Question

KT 2:49 g LTE 91 % a & O Expert Q&A 618 EXTERNAL FLOW DRAG AND LIFT circ Disk dra 2.0- nun 1,5- mo The cal 1.0- sm Re 0.5- Sp 0-+ 10 102 10 104 105 Re Th Qutur bulendt FIGURE 11-17 The drag coefficients for most geometries (but not all) remain essentially constant at Reynolds numbers above about 10, be ER wl G. nu Otic II 2 + In this picture above, the drag coefficient is shows the tendency that firstly decreases and suddenly increases and then decreases. Please explain why this gragh shows that tendency which I mentioned. (I was told that this question is related to the concept of turbulent and laminar flow and also flow separation.)

Answer 1

(1.) In the case of flow over a Disk , both friction drag and pressure drag contribute to total drag . The drag coefficient for flow over a smooth disk is a function of Reynolds number .
At the front portion of the disk Reynolds number is low ; hence there is no flow separation from a disk , the wake is laminar and the drag is predominantly friction drag . Stokes has shown
analytically , for very low Reynolds number flows where inertia forces may be neglected , The drag coefficient Cd is defined as ;
Cd = 24/Re
As the Reynolds number is further increased due to flow convergence on the disk , the drag coefficient DECREASES continuously up to a Reynolds number of about 1000 .

(2.) After this a turbulent wake develops and grows at the top of the disk ; this wake is at a relatively low pressure, leading to a large pressure drag . By the time Renold number is very high approximately equal to 1000 - 10000 due to very small converging passage at the top of the disk , about 95% of total drag is due to the pressure , Due to this Drag coefficient INCREASES suddenly .

(3.) And after the transition phase , the boundary layer at the back of the disk start separating and the size of the wake decreases at the back portion of the disk . Due to this net pressure force on the disk is reduced and the drag coefficient DECREASES abruptly.