ENGG 2230 Lecture Notes - Lecture 11: Buckingham Π Theorem

• School: University of Guelph
• Department: Engineering
• Course: ENGG 2230
• Professor: Bill Van Heyst

Document Summary

A process can be reduced to (cid:858)k(cid:859) di(cid:373)e(cid:374)sio(cid:374)less varia(cid:271)les or pi groups if the pro(cid:272)ess is di(cid:373)e(cid:374)sio(cid:374)ally ho(cid:373)oge(cid:374)eous a(cid:374)d it has (cid:858)(cid:374)(cid:859) di(cid:373)e(cid:374)sio(cid:374)al varia(cid:271)les. List the dimensions of each variable: the total (cid:374)u(cid:373)(cid:271)er of differe(cid:374)t di(cid:373)e(cid:374)sio(cid:374)s is (cid:858)j(cid:859) Fi(cid:374)d (cid:858)k(cid:859) usi(cid:374)g k = (cid:374) j: k is the number of pi groups. Choose (cid:858)j(cid:859) para(cid:373)eters that do(cid:374)(cid:859)t for(cid:373) a pi group (repeati(cid:374)g variables) Add an additional variable to each repeating variable in order to form a power product which can be solved. Write the final equation which is dimensionless: there are 3 different dimensions (m, l and t) therefore j=3. Example: k = n j = 1 pi group, there are 4 variables therefore n=4. T=f(cid:4666)(cid:3020) , ,(cid:4667) (cid:858)t(cid:859) is i(cid:374) [t] , (cid:3020) is in [l2] , m is in [m] , is in (cid:3014)(cid:3013)2(cid:3021)2: (cid:2869)=(cid:3028) (cid:3020)(cid:3029) (cid:3030) (cid:3031, [](cid:3028)[(cid:1838)(cid:2870)](cid:3029)[ (cid:3014)(cid:3013)2(cid:3021)2](cid:3030)[(cid:1839)](cid:3031)=[](cid:2868)[(cid:1839)](cid:2868)[(cid:1838)](cid:2868, (cid:2869)= (cid:3014, t: a 2c = 0. L: 2b 2c = 0: m: c + d = 0.