Page 113 - Aeronautical Engineer Data Book
P. 113
Basic fluid mechanics 89
where:
µ = velocity parallel to the surface
y = perpendicular distance from the surface
= boundary layer thickness
= mainstream velocity
U 1
� 1
u = velocity parameters u/U (non-dimensional)
�
y = distance parameter y/ (non-dimensional)
Boundary layer equations of turbulent flow:
�
∂u ∂u �
∂p ∂
�
�
�
�
u + = – +
∂y
∂x
∂x
∂y
∂u
�
�
�
�
= µ – u��v' �
'
∂y
∂p
�
= 0
∂y
∂u ∂ �
�
+ = 0
∂x ∂y
5.5 Isentropic flow
For flow in a smooth pipe with no abrupt
changes of section:
d du dA
continuity equation = 0+ +
u A
equation of momentum
conservation –dpA = (A u)du
isentropic relationship p = c k
dp
2
sonic velocity a =
d
These lead to an equation being derived on the
basis of mass continuity:
dp du
i.e. = – M 2
u
or
d �
du
2
M =
d u
