using dimensional analysis, the accuracy of relation 𝒗 = 𝒌𝒏 𝒓𝒅 , v is Velocity, k is constant, n is coefficient of viscosity [ML-1 T -1 ] , r is radius and d is density.

Asked by poo.pathak.orra | 6th May, 2020, 04:55: PM

Expert Answer:

v = kηrd .... (*)
 
L.H.S = v 
 
v space minus space space v e l o c i t y space
space D i m e n s i o n space o f space v e l o c i t y space equals space open square brackets L to the power of 1 T to the power of negative 1 end exponent close square brackets space space... space left parenthesis 1 right parenthesis space

R. H. S space equals space k eta r d space
k space minus space c o n s tan t space
eta space minus space c o e f f i c i e n t space o f space v i s c o c i t y space
r space minus space r a d i u s space
d space minus space d e n s i t y space

D i m e n s i o n s space o f space eta space equals space open square brackets M to the power of 1 L to the power of negative 1 end exponent T to the power of negative 1 end exponent close square brackets
D i m e n s i o n s space o f space r space equals space open square brackets L to the power of 1 close square brackets space
D i m e n s i o n s space o f space d space equals space open square brackets M to the power of 1 L to the power of negative 3 end exponent close square brackets space

T h u s comma space
D i m e n s i o n s space o f space R. H. S space equals space open square brackets M to the power of 1 L to the power of negative 1 end exponent T to the power of negative 1 end exponent close square brackets space space open square brackets L to the power of 1 close square brackets space open square brackets M to the power of 1 L to the power of negative 3 end exponent close square brackets space equals space open square brackets M squared space L to the power of negative 3 end exponent T to the power of negative 1 end exponent close square brackets space... space left parenthesis 2 right parenthesis

F r o m space e q u a t i o n space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis space

L. H. S space not equal to space R. H. S space

H e n c e comma space b y space t h i s space d i m e n s i o n a l space a n a l y s i s space i t space i s space p r o v e d space t h a t space space t h e space e q u a t i o n space left parenthesis asterisk times right parenthesis space i s space n o t space a c c u r a t e space

Answered by Shiwani Sawant | 6th May, 2020, 06:20: PM