Geoscience Reference
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C
D
A
B
Q in
A downstream-narrowing channel
with constant discharge ( Q )
The field situation depicted involves absolutely steady discharge, so that
at each section AB and CD there is no variation of discharge or velocity
with time … but there is a change in space
In symbols
d u /d t = 0
C
D
s
Water
surface
A
B
Bed of channel
Discharge in, Q in , equals discharge out, Q out . Area of cross-section AB >> area of
cross-section CD. By continuity: mean flow velocity u AB << mean flow velocity u CD .
Therefore a spatial acceleration takes place over distance, s, between cross-sections AB and CD.
Magnitude of the spatial acceleration is u AB ( u CD - u AB )/s
In differential form, u d u /d s
The full expression for acceleration is written below. It looks rather complicated, but is not. The numbered terms
are discussed in the text.
D
u
u
u
u
u
u
+
u
+
w
+
v
+
u
u
D t
t
x
z
y
t
term
1
2
3
4
Fig. 3.6 Spatial or advective acceleration and the full expression for total acceleration that includes the unsteady term. The Scale dog is Alaska,
1m long.
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