 4 degrees C. Ice always floats on water surface, because its density is less than water. An object dropped in water will sink, accelerating under the force of its weight (Mg), against the upthrust, as well as the viscous drag resulting from the downward motion; which increases as the speed of the object increase. There will ...


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Yes, you absolutely need to count the back pressure. Otherwise the force required would be essentially independent of flow rate or the properties of the fluid. For a given fluid, you need to assess the pressure needed inside the syringe to make the desired flow. The force on the plunger needs to overcome that. In many cases that will be the dominant ...


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I suggest that it would oscillate. Friction against the walls of the pipe would cause the average velocity profile across the pipe to decrease which would increase pressure which would then increase velocity.


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The force you have to exert on the plunger is $F_1 - F_2 + F_3$. If you didn't include the back pressure term it would be just as easy to squirt treacle as it would be to squirt water, which obviously isn't the case.


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This may not require an iterative method I guess. Write down the conservation of mass, conservation of momentum and conservation of energy (if there is heat exchange or some energy transfer which is not your case) equations considering a control volume with control surfaces on the two holes. This would help you to solve the problem


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Surface tension is plausible : it implies that, at the level of the hole, the pressure in water will be less than 1 atm. Thus the pressure isolines will look like this: Quantitatively, curvature $c$ will be of the order $1/(1 $mm$)$ because the hole looks about 1 mm size in your video, which with pure water would lead to a pressure difference drop of the ...


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The bird is hovering in the box. The only way for it to hover is to increase the pressure underneath its wings and decrease the pressure above its wings. This pressure differential times the area of the bird will balance the exact weight of the bird. The pressure differential may be thought of as a net downward impulse given to the air molecules by the ...


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This is not true, when the box is sealed you are weighing the total mass of the box and everything in it, not the weight of the bird plus the weight of the box


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Assuming is a black box seen from the outside, consider the following situation: After a while, the bird tries to fly higher and pushes the ceiling of the box upwards. Will the weight of the box decrease? Then, after a while, the bird dies and falls to the floor. Will the weight of the box increase? If the box is sealed, it cannot change the time averaged ...


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Let's assume that the box you have is perfectly closed and has a fixed amount of air in it. When the bird inside starts flapping it's wings it creates disturbances in the air present inside the box. The air molecules may start dancing in complex ways and it is difficult to completely describe this motion qualitatively. Consider the whole system (box + air ...


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The accepted answer is not complete. A projectile may travel very long distances underwater if it is supercavitating. A supercavitating object is a high speed submerged object that is designed to initiate a cavitation bubble at the nose which (either naturally or augmented with internally generated gas) extends past the aft end of the object, ...


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First you must find the speed when the ball comes out of water, the same way you calculate the speed of free fall of an item in the air. $$m\vec{a}=\Sigma{\vec{F_i}}$$ where the forces are : friction, weight, Archimedes force. Then again in the air where the Archimedes force may be neglected. If the air friction is neglected, it's easier using the potential ...


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The argument can be reasoned without using any "heavy handed" general-relativity, but it is a long road. We pretend that gravity is simply a potential well: objects lose energy when leaving it and gain energy when entering it. Part 1: Relativistic objects are "pulled toward" gravitational sources more than predicted by newtonian mechanics. Light is pulled ...


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This is outside of my area of expertise, but I figure I'll take a stab at it. You elaborate in a comment: We assume capillary action of flow of fluid, as any type of pressure may alter composition of the paper. The paper is similar to paper towels, except the sheets are folded. The height $h$ of a column in a capillary with radius $r$ is given by $$ ...


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You are not missing anything. $P = \frac{F}{A}$ so then your second equation becomes: $P = \mu \frac{u}{y}$ For the actual pressure: $P_a = \mu_a \frac{u_a}{y_a}$ Since $u_a = u_0$ because you require it to and $y_a = y_0$ because the boundary separation doesn't change, when you divide $P_a$ by $P_0$: $\frac{P_a}{P_0} = \frac{\mu_a}{\mu_0}$ and as ...


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Pneumatic circuit components are close to what you are looking for. You can buy pneumatic components that allow you to do a wide variety of operations online from places like McMaster-Carr, or directly from the manufacturer, e.g., from Clippard. I'm not so sure there are too many off-the-shelf components that are direct analogues to a particular electrical ...


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Don't get hung up on the algebra. Simplify it. First, you have conservation of energy. You know how high the water is above the bottom of the sluice gate where the hole is going to appear. That tells you how much potential energy some water coming down from the top has. That tells you what it's kinetic energy will be when it exits the gate, so that tells ...


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The "determinant set" requirement means that all of the variables are defined and related. In other words, it is a closed system of equations. This require models for the thermodynamic and transport properties. The heat flux and shear stress terms introduce new variables, specifically $\kappa$ and $\mu$ (the heat diffusion coefficient and the viscous ...


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I would give you a tip just reading this, they gave you the depth of the water for a reason. you should use the Continuity Equation to get the speed v1. And then apply Bernoulli.


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The downstream side of the nozzle is much more important to maintaining the efficiency of the nozzle by controlling expansion wave. It also influences the uniformity of the flow exiting the nozzle. Symmetry would be perfectly fine, but you'd end up making the converging section bigger than it needs to be. Here's a bit more about the design of the nozzle ...


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When water leaves the bottle, the pressure above it drops. This reduces the net force pushing the water out of the opening, until it stops and a bubble can rise up. When the bubble has left the mouth of the bottle, the water can start flowing again. The stop-start of the water, and the reduced pressure inside the bottle, contribute to the lower flow rate in ...


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A friend of mine once overheard a conversation between a father and his child on a public transit bus on a windy day. Child: "Why does the wind blow?". Father: "Some places are cold and some places are warm. That is not fair. Thus, the wind takes the cold air away and moves it to the warm place so that everybody's happy." - IRO-bot, from Earth Science ...


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Assuming you start with a full bottle of water, when you tip the bottle upside down, a 'partial vacuum' (ie below atmospheric pressure) is created at top of the bottle as the water pours out the bottom. Atmospheric air then 'bubbles through' the mouth of the bottle to compensate. This slows down the flow of water through the mouth of the bottle. Each time ...


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I think you've understood it all, air gets into the bottle faster. Without the vortex, the air is able to pull on the liquid, preventing it from escaping. This is why you can pour orange juice faster if the opening is at the top, rather than the bottom. It also stops it splashing.


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Enstrophy is defined as $\Omega = (1/2)\langle |\omega|^2\rangle$. The $\mathcal{E}(k)$ in your question is not the same as enstrophy. Enstrophy is the analog of kinetic energy density, except that the velocity in the latter is replaced by vorticity in the former.


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I know that 'Blowing air is called Wind' but what I don't know is, how is wind formed? And I don't want the answer from Google Search. I want to know more about wind in atomic or molecular level It is not out of a quirk of physicists that even though we have an enormous knowledge of how the microscopic framework of atoms and molecules works, we still ...


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When a region heats, and another region somewhere cools it creates a difference in pressure. Hot air rises, and it then goes towards the region of low pressure to equal the pressure at both regions. Now, why does the air rise? I mean, why hot air rises. A simple explanation is: Hot air is less dense and experiences a buoyant force, just like a bubble of ...


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Basicaly, atmospheric wind are created from pressure differences from one area respective to another, so air molecule are pushed toward the lower pressure zone. This air molecules movement is called "wind". One application of this simple principle can be described by the so called Venturi effect derived from Berbouilli's equation $$ P*_\text {1} + ...


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The rotation of the Earth causes a force called the Coriolis force. This does have an effect on ocean currents, but the effect is only significant on length scales of hundreds of miles. Over the diameter of a shell, even a big one, the Coriolis force is completely swamped by other effects like tides, local currents, random thermal fluctuations or whether a ...


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as the definition says that pressure is the force acting normally in a direction perpendicular to the the object per unit area .so it mean that the force would always be perpendicular to surface of object , no matter on which side of object it is acting but it will always be perpendicular , first i was thinking that formula of pressure is F/A and force is a ...


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As you rightly suspected, in general, if $\vec{v}_1$ and $\vec{v}_2$ are two solution of the Euler equation then $\vec{v}_1 + \vec{v}_2$ is not a solution because of the nonlinear term. However, in many cases, one (or both) of the velocities will make the nonlinear term zero allowing you to add them. For example, in the case of a steady flow in an ...


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The sound velocity depends on the sound frequency (dispersion). The flow must be locally faster than the frequency of the downstream disturbances. If the latter are such that their sound velocity is small, the local flow velocity may be chosen small too. Note, that the sound velocity depends also on the void fraction. If there are bubbles (even locally - ...


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Any form of heat will work, but there also needs to be a way to raise the pressure, such as ram air or a compressor. If you don't have a compressor, the air will flow out both ends, for zero thrust. A very simple way to do this is with a propane torch. The gas is under pressure in the bottle. Then it is allowed to escape into the burner at a slightly ...


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This is d'Alembert's principle. The basic, very general idea is to take Newton's second law applied to an accelerating mass, and write it as $F-ma=0$. That is, we take the $ma$ term and pretend it's another force balancing the $F$ term. This allows us to think about the dynamic, accelerating mass as if it's a static system. The $ma$ term is what's referred ...


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In this case, by inertial force, they do not refer to the pseudoforce from an non intertial reference frame. Instead, by inertial force, they refer to the force due to the momentum of the fluid. This is usually expressed in the momentum equation by the term (ρv)v. So, the denser a fluid is, and the higher its velocity, the more momentum (inertia) it has.


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In a jet engine, we burn hydrocarbons (jet fuel) which heat the air. When air (or any gas) is heated, the volume changes. We can calculate the change in volume by using Charles' law. $$\frac{T_1}{V_1}=\frac{T_2}{V_2}$$ When the air gets hot it expands and is forced out the back of the engine, producing thrust. All you need is something to heat the air. We ...


0

one side of the ball is rougher while the other side is softer .the rougher side brings the stream lines above the ball closer decreasing the cross sectional area.then the velocity at that side becomes greater decreasing the pressure at side. this doesnt happen on softer side causing a lesser velocity and greater pressure on that sidetherefore ball travels ...


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1) They are non-polar, which means that it does not have positive and negative ends and consequently do not attract each other. 2) Also the viscosity of these fluids is less and hence have low resistance to flow. Therefore, they are slippery


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This is essentially Pascal's law. I would like to add that it depends on the fluid being in equilibrium, as well as incompressible. Otherwise local pressure differences can build up and the fluid can behave rather differently. I like to look at this problem from a thermodynamics point of view. One way to think of this is that the pressure of a fluid is a ...


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It is not true that the pression of a fluid is due to gravity. Do you think fluids inside a bottle in the space station have no preassure? The right answer is the one you have quoted. The first link only refers to buoyancy, that does require gravity.


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The question is therefore : why doesn't a fluid flow out a bottle smoothly ? The "bottleneck" phenomenon is caused by the lack of pressure in the can/bottle. As the liquid flows out, the pressure inside decreases because the volume of the container is fixed. When the pressure inside the bottle reach a given threshold, the outside air tends to flow in the ...


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Because the bag deflates as milk leaves it, the volume of the bag decreases and the pressure remains constant so the milk pours smoothly. When pouring from a can, which does not deform like the bag, the pressure inside the can decreases as liquid leaves the can. The pressure differential creates a potential that pulls air into the can, interrupting the flow ...


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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 ...


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I don't believe that this would be necessary. Most pumps (not constant volume ones) have a relationship between flow rate and pressure jump (often called a pump curve). Since the entrance diameter of the pump doesn't change, you've got (basically) the same momentum in the pipe at a given flow rate regardless of how it gets that way. Another way of looking ...


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Consider the following image, we have some fluid volume, $V$, having density $\rho$ and traveling at a velocity $v$ along a pipe with some cross-sectional area $A$. The rate at which the water flows through the pipe is called the volumetric flow rate. This is given by, $$ \frac{dV}{dt}\equiv Q=\mathbf v\cdot\mathbf A $$ where $V$ is the volume of the ...


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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 ...


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The specific gravities would be the same if the levels of the two side were the same after liquid-II was added. When I try this, my logic seems to be flawed too. I don't get 1.12. The level on side II has not changed. The level on side I has risen 2 cm. So 2 cm of liquid-II were added. Consider the horizontal plane 2 cm below the top of side II. Below ...


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Pascal used a serynge that allowed leakage of fluid, to demonstrate that increasing pressure at one point would increase pressure at all points. Although water is leaking, as Babou said, we can still consider the fluid enclosed, where, instead of holes (that allow leakage) we could use sensors to mesure pressure. Watch a Wolfram demonstration of the ...



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