REYNOLDS NUMBER

REYNOLDS NUMBER

The Reynolds number is the ratio of a fluid's inertial force to its viscous force. Inertial force involves force due to the momentum of the mass of flowing fluid. Think of it as a measure of how difficult it would be to change the velocity of a flowing fluid. Viscous forcesdeal with the friction of a flowing fluid. Think of pouring a cup of tea versus pouring cooking oil. The cooking oil has a higher viscosity because it is more resistant to flow.

If you are thinking inertial force and viscous force are very similar, you are correct. In fact, they are so similar that they have the same units! This means the Reynolds number is unitless. We can determine whether fluid flow is laminar or turbulent based on the Reynolds number.

If the Reynolds number is less than 2300 the flow is laminar. Any Reynolds number over 4000 indicates turbulent flow. In between these values indicates transient flow, which means the fluid flow is transitioning between laminar and turbulent flow. This usually happens only for a short period of time at the beginning or end of fluid flow when a valve or faucet is turned on or off. Let's look at the equation for the Reynolds number.

a) laminar flow ...all the particles of fluid flow in an its one path in smooth manure.

b) turbulent flow ...all the particles of fluid collides with each other 

• R is the Reynolds number, which is unitless
• ρ is the fluid density in kilograms-per-cubic-meter (kg/m3)
• v is the velocity in meters-per-second (m/s)
• D is the diameter of the pipe in meters (m)
• μ is the viscosity of the fluid in pascal-seconds (Pa⋅s)

Now let's look at the calculations for the flow through two different pipes.