Help required with Reynolds number calculation

Because, the Reynold's number is dimensionless, you cannot mix and match units. I calculate a velocity in your pipe of 9.1 fps.

Since Darcy-Weisbach and Colebrook relationships are based upon using a Reynold's number which varies inversely with the kinematic viscosity and which is obtained by dividing the dynamic (absolute) viscosity by the mass density, it is the usual practice to use units of kinematic viscosity which have the dimensions of :

(length square)/time

The unit of kinematic viscosity in English measure is the square foot per second. The unit of kinematic viscosity in metric measure is the square centimeter per second called the stoke. It is usually more convenient to express numerical values in centistokes such that 100 centistokes equals one stoke.

When English system units are used in converting from dynamic to kinematic viscosity the density, w/g (or mass density) rather than the specific gravity must be used were w is the weight in lb/ft3 and g is the acceleration due to gravity (32.174 ft/sec2)

When metric system terms centipoise and centistokes are used the density is numerically equal to the specific gravity.

I suspect you have run into this very common gotcha and that this is the reason that weird solutions are being rendered.

eriew

We use to practice the Re formula for air flow measurements that is

Re= ( Hydraulic dia x Velocity x Density)/ 60 Viscosity

Units are

Diameter in Feet = 0.41666 ft

Velocity fpm 45.5 cfm = 343 ft/m

Density Lb/ft Cube = 67 lbs/ft cube

Viscosity Ft square/sec = 0.000 044 1

In my calculations Reynold's number is 3618248. Please verify.

Is this the what you are using too?

Sorry HydroScot there was an error in units and values so here are fresh calculations.

Diameter in Feet = 0.41666 ft

Velocity fpm 45.5 cfm = 343 ft/m

Density lb/ft Cube = 67 lbs/ft cube

Viscosity lb/Ft-sec = 0.00294806 lb/ft-sec

Reynold's number is 54126 Please verify.

Does this site help you understand?

http://www.engineeringtoolbox.com/reynolds-number-d_237.html

Equation looks good, it has to be something in the units conversion.

Hi all - rakesh, quest and betomachine. Please excuse the late response but I was away from my work yesterday. Many thanks for your input to date.

The problem seems to be in the interpretation of the formula, particularly the L dimension. In most formula this is stated as the length of pipe run OR the inside diameter of the tube. Applying both gives quite different answers as follows:

1. Re = 1080 (density in kg/m3) x 9.1 (velocity in M/sec) x 20.9 (Meters, length of pipe run) / 4.1 (viscocity in Cst) = 50,098

2. Alternatively using the L = bore dia (12 mm) = 0.012M = 1080 x 9.1 x .012 / 4.1 = 28.76.

I am not convinced that using the pipe run length is correct, but presuming that the inclusion of the pipe bore is, then the number is ridiculously low. Applying the similar numbers to smaller bore pipe makes the number even lower.

Where am I going wrong?

Hello HydroScot

Your formula is slightly wrong.

Should be Re = v*D/uV (same as P*v*D/μ where μ = dynamic viscosity, as uV = μ/P)

I make it Re = 8523 (or rather Mathcad does, it automatically takes care of units)

Note P is density, not relative density. Length of pipe doesn't come into it. As other posters have said, Re is dimensionless so any system of units can be used, but they have to be consistent.

Cheers.....Codey

Hi codey,

Thanks for the response. I did try a different formula, specifically for pipes: Re = 7745.8 u dh/v and converted metric units to enable the use of Cst. My calculation came out at 8598, so seems to work as it is close to your own (which I will try now!)

Thanks again to you and all the subscribers.

Scot