In this video we will be discussing the Reynolds number. The Reynolds number is a dimensionless quantity to help determine if a fluid flow will be..
Laminar flow or orderly flow, This is depicted at the bottom right as multiple layers of fluid that are all going parallel and in the same direction right ward.
Turbulent flow or chaotic flow, This is depicted at the top right as flow that is going chaotically in all direction but in general is going right ward
or transient which is a mixture of both laminar and turbulent flows.
The equation for the Reynolds number is inertial force of the fluid divided by the viscous force of the fluid. This is essentially a formula that compares the inertial force or force that keeps the fluid moving to the viscous force or internal resistance for the fluid to flow which allows us to compare to tested amounts to determine if the Reynolds number is laminar transient or turbulent. If the Reynolds number is below 2,300 it is laminar if the Reynolds number is between 2,300 to 4,000 it is transient if the Reynolds number is 4,000 or above it is turbulent. So a rule of thumb is that if the Reynolds number is smaller the flow will be more laminar and if the Reynolds number is larger the flow will be more turbulent
Breaking down the Reynolds number equation further it is the density or mass of fluid divided by volume of the fluid in kilograms per metercubed multiplied times the..
Velocity of the fluid relative to the object the fluid is moving through in meters per second multiplied times
The length or characteristic dimension which is a dependent on the convention for your particular application, for pipes many times radius or diameter of the pipe is used. For aircraft or ships sometimes length or width is used. For non circular object the equivalent diameter may be used.
This all is divided by The dynamic viscosity of the fluid which is the internal resistance of a fluid to flow. It is equal to the kinematic viscosity of the fluid times the density of the fluid.
Being that density is in both the numerator and denominator of the formula it can be canceled out. We are left with velocity times length divided by kinematic viscosity being equal to the Reynolds number. Incase you were wondering kinematic viscosity is equal to the dynamic viscosity divided by the fluid density.
Looking at this equation we notice that if 1 or more of the values in the numerator (velocity or characteristic linear dimension) increase then the flow will drift closer to being turbulent. There will be a higher Reynolds number.
So if the inertial force increases meaning there is more energy in the fluid. it is more likely the fluid will be chaotic and turbulent. Generally if there is a larger area or higher velocity this will cause more energy to be in the fluid at a given cross sectional point.
If 1 or more the the values in the numerator decrease then the Reynolds number will decrease and the flow will go towards being more laminar.
If the inertial force decreases then there will be less energy in the fluid. it is more likely the fluid will be orderly and laminar. Generally if there is a smaller area or smaller velocity this will cause less energy to be in the fluid at a given cross sectional point
Now if the values in the denominator (dynamic viscosity or the kinematic viscosity) increase then the Reynolds number will decrease which will results in a flow that is more towards laminar flow.
If the viscous force is greater meaning there is more resistance for the molecules within the fluid to move it is more likely that the molecules will remain in a straight path and the fluid flow will be laminar.
If the dynamic viscosity or kinematic viscosity decrease then the Reynolds number will increase and the flow will go more towards the turbulent side.
If the viscous force is less then it is easier for the fluid molecules to change path within the fluid as a result the fluid will be more turbulent

Disclaimer
These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.