Problem 8.121

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Problem 8.121 [Difficulty: 3]
Given: Data on tube geometry
Find: Plot of reservoir depth as a function of flow rate
Solution:
Basic equations: p1
ρ
α1
V1
2
2
⋅+ g z1⋅+
⎛⎜⎜⎝
⎞
⎠
p2
ρ
α2
V2
2
2
⋅+ g z2⋅+
⎛⎜⎜⎝
⎞
⎠− hlT=
major
hl∑
minor
hlm∑+= (8.29)
Re
ρ V⋅ D⋅
μ
= hl f
L
D
⋅ V
2
2
⋅= (8.34) hlm K
V2
2
⋅= (8.40a) hlm f
Le
D
⋅ V
2
2
⋅= (8.40b)
f
64
Re
= (8.36) (Laminar) 1
f
2.0− log
e
D
3.7
2.51
Re f⋅+
⎛⎜⎜⎝
⎞
⎠⋅=
(8.37) (Turbulent)
The energy equation (Eq. 8.29) becomes g d⋅ α V
2
2
⋅− f L
D
⋅ V
2
2
⋅ K V
2
2
⋅+=
This can be solved expicitly for height d, or solved using Solver
d
V2
2 g⋅ α f
L
D
⋅+ K+⎛⎜⎝
⎞
⎠⋅=
In Excel:
Required Reservoir Head versus Flow Rate
0
25
50
75
0 2 4 6 8 10 12
Q (L/min)
d (m)