1. Assume a vertical pipe and include gravity in the list of variables in Prob. 6.12 and ?nd an expression for the pressure drop.
2. The drag force on a sphere depends on the sphere's diameter and velocity, the ?uid's viscosity and density, and gravity. Find an expression for the drag force.
3. The drag force on a cylinder is studied in a wind tunnel. If wall effects are negligible, relate the drag force to the wind's speed, density and kinematic viscosity, and the cylinder's diameter and length.