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7

Convection is the collective motion of particles in a fluid and actually encompasses both diffusion and advection. Advection is the motion of particles along the bulk flow Diffusion is the net movement of particles from high concentration to low concentration We typically describe the above two using the partial differential equations: \begin{align} ...


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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 ...


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The flow rate is the average velocity times the area. If the velocity was constant, you would get a flow rate that scaled with $r^2$ (the area). But the velocity goes up for larger pipes - in fact, velocity scales with the square of the radius. And the product of these two squares gives us the 4th power relationship. Let's break this into a few steps: ...


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convection = diffusion + advection. That is, convection is the sum of fluid movement due to bulk transport of the media (like the water in a river flowing down a stream - advection) and the brownian/osmotic dispersion of a fluid constituent from high density to lower density regions (like a drop of ink slowly spreading out in a glass of water - diffusion).


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For viscous hypersonic flows, the heating takes a form: $$ q_w = \rho_\infty^N V_\infty^M C $$ where the parameters $N$, $M$, and $C$ depend on the configuration and $q_w$ is the heating in $W/cm^2$ (this is all from Hypersonic and High Temperature Gas Dynamics and I highly recommend this book). For the stagnation point (like the leading edge of a body): ...


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The sine function is just an idealized way to approximate wave motion, and indeed suitable for teaching the basic principles of how waves propagate, reflect and interfere with one another to create standing waves, but as with any real physical system, including the motion of waves, the closer you look the more you see non-ideal behavior. For surface waves ...


2

Inviscid flow doesn't exist. That's so important to understand, I'll say it again: Inviscid flow doesn't exist! However, we use it all the time. So what gives? It turns out that many of the effects we are interested in are viscous, but the viscous effects can be modeled various other ways. This is effectively the same type of question as Does a wing in a ...


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Since the force is based on the wetted perimeter, any configuration that would make the perimeter very large in a very small area would be overwhelmed by the surface tension of the water droplets connecting nearby perimeters. So the effective perimeter would be much lower. So you are sunk!


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You are referring to the equation: $$\frac{\partial \rho}{\partial t} + \frac{\partial \rho u_i}{\partial x_i} = 0$$ which is the conservative form of the continuity equation in Eulerian form (fixed domain, fluid moving through it). This can also be written as: $$\frac{D \rho}{D t} = 0$$ which is the Lagrangian form (the density of a moving region of ...


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First up thanks to all who took an interest especially @irishphysics who stuck with the question for some time. It turns out that the phenomena was analysed and solved by Lord Kelvin and is known as the Kelvin wave pattern. The pattern itself is the result of a spreading pressure wave which manifests itself as the curved diverging wave crests (the ones I ...


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Consider a control volume $\Sigma(t)$ of a fluid with density $\rho(\mathbf x,t)$. The mass inside $\Sigma(t)$ is clearly given by $$M(t):=\int_{\Sigma(t)}\rho(\mathbf x,t)\text d^3\mathbf x.$$ The way $\Sigma(t)$ is defined is that its mass content doesn't change with time, that is, a control volume is representing the time evolution of a certain amount of ...


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Flutter is only possible if you have similar structural and aerodynamic frequencies. One without the other would produce much lower amplitudes. Look at a mass-spring system suspended on an eccentric tappet which sits on the edge of a small rotating wheel. When the wheel turns, it raises and lowers the top of the spring, and the mass on the bottom will ...


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Intuitively, the rate goes up by faster than r squared because for laminar flow, there is no flow at the walls of the pipe. So the extra r squared term is due to a larger pipe having more area away from its walls.


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I don't really conceptually understand why the mass flux/mass flow rate into the arbitrary volume BCDE is given by [...] $u$ is speed. This is a distance per second. Multiply a distance (per second) with a cross-section area, and you get volume (per second). So $$\dot V=Au$$ where the dot in $\dot V$ simply means per second. If some particles of water ...


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The continuum hypothesis means the following: at each point of the region of the fluid it is possible to construct one volume small enough compared to the region of the fluid and still big enough compared to the molecular mean free path. Why is that important? Because of two things. First, since the volume you can build at each point is very small compared ...


1

You're calculating the rate of liquid flow through a tube under a specified pressure gradient. The rate of flow changes depending on whether the flow is laminar or turbulent. Laminar flow is described by the Hagen-Poiseuille equation: $$ \Delta P = \frac{8\mu\ell V}{\pi r^4} $$ where $\Delta P$ is the pressure drop, $\mu$ is the viscosity of your saline ...


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You are missing the bit under-braced here: $$ \dot{m}=\rho\underbrace{\mathbf A\cdot\mathbf v} $$ This is a dot product, which takes two vectors and returns a scalar: $$ c=\mathbf a\cdot\mathbf b=a_xb_y+a_yb_y+a_zb_z $$ So the mass flow rate is indeed a scalar value.


1

Your fractal pattern will fail for reasons already given. However, given a large enough lake, you should be able to stand on a frame which is supported by a very long (perhaps circular) wire. All you need is for the force per meter (assuming uniformly applied) caused by your body weight and the structure itself to be less than the surface tension force ...


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If your tube has a hole in which mass can flow out, then we can lose mass at a rate $Q$. Similarly, if your tube has an inlet, then the mass can accumulate at a rate $P$. Thus, the time rate of change of mass would be $$ \frac{dm}{dt}=P-Q $$ However, with a tube, we usually consider it closed, such that $P=Q=0$, leading directly to $$ \frac{dm}{dt}=0 $$ from ...


1

The problem lies in your simplistic assumption that the perimeter is the only thing that matters. The actual force can be no greater that the weight of displaced water (see for example a capillary) and as the force you try to exert, so the amount of water displaced will increase. That doesn't mean you could not use surface tension to "walk on water" - just ...


1

In every boundary layer (except for exotic hypersonic cases), the speed at the wall is zero. At the trailing edge, the upper and lower layers meet, and if you imagine a plane which extends from the trailing edge backwards and follows the streamlines, the speed at the trailing edge is equally zero. The more you now move away from the trailing edge along this ...


1

With no gravity and no impulse given to the blobs of fluid, my guess is that they would remain one inside the other and do nothing. If present, gravity would play on the blobs of fluid by making the less dense fluid (the oil) rise relative to the denser fluid, due to buoyancy. The oil would also "rise" if the spacecraft were rotating due to the greater ...


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As if you will see that a capillary tube kept in a beaker filled with water,so the water level rises but if the length of the capillary tube is insufficient than the angle of cos theta will be of 90 it means that its just impossible,and the surface tension force will be just stopped.


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You asked a similar question on worldbuilding for a story. Hit youtube for Operation Crossroads, Baker test. The US Navy detonated a 21kt device 90 feet underwater. Produced a nice fountain but no overly-destructive wave action after a few kilometers. A few years later, Castle Bravo (15Mt) also failed to produce any significant damage* outside the ...


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No,the velocity increases but the pressure decreases. This pressure that you are refering to,is the dynamic pressure,it is the pressure that drives the fluid.That keeps the momentum going. The fluid entering the narrower piece of pipe means that fluid tends to push back the fluid that tries to enter after it.That compresses the micro movements of the tiny ...


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I think it will be clear if you understand where Bernoulli's principle comes from. If you have a duct, and you decrease its diameter, the same amount of water you put in has to come out the other side. If furthermore, the fluid is incompressible you have that: $A_1V_1=A_2V_2$ where $V_{1,2}$ is the velocity of the fluid where the duct cross section area ...


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Since the pressure is dependent on depth, and your depth will vary if the structure (like a dam) is vertical, you will need to take the derivative of a vertical slice of the structure, and from there you will be able to multiply it by the horizontal (XY plane) area. your dx will be the change in depth making up for the "height" of the area for that ...


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Diffusion is when single particles move about and transports its momentum and energy to other particles. Convection is a large movement (in roughly the same direction) of a large mass of particles. For the difference see this.


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I will quickly post an answer here and will edit/expand on the answer with time. I used the model for nitrogen gas viscosity based on the PhD thesis by Kegang Ling from Texas A&M university, 2010 The model requires temperature and density. Density was calculated using the real gas law. The real gas law requires the compressibility factor of gas at ...



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