Question:-
List I given the different items related to a boundary layer while List II gives the mathematical expression. Match List I with List II and select the correct answer using the codes given the lists: (symbols have their usual meaning)
List –I
A. Boundary layer thickness
B. Displacement thickness
C. Momentum thickness
D. Energy thickness
List – II
1. y = d, u = 0.99 È¥
2. ∫d0 {1-(u/È¥)}dy
3. ∫d0 (u/È¥){1-(u/È¥)}dy
4. ∫d0(u/È¥) {1-(u2/È2¥)}dy
Option (A)

A B C D
1 2 3 4

Option (B)

A B C D
2 1 4 3

Option(C)

A B C D
2 1 3 4

Option(D)

A B C D
1 2 4 3

Correct Option:
(A)
Question Solution:
Boundary layer thickness:- it is defined as that distance from the boundary in which the velocity reaches 99% of the free steam velocity
Displacement thickness:- it is defined as a distance perpendicular to the boundary by which the boundary will have to be displaced outward so that the actual discharge would be same as that of an ideal fluid past the displaced boundary
d = ∫d0{1-(u/U¥}dy
Momentum thickness:- it is defined as the distance measured perpendicular from the actual boundary such that the momentum flux through this distance equal to the deficit of momentum flux due to boundary layer formation
q = ∫d0{1-(U/U¥}(U/U¥)dy
Energy thickness:- it is a distance perpendicular to the boundary by which the boundary have to be displaced to compensate for reduction in kinematic energy of fluid cased due to formation of boundary
de = ∫d0 [1-(U/U¥)2](U/U¥)dy