In this lesson, we will discuss the following topics:
1. What is Flow Past Immersed Bodies
2. Example – Calculating Distance to a given Boundary Layer Thickness
video coming soon
What is Flow Past Immersed Bodies
Since this is the first lesson in this chapter, let’s discuss what this chapter is even about – Flow Past Immersed Bodies. An immersed body is something that is completely immersed/submerged in a fluid. This chapter is dedicated to studying external/unconfined (not in a pipe or duct) flows around these immersed bodies – for example, fluid flow around a flat plate. This type of flow usually has viscous effects (eg. friction/viscosity is present) but the farther you get from the submerged object, the less these viscous effects come into play. At this point, these are unconfined boundary layer flows. Here is what flow past an immersed body looks like for a smooth sphere versus a bumpy sphere (eg. a golf ball):
There are certain equations that come into play here. One equation is in the situation where fluid is flowing along a flat plate. The equations below are used for Reynolds number values within certain ranges. The delta (curvy S) is the thickness of the boundary layer, and the x is the length of the plate. Re is the Reynolds Number.
The Reynolds Number used in the above equation is the local Reynolds Number of the flow along the plate surface, and can be found through the following formula:
x is the same as it is in the above equation, but U is the external velocity outside of the plate, and v is the kinematic viscosity of the fluid.
Example – Calculating Distance to a given Boundary Layer Thickness
(a) Let’s write out the given variables and draw a picture. The boundary layer thickness will be 1 inch (which should be converted to feet, since the velocity U of 20 ft/s is given with feet). The temperature is 68F, and you can find the kinematic viscosity of water at this temperature to be the value I have used below:
(b) Let’s assume laminar flow and use the equations given above. We have an equation that uses the boundary layer thickness and the local Reynolds Number above. Let’s use these equations and the information in part (a) to fill them out:
The purple x circled in the first two equations of the last picture above is what we were trying to find. I substituted in the local Reynolds Number equation into the boundary layer thickness equation. Then solving for x, the plate length is 513 feet. This is very long, which seems unreasonable. It should only be a couple feet long, so this actually means that our assumption of laminar flow was incorrect – we need to use the second equation for turbulent flow from this picture:
(c) Use this second equation and substitute everything in the same way we did in part (b):
(d) This answer for the plate length x seems much more reasonable – 5.17 feet. This is the final answer.