Reynolds number calculation
 

Reynolds number has to do with a bodies size in relation to its velocity,moving through a viscous fluid and boundary layer conditions,whether the boundary layer is laminar or turbulent is dependent upon it.
The number is named after Osborne Reynolds who introduced it in 1882.
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For road vehicle work the Reynolds number is defined by:

Length X Velocity / Kinematic viscosity

L X V / v

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Kinematic viscosity is the 'coefficient of viscosity',also 'absolute viscosity',also 'dynamic viscosity',and also just 'viscosity', divided by density,or

viscosity / density ( Mu over Rho )
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EXAMPLE: Toyota Prius,approx. 14-foot length,at 60-mph ( 88 feet per second ),on a 50-degree F day,( v = 0.00015 ft-squared/second )
Then,--------------- 14 X 88/ 0.00015 = 8,213,333 = Reynolds number

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Kinematic viscosity can be found in tables.You can directly measure your vehicles length,and you just pick a velocity in feet per second.
P.S. v at standard temp and pressure is 0.000158.
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Knowing the Reynolds number allows calculation of surface-friction drag,or the 'skin-friction' component of your vehicles profile drag.Subtracting the skin friction component from the profile drag reveals the 'pressure drag' of your vehicle which is governed by flow separation.A perfectly streamlined vehicle will have zero pressure drag and only a bit of skin friction which is unavoidable to the viscous qualities of the air.

If you're working with these equations, it will make a difference on whether you use absolute or kinematic viscosity.

The units for absolute viscosity are quite a bit different than kinematic viscosity.

Jim.

20,000,000 seems awfully high. From memory (it's been a long time . . .) the rule of thumb for Reynolds number at STP was 10,000 X MPH X length in feet, which would yield 10K X 60 X 14 = 8,400,000. This seems more reasonable to me.

difference
 

Jim,yes it absolutely critical that kinematic viscosity be used.

6380?
 

Patrick,sometimes kinematic viscosity is given as it's reciprocal,which for standard air is 6380.
In my table of SI units kinematic viscosities listed have been multiplied by 10,000.

The formula I have for Reynolds number is also from Daugherty.Hucho uses the same equation.

goof and correction
 

In the Prius example I transposed the Reynolds number of a 35-foot moving van into the solution for the Prius.
Patrick caught the numerical mistake and the whole thing didn't register with me until last night.
I went back and edited the original thread where you will find a significantly lower value.
My 'math' is good enough now that I think I may be ready for Arthur Anderson,ENRON,or Moody's Investment Services.
I'll see if I can clean up the skin-friction thread.

reynold number calc
 

hi,

i want to calculate the Reynolds number of exhaust gas with a given temperature(°c) and massflow(g/s).
What is the fastest way?

thanks in advance

That's flow through a tube, which is a different calculation than the above equations for flow across a plate. Use this:

Re=D*V*rho/mu,

where D=dia, V=velocity, rho=density of exhaust gas, mu=viscosity.

The assumption that exhaust gas = air (rho=1.3kg/m^3 at STP) should get you within an order of magnitude.

One of the fun parts with that equation is that exhaust gas is HOT. And it cools relatively rapidly as it moves through the exhaust system. So its density changes by a decent amount...

-soD

While we're doing the math, what is the effect of temperature on skin friction and pressure drag. I'm thinking warm day vs cool day vs cold snap like we recently had.

(I should do it myself, but it's been so long I don't even know where to look for the numbers)