1. The rise velocity V b of a bubble with diameter D in a liquid of density ρ l and viscosity μ depends on the acceleration due to gravity, g, and the density difference between the bubble and the...

1. The rise velocity V_b
of a bubble with diameter D in a liquid of density ρ_l
and viscosity μ depends on the acceleration due to gravity, g, and the density difference between the bubble and the fluid, ρ_l
– ρ_b. Find the π-groups in the form

2. The discharge of a centrifugal pump is a function of the rotational speed of the pump, N, the diameter of the impeller, D, the head across the pump, hp , the viscosity of the fluid, μ, the density of the fluid, ρ, and the acceleration due to gravity, g. The functional relationship is

By dimensional analysis, find the dimensionless parameters. Express your answer in the form