Question

H11.2 At a sudden contraction in a pipe the diameter changes from Dito D2. The pressure drop, Ap, which develops across the contraction is a function of D, and D2, as well as the velocity, V, in the larger pipe, and the fluid density, P, and viscosity, u. a) Why shouldn't you choose both D, and D2 as repeating variables? b) Use D, V, and u as repeating variables to determine a suitable set of dimensionless parameters using the Buckingham Pi process using the FLT system.

Answer 1

a) D1 and D2 both cannot be choosen as repeating variable because repeating variables themselves rae not allowed to be formed into a dimensionless group.

Therefore any one of them has to be chosen.

b)

Ap fol , V, P.) -633 - fcap, P. Do, V, PM) = 0 here. no.df romablost (m) ob fundonats) d escons 3 4 Buckingham -theorem No of dimensiones group - VA BOVIM as reperating roolak D. [LT] [L] : -(17"): M '] Re-etang diressors to terms of rearables choon [2] - E - D DVF] = MVD S 350D Now, choosing remaining rearables Do, AP, 8 De has dimension [L] Da L is dimensionless T = De Foto - D₂ (D) & Dolo. A has dimension (FL2] .: Ap F" L² is dimensionless The - Ap F-1 L2 = Aplura) (D.² - AP DE ARDI NIV MVR s has dimension [F921"] PF-2"q2 u alimensionlees. T3 - Pluro) (0.54 (0, V-12 - P Wro, u vpi lly = P furrow]