What is the relationship between turbulence, laminar flow, and Reynolds number?

What is the relationship between turbulence, laminar flow, and Reynolds number? — DD, SC

The Reynolds number is a measure of the way in which a moving fluid encounters an obstacle. It’s equal to the fluid’s density, the size of the obstacle, and the fluid’s speed, and inversely proportional to the fluid’s viscosity (viscosity is the measure of a fluid’s “thickness”—for example, honey has a much larger viscosity than water does). A small Reynolds number refers to a flow in which the fluid has a low density so that it responds easily to forces, encounters a small obstacle, moves slowly, or has a large viscosity to keep it organized. In such a situation, the fluid is able to get around the obstacle smoothly in what is known as “laminar flow.” You can describe such laminar flow as dominated by the fluid’s viscosity—it’s tendency to move smoothly together as a cohesive material.

A large Reynolds number refers to a flow in which the fluid has a large density so that it doesn’t respond easily to forces, encounters a large obstacle, moves rapidly, or has too small a viscosity to keep it organized. In such a situation, the fluid can’t get around the obstacle without breaking up into turbulent swirls and eddies. You can describe such turbulent flow as dominated by the fluid’s inertia—the tendency of each portion of fluid to follow a path determined by its own momentum.

The transition from laminar to turbulent flow occurs at a particular range of Reynolds number (usually around 2500). Below this range, the flow is normally laminar; above it, the flow is normally turbulent.