Check the correctness of the equation, When the rate of flow of a liquid having a coefficient of 
viscosity ‘η’ through a capillary tube of length ‘l’ and radius ‘a’ under true pressure head ‘p’ is given by

𝑑𝑉 ÷ 𝑑t = 𝜋𝑝𝑎^4 ÷ 8lη

Asked by hemaborate26 | 13th Jul, 2020, 09:56: PM

Expert Answer:


G i v e n space e q u a t i o n comma space
fraction numerator 𝑑 𝑉 over denominator 𝑑 t space end fraction space equals space fraction numerator 𝜋 𝑝 a to the power of 4 space over denominator 8 l eta end fraction
D i m e n s i o n space f o r m u l a space f o r space L H S space
V space equals open square brackets space L cubed close square brackets space
fraction numerator 1 space over denominator t end fraction equals space open square brackets T to the power of negative 1 end exponent close square brackets
T h u s comma space
D i m e n s i o n space f o r space fraction numerator 𝑑 𝑉 over denominator 𝑑 t space end fraction space equals space open square brackets L cubed T to the power of negative 1 end exponent close square brackets space... left parenthesis 1 right parenthesis
pi space a n d space 8 space a r e space c o n s tan t space
D i m e n s i o n a l space f o r m u l a space f o r space R H S space w i l l space b e comma space
fraction numerator 𝜋 𝑝 a to the power of 4 space over denominator 8 l eta end fraction space equals space fraction numerator open square brackets M L to the power of negative 1 end exponent T to the power of negative 2 end exponent close square brackets open square brackets L to the power of 4 close square brackets over denominator open square brackets M L to the power of negative 1 end exponent T to the power of negative 1 end exponent close square brackets open square brackets L close square brackets end fraction space equals space open square brackets L cubed T to the power of negative 1 end exponent close square brackets... left parenthesis 2 right parenthesis
L H S thin space equals space R H S 
 
Thus, we can say that the equation given is dimensionally correct. 

Answered by Shiwani Sawant | 14th Jul, 2020, 09:29: PM