The upper layer of river water moves at 36 km h⁻¹. The shearing stress between horizontal layers is 10⁻³ N m⁻² and water viscosity is 10⁻² Pa·s. Find the river depth in metres.
Physics · Properties of solid and fluid
JEE Mains 2022

Question

The upper layer of river water moves at 36 km h⁻¹. The shearing stress between horizontal layers is 10⁻³ N m⁻² and water viscosity is 10⁻² Pa·s. Find the river depth in metres.

G1 Physics · Accepted Answer

Step 1: Use viscous-force relations: shear F = ηA(dv/dy), Stokes force 6πηrv, or Reynolds number Re = ρvD/η as appropriate. Step 2: At terminal speed set net weight/buoyancy equal to viscous drag and use the given geometry. Applying these relations to the given data gives 100. Final answer: 100.