Question:-
Assertion (A): For a fully developed viscous flow through a pipe the velocity distribution across any section is parabolic in shape.
Reason (R): The shear stress distribution from the centre line of pipe upto the pipe surface increases linearly.
Option (A)
Both A and R are individually true and R is the correct explanation of A
Option (B)
Both A and R are true but R is not the correct explanation A
Option(C)
A is true but R is false
Option(D)
A is false but R is true
Correct Option:
(A)
Question Solution:
For laminar flow through a circular pipe (Radius R)
Shear stress distribution p = (-(p/x))r/2 i.e. p a r [linear variation ]
Vel. Distribution
u = 1/4m (-(P/x)R2[1-(r2/R2)]
u = Umax {1-(r2/R2)}
where
Umax = 1/4m{-(P/x)}R2
This velocity distribution is derived from linear stress profile
t = -m(du/dr)= (-(P/x))r/2
Þ 1/2m (P/x)rdr = du
Integrating 1/2m(P/x)(r2/2)+c = u .....(i)
Boundary conditions
At r = R, u = 0 [fixed plate / pipe]
1/2m(P/x)(R2/2)
Putting constant c in equation (1)

Þ u = 1/4m (-(P/x))[R2-r2]
Þ u = 1/4p (-(P/x))R2[1-(r2/R2]
Parabolic distribution of velocity