NTA Abhyas JEE Main2020PhysicsMechanical Properties of FluidsPractice
A tube of length l and radius R carries a steady flow of fluid whose density is ρ and velocity η . The fluid flow velocity depends on the distance r from the axis of the tube as v = v 0 1 - r 2 R 2 . Find the friction force exerted on the tube by the fluid.
Options
- A4 π η l V 0
- B2 π η l V 0
- Cπ η l V 0
- D2 3 π η l V 0
Correct answer
A. 4 π η l V 0
Step-by-step solution
v = v 0 1 - r 2 R 2 d v d r = - 2 v 0 r R 2 f = - η A d v d r = η A . 2 v 0 r R 2 = η . 2 π R l . 2 v 0 . R R 2 = 4 π η l v 0