A vacuum cleaner creates a pressure drop Ap across its fan. Relate this pressure drop to the impeller diameter D and width h, its rotational speed o, the air density p, and the inlet and outlet diameters di and do. Write the final form in terms of dimensionless parameters using Buckingham n theorem.
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- Using primary dimensions, verify that the Rayleigh number is indeed dimensionless. What other established nondimensional parameter is formed by the ratio of Ra and Gr?By dimensional analysis, obtain an expression for the drag force (F) on a partially submerged body moving with a relative velocity (u) in a fluid; the other variables being the linear dimension (L), surface roughness (e), fluid density (p), and gravitational acceleration (g).In studying sand transport by ocean waves, A. Shields in1936 postulated that the threshold wave-induced bottomshear stress τ required to move particles depends on gravityg , particle size d and density ρ p , and water density ρ andviscosity μ . Find suitable dimensionless groups of thisthe problem, which resulted in 1936 in the celebrated Shieldssand transport diagram.
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