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This equation is valid for incompressible flows (steady or unsteady), and for compressible flows in steady state. In steady state, mass inside a control volume cannot change with time, hence mass comi …

If pressure difference driving the flow is constant, then it is not obvious that introducing a constriction in the flow will necessarily increase the flow speed there (compared to the flow speed before … This argument doesn't assume a compressible flow. …

Suppose geometry of your flow restrictive device is fixed, so that we can take any one geometric dimension of the device (which is relevant to the flow) as your length scale, call it $d$. … This is laminar flow regime, and calling $K_1$ laminar flow factor is again only by way of resemblance. …

You see laminar flow becomes turbulent by growth of disturbances introduced into it either by uncontrollable vibrations from the walls (which are ever present) or deliberately by using a trip wire. … Beyond a Reynolds number smallest disturbances get amplified (in time and/or space) and laminar flow becomes turbulent. This state of the flow is analogous to a pencil standing on its pointed end. …

I can't find a definition for laminar flow that includes vortex structures. … Vortex structures don't figure directly in the definition of laminar flow, in the sense that we can have laminar flow with or without vortex/eddy structures. …

The tiny particles (of micron size) that the mask filters out is still much bigger than the dimensions of the gas molecules (of nano meter size) that we breathe. So the mask's ability to filter parti …

But here is something that comes close: A turbulent flow is characterised by a wide range of length and time scales, while a laminar flow is not. … flow becomes turbulent. …

So you can apply D-W equation provided flow is laminar. …

The textbook is trying to show you the effect of varying only $Re$ while keeping everything else the same while you scale your system. Therefore you need to keep geometric parameters (among others) of …

In the continuum limit the body (i.e. aggregate of blobs) seems to become a cylinder, but with increasing radius along X direction. Area of elemental circular strip at distance $x$ will be (circumfere …

I don't know which turbulent flow you are dealing with. … If it is has a large value of mean flow compared to turbulent fluctuation velocity (for example in a wind tunnel) and if the turbulence is homogeneous in the direction of mean flow, then as a first approximation …

"preserved following the flow" means preserved as you follow a fluid particle during its motion. Suppose that a fluid particle is located at position $(x,y,z)$ at time $t$ and has velocity $(u,v,w)$. …

In other words while mean flow may be 2-dimensional, fluctuations of flow exist in all 3 dimensions. … This means that if $(u,v,w)$ is the total flow velocity field, then it is to be decomposed as $(\bar{u}+u',v',w')$ because $\bar{v}=\bar{w}=0$. So Reynolds stress will be present. …

More precisely, say you wish to measure pressure at a point P in the flow, where the fluid velocity is $\mathbf{v}$. … In any other reference frame the area must be oriented such that its normal is perpendicular to $\mathbf{u}$, i.e. there should be no flow across the area. …

...volume integral is to be performed over the region where ... the fluid is not actually present in the volume where the divergence of its stress tensor is being integrated. You are correct, but …