question_answer 68)

                  The volume of a liquid flowing out per second of a pipe of length \[l\] and radious \[r\] is written by a student as  \[V=\frac{\pi }{8}\frac{{{\Pr }^{4}}}{\eta l}\]                 Where P is the pressure difference between the two ends of the pipe and n is coefficient of viscosity of the liquid having dimensional formula \[M{{L}^{-1}}{{T}^{-1}}\].                 Check whether the equation is dimensionally correct.                

Answer:

                  \[\text{L}\text{.H}\text{.S}\text{.V =}\frac{\text{Volume}}{\text{time}}=[{{L}^{3}}{{T}^{-1}}]\]                 \[\text{R}\text{.H}\text{.S}\text{.}=\frac{\pi {{\Pr }^{4}}}{8nl}=\frac{M{{L}^{-1}}{{T}^{-2}}\times {{L}^{4}}}{M{{L}^{-1}}{{T}^{-1}}\times L}\]                 \[=[{{L}^{3}}{{T}^{-1}}]\]                 \ equation is dimensionally correct.