Analytical approach to estimate supercavity length based on cavity and Reynolds numbers

Cavity length estimation is important as supercavity condition is generated. The cavity length is function of cavity number and is calculated by relations deduced from experimental results which are different from each other and are not driven from analytical approaches. Literature survey shows that correlations based on cavity length in relation with Reynolds and cavity numbers have not been attempted. The present work purpose is to estimate analytical based relations for cavity length with respect to mass transfer, continuity and momentum conservation equations. This effort which has been conducted by order of magnitude method resulted in three relations. The first analytical based relation calculates cavity length versus cavity number. The obtained relation shows that cavity length is proportional with the inverse square root of cavity number. The second analytical relation calculates cavity length in respect to Reynolds number. It shows cavity length has proportional relation to Reynolds square root. The third analytical relation considers cavity number in respect to Reynolds number. The third relation shows that cavity number has inverse relation to Reynolds number. Unknown coefficients values of the relations obtained through comparison with the already existed experimental results. These analytical relations which are appropriate alternative to experimental based relations estimate cavity length in respect to cavity and Reynolds number.