Power P of a centrifugal pump is assumed to be a function of the volume flow...

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Power P of a centrifugal pump is assumed to be a function of the volume flow rate Q, the impeller diameter D, angular rotation rate , density p, and viscosity μ of the fluid. Using Buckingham II theorem, rewrite this as a dimensionless relationship between three II groups using: (a) p, and D as the repeated variables. (b) Q, μ, and p as the repeated variables. (c) Let's call the set of non-dimensional groups from (a) as II₁, I₂ and II3 and from (b) as N₁, N₂, and N3. It may be possible, through appropriate algebraic manipulations, to transform II groups into the N groups. Find how II₁, Pi2, and Pi3 are related to N₁, N2, N3. Power P of a centrifugal pump is assumed to be a function of the volume flow rate Q, the impeller diameter D, angular rotation rate , density p, and viscosity μ of the fluid. Using Buckingham II theorem, rewrite this as a dimensionless relationship between three II groups using: (a) p, and D as the repeated variables. (b) Q, μ, and p as the repeated variables. (c) Let's call the set of non-dimensional groups from (a) as II₁, I₂ and II3 and from (b) as N₁, N₂, and N3. It may be possible, through appropriate algebraic manipulations, to transform II groups into the N groups. Find how II₁, Pi2, and Pi3 are related to N₁, N2, N3.

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a Using Buckingham Pi theorem the dimensionless groups can be expressed ... View the full answer