Correct Answer - Option 4 :
\(\frac{{16\mu {u_0}L}}{{{D^2}}}\)
Explanation:
Pressure drop across a length L of pipe is:
\({\rm{\Delta }}p = \frac{{32\mu\ {u_{av}}L}}{{{D^2}}}\) ......(i)
where uavg = average velocity.
Given velocity profile is
\(u = {u_0}\left( {1 - \frac{{4{r^2}}}{{{D^2}}}} \right)\)
For parabolic velocity profile, maximum velocity occurs at r = 0 i.e. umax = u0.
Relation between average and maximum velocity is
\({u_{av}} = \frac{{{u_0}}}{2}\) ......(ii)
From equation (i) and (ii):
\({\rm{\Delta }}P = \frac{{16\mu {\mu _0}L}}{{{D^2}}}\)