How to Calculate Reynolds Number for Fluids

This is my second article addressing mold design engineering calculation. This dimensionless parameter is used to determine the type of flow that is occurring in a passage.

Instructions

Difficulty: Moderate

Things You’ll Need:

• A problem to solve, pencil, paper, a calculator or piece of software, like DZynSource for Molds, to make it easier and quicker.

1. Flow is either Laminar, Turbulent, or Transitional. A Reynolds Number of 2000 or less is generally accepted to be indicative of Laminar Flow. There are widely varying opinions of the Reynolds Number required to indicate turbulent flow in round passages. There is literature that claims turbulent flow will exist at an Re as low as 2600, or as high as 10,000. It is often accepted that a Reynolds Number greater than 4000 is a good indicator of turbulent flow for fluids like water and oil in circular passages.
2. In the design of hydraulic circuits, it is desirable to keep the Reynolds Number below 2000. Higher flow rates generate more resistance to flow, cause a mixing action and energy losses. The hydraulic oil temperature increases and this causes the oil properties to break down. If the calculation shows the flow to be turbulent, or transitional, it is good practice to increase the hydraulic line size to insure laminar flow.
3. As a form of visual description, it is often convenient to visualize water flowing from a faucet. During laminar flow, there is very little mixing action in the fluid. Laminar flow from a faucet appears clear, or "see through". If you open the faucet until the water appears "white", or "not see through", you have turbulent flow. Transitional flow is the description for the types of flow that occur during the change from Laminar to Turbulent flow.
4. The mixing action that occurs during turbulent flow works to our advantage for mold cooling. It is critical to have turbulent flow in cooling passages in the mold. The heat transfer rate is proportionate, although in a non-linear fashion, to the Reynolds Number. It is often accepted practice to design for a Reynolds Number of 10,000 for mold cooling systems.
5. There are several convenient formulae used to calculate Reynolds Number, but they are all based on the following relationship:
   
   Re = vDr/m
   
   Where,
   Re = Reynolds Number
   v = fluid velocity
   D = fluid passage diameter
   r = Fluid mass density
   m = Fluid absolute viscosity
6. The viscosity of water at some various temperatures, Fahrenheit, is as follows:
   
   Degrees versus Viscosity
   
   32 = 1.79 centiStokes
   40 = 1.54 centiStokes
   50 = 1.31 centiStokes
   60 = 1.12 centiStokes
   70 = 0.98 centiStokes
   80 = 0.86 centiStokes
   90 = 0.76 centiStokes
   100 = 0.69 centiStokes
   120 = 0.56 centiStokes
   140 = 0.47 centiStokes
   160 = 0.40 centiStokes
   180 = 0.35 centiStokes
   200 = 0.31 centiStokes
7. The equation, or formula, that I usually find most convenient is:
   
   Re = (3600 Q)/Dn
   
   Multiply the 3600 times the gallons per minute of fluid flow, then divide that number by the diameter of the passage, in inches, multiplied by the viscosity of the fluid in centiStokes.
8. For non-cricular flow passages, see my article on equivalent hydraulic diameter here http://www.ehow.com/how_2321165_calculate-equivalent-hydraulic-diameter.html
9. That's it! Not so bad, huh. There was just a lot explaining leading up to the anticlimactic conclusion.

Tips & Warnings

• Adding a Glycol antifreeze to your water increases the viscosity substantially, and therefore reduces the water' s capacity to remove heat.
• Always double-check your work. If in doubt, get professional advice.