When the air blows over a flat plate the horizontal velocity

When the air blows over a flat plate, the horizontal velocity u (velocity in the x direction) gradually increases from 0 at the wall to the free stream velocity as the distance from the wall increases. As you can see in the figure below, the average velocity profile is different when the flow is laminar and when it is turbulent. Using the figure, explain which one (laminar flow or turbulent flow) will create a larger drag on the flat plate and what is the reason. Golf balls have dimples as shown below. The dimples allow the rapid formation of a turbulent flow around the golf ball in flight. Explain how the formation of turbulent flow help a golf ball to fly farther. You may refer to the articles on the internet, but please make sure that you explain the answer in your own words.

Solution

A) From the figure of the velocity profile diagram for both laminar and turbulent flows, it is evident that the velocity variation along the y-axis is different for both the flows schematics.

We can also see that the flow variation is substantial and consistent in the laminar flow as we can see a steeper parabolic profile. Whereas in the velocity profile for the turbulent flow, the variation is very less almost 80 of the y-axis. Drag is a direct measure of the variation of the velocity over the y-axis. Hence the drag is more in laminar flow compared to the turbulent flow.

B) Air flows smoothly over the contours of the front side of any object and eventually separates from the object toward the back side. A moving object also leaves behind a turbulent wake region where the air flow is agitated, resulting in lower pressure behind it. The size of the wake affects the amount of drag on the object. Dimples on a golf ball create a thin turbulent boundary layer of air that clings to the ball\'s surface. This allows the smoothly flowing air to follow the ball\'s surface a little farther around the back side of the ball, thereby decreasing the size of the wake. A dimpled ball thus has about half the drag of a smooth ball.