Question

Given that V=r²p/4hl,where p/l=pressure gradient,h=coefficient of viscosity,obtain an expression for the dimensionless constant in the expression V

Answer 1

All variables have units:

$$\frac{p}{l}=[\frac{\text{Pa}}{\text{m}}],$$ $$r=[\text{m}],$$ $$h=[\text{Pa}\cdot \text{s}],$$ $$v=\frac{r^2p}{4hl}=\frac{[\text{m}^2]\cdot [\text{Pa}]}{4[\text{Pa}\cdot \text{s}]\cdot[\text{m}]}=[\frac{\text{m}}{\text{s}}].$$

For the dimensionless constant we have

$$4=\frac{r^2p}{vhl}.$$