
179The Aerodynamics of Solid-Particle Jets
© 2010 Taylor & Francis Group, LLC
l
n
l
dx
n
=
∫
υπsi
(4.288)
The latter equation determines the factors for decomposing the owing material
velocity into a sine Fourier series. In particular, in the case of a linearly accelerated
ow with an initial velocity of υ
0
, it holds that
l
nk
k
=⋅
υξ
υ
,,
0
0
2
2 (4.289)
υ
υ
υυ
π
υυ
z
k
k
,
/
sin
/
0
2
2
0
4
=
−
−
− υυυ
2
2
1
/
zdz
∫
(4.290)
Tables 4.6 and 4.7 list values of the function
υ
n
0
determined numerically.
One should keep in mind that Fourier series used by us (Equation 4.286) have a
peculiar feature where the manifestation is ...