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.
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