For laminar flow in a pipe of circular cross-section, the Darcy’s friction factor f is________________?

A. directly proportional to Reynolds number and independent of pipe wall roughness
B. directly proportional to pipe wall roughness and independent of Reynolds number
C. inversely proportional to Reynolds number and indpendent of pipe wall roughness
D. inversely proportional to Reynolds number and directly proportional to pipe wall roughness
✅ The correct answer is option C.

In a forced vortex motion, the velocity of flow is________________?

A. directly proportional to its radial distance from axis of rotation
B. inversely proportional to its radial distance from the axis of rotation
C. inversely proportional to the square of its radial distance from the axis of rotation
D. directly proportional to the square of its radial distance from the axis of rotation
✅ The correct answer is option A.