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Be@ner boy reminding everyone he's a 9th year senior majoring in engineering at a tier university par per etc
In fluid mechanics, the Reynolds number (Re) is a dimensionless quan y that is used to help predict similar flow patterns in different fluid flow situations. The concept was introduced by George Gabriel Stokes in 1851,[2] but the Reynolds number is named after Osborne Reynolds (1842–1912), who popularized its use in 1883.[3][4]
The Reynolds number is defined as the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions.[5] Reynolds numbers frequently arise when performing scaling of fluid dynamics problems, and as such can be used to determine dynamic similitude between two different cases of fluid flow. They are also used to characterize different flow regimes within a similar fluid, such as laminar or turbulent flow: laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion; turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities.
In practice, matching the Reynolds number is not on its own sufficient to guarantee similitude. Fluid flow is generally chaotic, and very small changes to shape and surface roughness can result in very different flows. Nevertheless, Reynolds numbers are a very important guide and are widely used.
The Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface.[n 1] These definitions generally include the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension. This dimension is a matter of convention – for example radius and diameter are equally valid to describe spheres or circles, but one is chosen by convention. For aircraft or ships, the length or width can be used. For flow in a pipe or a sphere moving in a fluid the internal diameter is generally used today. Other shapes such as rectangular pipes or non-spherical objects have an equivalent diameter defined. For fluids of variable density such as compressible gases or fluids of variable viscosity such as non-Newtonian fluids, special rules apply. The velocity may also be a matter of convention in some cir stances, notably stirred vessels. The Reynolds number is defined below for each case.
[6]where:
is the mean velocity of the object relative to the fluid (SI units: m/s)
is a characteristic linear dimension, (travelled length of the fluid; hydraulic diameter when dealing with river systems) (m)
is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s))
is the kinematic viscosity (
) (m²/s)
is the density of the fluid (kg/m³).
Note that multiplying the Reynolds number byyields
, which is the ratio of the inertial forces to the viscous forces.[7] It could also be considered the ratio of the total momentum transfer to the molecular momentum transfer.
Flow in pipe[edit]
For flow in a pipe or tube, the Reynolds number is generally defined as:[8]
where:
is the hydraulic diameter of the pipe; its characteristic travelled length,
is the volumetric flow rate (m3/s).
is the pipe cross-sectional area (m²).
is the kinematic viscosity (
(m²/s).
For shapes such as squares, rectangular or annular ducts where the height and width are comparable, the characteristical dimension for internal flow situations is taken to be thehydraulic diameter,, defined as:
where A is the cross-sectional area and P is the wetted perimeter. The wetted perimeter for a channel is the total perimeter of all channel walls that are in contact with the flow.[9]This means the length of the channel exposed to air is not included in the wetted perimeter.
For a circular pipe, the hydraulic diameter is exactly equal to the inside pipe diameter,. That is,
For an annular duct, such as the outer channel in a tube-in-tube heat exchanger, the hydraulic diameter can be shown algebraically to reduce to
where
is the inside diameter of the outside pipe, and
is the outside diameter of the inside pipe.For calculations involving flow in non-circular ducts, the hydraulic diameter can be subs uted for the diameter of a circular duct, with reasonable accuracy.
Flow in a wide duct[edit]
For a fluid moving between two plane parallel surfaces—where the width is much greater than the space between the plates—then the characteristic dimension is twice the distance between the plates.[10]
Flow in an open channel[edit]
For flow of liquid with a free surface, the hydraulic radius must be determined. This is the cross-sectional area of the channel divided by the wetted perimeter. For a semi-circular channel, it is half the radius. For a rectangular channel, the hydraulic radius is the cross-sectional area divided by the wetted perimeter. Some texts then use a characteristic dimension that is four times the hydraulic radius, chosen because it gives the same value of Re for the onset of turbulence as in pipe flow,[11] while others use the hydraulic radius as the characteristic length-scale with consequently different values of Re for transition and turbulent flow.
Flow around airfoils[edit]
Reynolds numbers are used in airfoil design to (among other things) manage "Scale Effect" when computing/comparing characteristics (a tiny wing, scaled to be huge, will perform differently).[12] Fluid dynamicists define the chord Reynolds number, R, like this: R = Vc / ν where V is the flight speed, c is the chord, and ν is the kinematic viscosity of the fluid in which the airfoil operates, which is 1.460x10−5 m2/s for the atmosphere at sea level.[13] In some special studies a characteristic length other than chord may be used; rare is the "span Reynolds number" which is not to be confused with span-wise stations on a wing where chord is still used.[14]
Object in a fluid[edit]
Qualitative behaviors of fluid flow over a cylinder depends to a large extent on Reynolds number; similar flow patterns often appear when the shape and Reynolds number is matched, although other parameters like surface roughness have a big effect
The Reynolds number for an object in a fluid, called the particle Reynolds number and often denoted Rep, is important when considering the nature of the surrounding flow, whether or not vortex shedding will occur, and its fall velocity.
In viscous fluids[edit]
Where the viscosity is naturally high, such as polymer solutions and polymer melts, flow is normally laminar. The Reynolds number is very small and Stokes' Law can be used to measure the viscosity of the fluid. Spheres are allowed to fall through the fluid and they reach theterminal velocity quickly, from which the viscosity can be determined.
The laminar flow of polymer solutions is exploited by animals such as fish and dolphins, who exude viscous solutions from their skin to aid flow over their bodies while swimming. It has been used in yacht racing by owners who want to gain a speed advantage by pumping a polymer solution such as low molecular weight polyoxyethylene in water, over the wetted surface of the hull.
It is, however, a problem for mixing of polymers, because turbulence is needed to distribute fine filler (for example) through the material. Inventions such as the "cavity transfer mixer" have been developed to produce multiple folds into a moving melt so as to improve mixingefficiency. The device can be fitted onto extruders to aid mixing.
Sphere in a fluid[edit]
For a sphere in a fluid, the characteristic length-scale is the diameter of the sphere and the characteristic velocity is that of the sphere relative to the fluid some distance away from the sphere, such that the motion of the sphere does not disturb that reference parcel of fluid. The density and viscosity are those belonging to the fluid.[15] Note that purely laminar flow only exists up to Re = 10 under this definition.
Under the condition of low Re, the relationship between force and speed of motion is given by Stokes' law.[16]
Oblong object in a fluid[edit]
Be@ner boy reminding everyone he's a 9th year senior majoring in engineering at a tier university par per etc
Physics is bull ain't it swastika boy?
we germans are the best engineers and the reich did more in a few years for science than you could ever do in a hundred lifetimes, skin.
the knowledge that Physics generates ain't what you need today, but what's gonna be tremendously useful in two or three centuries, tbh.
Attend any good hitler youth movements lately?
gay
attended any communist club meetings lately?
>hates self respecting whites, calls them "nazi"
>lives in white country
top kek
So no Hitler youth movements?
Muh nazis
You're a good goy who's either:
A) proud of attacking his ethnic brothers since most americans at that time had german heritage, or
B) an idiot skin trying to bandwagon german-americans killing actual germans
none of your post makes any sense except the one saying that america bombs countries under the pretext of "freedom"
Biggest war crime of that entire conflict was firebombing Dresden, Munich, etc. I can see why the UK took part in that (Coventry and whatnot), but curious why murica did since we have always been holier than thou...at least dets what I was taught
Still butt hurt over that ass whipping Patton gave you es huh....
Patton regretted his actions and said he fought for the wrong side before he was assassinated. Nice self ownage.
isn't germany 0-2 in world wars?
Patton assassinated??? I guess his jeep assassinated him....
Do you know anything about WWII history???
We are in a "Today's Math Lesson" thread...so I'll break it down for you.
That comes out to a 0% win percentage....
lol kids these days. America won those 2 wars like DJ Mbenga won b2b rings. If you wanna celebrate WWII do it the right and just way, and sing The Internationale
Yeah but history remembers the winners and losers, so bragging about germany's valiant efforts in their losses is sorta weak too
I'll put it in a way a Laker fan can get:
USA - Shaq
Britain - Kobe
Russia - Mbenga
and I'm not doing that, so.....
But Americans (me being one of them) bragging about World War accomplishments is laughable. We really shouldn't even cite WWI in the first place (if we're being honest)...and WWII we can claim victory over the Japs and that's about it.
You really have no grasp on that war and it's appallingly obvious. You definitely learned about WWII in a red state
Actually, here's the best analogy possible to describe America in World Wars: Russell Wilson in the SB. Non-factor when it was in the balance, superb when it already was.
you aren't, but m>s is doing his thing
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