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. (b) 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

2.a.

The laminar boundary is very smooth flow, whereas the turbulent boundary layer contains swirls or \"eddies.\" The laminar flow creates less skin friction drag than the turbulent flow, but is less stable. Boundary layer flow over a wing surface begins as a smooth laminar flow. As the flow continues back from the leading edge, the laminar boundary layer increases in thickness.

The mixing of velocity fluctuations in turbulent flow creates a steeper profile than that of a laminar flow, with a larger boundary layer and higher wall shear stress.By understanding turbulence, we can alter designs to take advantage of turbulent effects, such as increased heat transfer and reduced drag.

2.b. Golf ball dimples are used on the golf balls because a dimpled golf ball has very less air resistance compared to a smooth ball of the same size and weight. This means there is less drag force and the ball can go farther. The lower air resistance is due to the reason that the golf ball dimples cause a turbulent boundary layer that stays attached farther around to the back of the ball, making a smaller turbulent wake , a smaller pressure drag coefficient, and less pressure drag force on the ball.