### Reynolds Number and Velocity Profile

#### Learning Outcomes

At the end of this module, you will be able to:

- derive the continuity equation
- use Reynolds number to distinguish between laminar and turbulent flow
- show that the velocity profile for laminar flow in a pipe is parabolic

In this module, we will apply the principle of conservation of mass to fluid flow. In the next video, we will derive the Continuity Equation. We will revisit this equation often when we later explore fluid flow in a pipe.

The characteristics of fluid flow in a pipe can be either streamlined or chaotic. In the next video, we will define a dimensionless number called Reynolds number to distinguish between different types of fluid flow

When fluid enters a pipe, its velocity profile (how the magnitude of velocity changes across the cross-section) will vary depending upon where along the pipe you make your observations. The velocity profile at the entrance to a pipe will differ from further downstream. The next video is about the flow characteristics at the entrance and under fully developed conditions.

In the next video, we will develop a mathematical derivation of the velocity profile for a fluid flowing in a pipe under fully developed conditions. The steps, described in their entirety, will give you an understanding of why the flow profile for a laminar flow in a pipe is parabolic in shape.

Recap

In this module, you learned the development of the Continuity equation and its importance in fluid flow. To distinguish between laminar and turbulent conditions for fluid flow in a pipe, you learned the role of a dimensionless number, called Reynolds number. Furthermore, you observed the differences between fluid flow in the entrance region vs. under fully developed conditions. Finally, you learned why the velocity profile for laminar flow under fully developed conditions has a parabolic shape.