Homework Help: Pressure drag acting on a sphere

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1. Nov 8, 2017

Zar139

1. The problem statement, all variables and given/known data
I am trying to show that the pressure drag acting on a sphere is 2πμaU by integrating around the surface of the sphere where U is the speed of the fluid the sphere is in, a is its radius, and μ is the viscosity.

2. Relevant equations
The pressure at a given position r can be written as:
P-P0 = -1.5μUacos(Θ)/r2

3. The attempt at a solution
I have tried integrating the above equation for Θ from 0 to 2π over the surface of the sphere but my answer is 0 which is clearly not the correct answer. I feel like this should be a fairly easy integration but I do not know how else to go about it. Any suggestions would be greatly appreciated.

Thank you!

2. Nov 9, 2017

Staff: Mentor

The pressure acts normal to the surface of the sphere at all locations. So, you have to include this directionality in your determination of the drag force.

3. Nov 9, 2017

Zar139

Does this mean that I should multiply the area element dS by the unit normal vector?

4. Nov 9, 2017

Staff: Mentor

You definitely have to integrate the forces vectoriallly. How you do this depends on how you want to approach it.