<Tr> <Td> d v d r = 0 at r = 0 (\ displaystyle (\ frac (dv) (dr)) = 0 \ quad (\ mbox (at)) r = 0) </Td> <Td>--axial symmetry . </Td> </Tr> <P> Axial symmetry means that the velocity v (r) is maximum at the center of the tube, therefore the first derivative dv / dr is zero at r = 0 . </P> <P> The differential equation can be integrated to: </P> <Dl> <Dd> v (r) = − 1 4 μ r 2 Δ P Δ x + A ln ⁡ (r) + B . (\ displaystyle v (r) = - (\ frac (1) (4 \ mu)) r ^ (2) (\ frac (\ Delta P) (\ Delta x)) + A \ ln (r) + B .) </Dd> </Dl>

Show that for poiseuille flow in a tube of radius r