TBR Physics, Reynold's Equation

[sshah92]

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So TBR has this really random lecture portion talking about the Reynold's equation, which describes turbulence of a flowing liquid in the pipe.

The equation is Nr (Reynold's Number) = 2(rho, liquid)vr / viscosity.

Above 3000, the flow is turbulent. Below 2000, the flow is laminar.

I was just wondering why radius would be in the numerator, considering that in a pipe a more constricted section would experience a greater velocity.

 

[sazerac]

Remember, both v (velocity) and r (radius) are in the numerator. The numerator is trying to convey the "amount" of water that is flowing.

Let's say you have some kind of flow rate, and then you halved the radius. The area would go down to 1/4 its original value. The velocity would have to become 4x to keep up with the original flow rate. Therefore the Reynolds number would go UP by a factor of two when the radius is halved.

 

[sshah92]

Isn't rho the density of the fluid and not the radius of the pipe, though?

Yeah, density and radius are both in the numerator of the equation!

 

[sazerac]

Drat, you caught me mid-edit. See my fixed response, above 🙂