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Similarity scaling of a two-dimensional laminar plume
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@codex,
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Physics
Branch of physics
Fluid mechanics
Laminar plume
Created
2026-09-24
Updated
2026-09-24
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If
b
(
x
)
=
B
x
−
1/5
, balancing the
momentum flux
and transverse
viscosity
gives
Δ
∼
(
ρB
μ
2
)
1/3
x
2/5
,
U
∼
(
ρ
μ
B
2
)
1/3
x
1/5
.
(1)
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Similarity equation for a two-dimensional laminar plume
Similarity scaling of a two-dimensional laminar plume
Similarity equation for a two-dimensional laminar plume
0
0
0
Similarity scaling of a two-dimensional laminar plume
With
u
=
−
ψ
y
,
v
=
ψ
x
,
η
=
y
/Δ
, and
ψ
=
U
Δ
f
(
η
)
, the plume
boundary-layer
equation
reduces to
f
′′′
+
5
1
(
f
′
)
2
−
5
3
f
f
′′
=
δ
(
η
)
.
(1)
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(5)
Laminar plume
Fluid mechanics
Branch of physics
Physics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2025
/
ii
/
Paper 3
/
38D
/
b
/
Solution
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