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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 ...

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In general, if you have a system in steady state, if you have 25 l/min coming in, you must have 25 l/min going out. If you have more or less than 25 l/min going out, then the pressure will fall or rise respectively. Since you specify that the pressure remains fixed at 5 bar, this implies that the outflow is also 25 l/min. For 4 output branches, the sum of ...

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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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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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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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How about introducing one more independent variable: $\zeta =\omega t+kx$ ? Then: $t=\tfrac{1}{2\omega }\left( \zeta +\xi \right)\quad ,\quad x=\tfrac{1}{2\kappa }\left( \zeta -\xi \right)$ The partial derivatives w.r.t. $t$ and $x$ would be: $\frac{\partial }{\partial t}=\frac{\partial \zeta }{\partial t}\frac{\partial }{\partial \zeta }+\frac{\partial ... 2 The surface wave formed in a Rayleigh-Taylor instability is caused mainly by surface tension. Like i mentioned before, a liquid tends to minimize its surface area and$n$droplets of volume$V/n$have more surface area than a liquid column of volume$V$. Initially, the film is uniform and surface tension will minimize the area by starting to form waves. The ... 2 The growth rate of the instability is the characteristic rate$r$at which a pertubation grows in an unstable dynamic system. A good reference on this type of instabilities is: Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves by Pierre-Gilles de Gennes, Francoise Brochard-Wyart, David Quere ISBN 0-387-00592-7 On page 120, it describes a ... 5 It's intuitively clear that this current must exist because the integral of the Wigner function is conserved by unitary evolution. This current is known as the Wigner flow, and it exists but it's not particularly pretty. For an example of the Wigner flow in use, see arXiv:1208.2970; in short, it is the current$$J=\begin{pmatrix}J_x\\J_p\end{pmatrix} ... 1 Surface tension is the result of a mismatch in interaction energies between neighbouring fluid particles. Imagine a water molecule in the bulk of the fluid; everywhere around it the molecules are similar to it and it will therefore experience the same interaction everywhere around it. The net interaction force is therefore zero. Now imagine a water ... 2 Edit: please see duplicate answers as well This could be a hydrodynamic instability known as the Rayleigh-Plateau instability. In short, liquids, because of surface tension at the liquid-gas interphase, tend to minimize their surface area. A liquid column of volume$V$always has a larger surface area than$n$droplets of volume$V/n\$. As it turns out ...

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A gas can expand by filling more volume than before. Like a balloon in a pressure chamber where the pressure is suddenly lowered. No net motion (no flow) happens here. A water stream can flow continously without simultaneous expansion. Consider a circular stream that ends where it starts. As a bathtub where there is a big plastic bucket in the center. By ...

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Find the velocity using bernoulli's equation Pressure + G.P.E per unit volume + K.E per unit volume = constant and apply the equation for flow rate. Flow rate = Area x Velocity

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Why not? You expect heat to transfer differently at another point on the plate. Any point on plate one has a plate two at the same temperature, the same distance apart, and the same fluid in between. The movement of the plate does not introduce a difference as the fluid in between still has the same history.

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