Page 100 - Aeronautical Engineer Data Book

Basic fluid mechanics 79
The stream tube for conservation of mass
2
1 s p 2
p 1
v
v 1 2
A 1 A 2
The stream tube and element for the momentum equation
z
δs
p p dp δs
ds
α
s
W
The forces on the element

δs
F dp
(p+ δs) (A+δA)
ds

pA dp δs
α (p+ )
ds 2
W
Control volume for the energy equation
2
1 s
q
v 2 p 2
v 1 p 1 T 2 p 2
α
T 1 p 1
q
z 1 z 2

Fig. 5.2 Stream tube/fluid elements: 1-D flow

(3D) depending on the way that the flow is
constrained.

5.2.1 1D Flow
1-D flow has a single direction co-ordinate x and
a velocity in that direction of u. Flow in a pipe
or tube is generally considered one dimensional.