question_answer

The rate of flow (V) of a liquid through a pipe of radius (r) under a pressure gradient (P/l) is given by where is coefficient of viscosity of the liquid. Check whether the formula is correct or not

Answer:

                V = volume/sec = \[\left[ {{\text{L}}^{\text{3}}}{{\text{T}}^{\text{-1}}} \right]\] \[\frac{P}{l}=pressure\,gradient=\frac{M{{L}^{-1}}{{T}^{-2}}}{L}=\left[ M{{L}^{-2}}{{T}^{-2}} \right]\] Now L.H.S. = \[V=\left[ {{L}^{3}}{{T}^{-1}} \right]\] R.H.S. = \[\frac{\pi }{8}\times \frac{P}{l}.\frac{{{r}^{4}}}{\eta }=\frac{\left( M{{L}^{-2}}{{T}^{-2}} \right){{L}^{4}}}{\left( M{{L}^{-1}}{{T}^{-1}} \right)}=\left[ {{L}^{3}}{{T}^{-1}} \right]\] As L.H.S. = R.H.S., dimensionally, therefore the formula is correct.