Physics

In the relation $$V=\dfrac { \pi  }{ 8 } \dfrac { { Pr }^{ 4 } }{ tl } $$, $$P$$ is pressure, $$r$$ is the radius, $$t$$ is time and $$l$$ is length. The dimensions of $$V$$ are:


ANSWER

$${ M }^{ 1 }{ L }^{ 2 }{ T }^{-3}$$


SOLUTION
$$\pi$$ is dimensionless, thus $$|V| = \dfrac{|P||r^4|}{|t||l|}$$
Now, $$Pressure = \dfrac{Force}{Area}$$, thus its dimensions are $$\dfrac{MLT^{-2}}{L^2}=ML^{-1}T^{-2}$$
Thus, $$|V|=\dfrac{ML^{-1}T^{-2}L^4}{TL} = ML^2T^{-3}$$
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