Water flows steadily through a reducing pipe section The flow upstream with a radius of R 1 is laminar with a velocity profile of u 1 (r) u 01 (1 r 2 R 2 1 ) while the flow downstream is turbulent with a velocity profile of u 2 (r) u 02 (1 r R 2 ) 1 7 For incompressible flow with R 2 R 1 4 7, deter...

Water flows in a reducing pipe section The f ...

Water flows steadily through a reducing pipe section. The flow upstream with a radius of R 1

Question:

Water flows steadily through a reducing pipe section. The flow upstream with a radius of R₁ is laminar with a velocity profile of u₁(r) = u₀₁(1 - r²/R²₁) while the flow downstream is turbulent with a velocity profile of u₂(r) = u₀₂(1 - r/R²)^1/7. For incompressible flow with R²/R¹ = 4/7, determine the ratio of centerline velocities u₀₁/u₀₂.