Question

The spray characteristics of a highly poisonous liquid fuel, especially particle diameters, are desired to known. It has been suggested that particle diameters d_p, spray outlet speed U, liquid viscosity μ , surface tension Y, density ρ and spray injector outlet diameter D are connected. Design a experiment which will be done with with water and specify the necessary conditions for the experiment . Write the data with mathematical expressions, if necessary, with dimensionless numbers.

Answer 1

we have: dp-flu, et, T,S,D). variables are listed SI units of dimensions of above below: Variable unit Dimension (M, L,T). de L U mis LT-1 u kglms MLT-1 r Nim MT-2 P kg lm3 ML-3 D m L m. 3 Let No. of variables = = 6 No. of fundamental units: :. Dimension less t terms 6-3=3. (tiga & X3): US&D be repeating variables. Leti Ti= dp uapboo comparing dimensions on both sides: [MOLOTO] - [L] CLT-] a [M[3] "CL]

comparing powers of M,T&L on both sides: . b=0 (n ) * (T) 1+ a-3b+c=0 (L) 4 :. c=-1 :Tis dp Uºpop! ñia de la Let: Xz=ruaphoc :- [MOLºgº] = [m7-2] Cut-1][me-33% [4] ° bt1=0 =D bio| ocm) 2- a co a = -2 (T) a -3b+CSU + (2) - 2-3(-1) +0:0 :, Tz -Yu-lp-lo ñ 2 - r POUZ 2 2 Let *3=muagboc .. [Morogo] = [menit-1] [LT-1]" [ML-3]b[2]

:. lt bio =P 11 (mm) (1) -1-90 a = -19-3b +=0 an (L) .. -|-|-3(-1) + (su CE-1 3 T 32 PUD From 0, @ +3 T,= f ( Tz, 13) de f ( M PVD D POUR :Tdp = of ( A Mour evo) PUD water instead of fuel we should equation Nowi To use ufa that must be wed dimensionless terms to find for water. ice. (T2) fuel = (( 2 ) water f (*3) fuel = (*3 l water D get UED from here.