Head Loss in Pipe Flow
Major and Minor Losses
ME 322 Lecture Slides, Winter 2007
Gerald Recktenwald∗
January 23, 2007
∗ Associate Professor, Mechanical and Materials Engineering Department Portland State University, Portland, Oregon,
gerry@me.pdx.edu
Head Loss Correlations (1)
Empirical data on viscous losses in straight sections of pipe are correlated by the
dimensionless Darcy friction factor
f ≡
∆p D
1
2
2 ρV L
(1)
For fully-developed laminar flow in a round pipe
flam =
64
ReD
For fully-developed turbulent flow in a round pipe
„
«
1
ε/D
2.51
+
√ = −2 log10
√
3.7
f
Re f
Head Loss in Pipe Flow: January 23, 2007
(2)
page 1
Moody Diagram
Wholly turbulent
f
ε/D
increases
Transition
Laminar
Sm
oo
th
ReD
Head Loss in Pipe Flow: January 23, 2007
page 2
Head Loss in a Horizontal Pipe (1)
Consider fully-developed flow (laminar or turbulent) in a horizontal pipe
1
2
D
Q
L
Apply the steady-flow energy equation
»
p
V2
+
+z
γ
2g
–
»
=
out
p
V2
+
+z
γ
2g
–
+ hs − hL
in
Use zout − zin (horizontal), hs = 0 (no pump), and Vout = Vin (constant cross section),
to simplify as
pin − pout
∆p
hL =
=
(3)
γ
γ
Head Loss in Pipe Flow: January 23, 2007
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Head Loss in a Horizontal Pipe (2)
Use the definition of the Darcy friction factor – Equation (1)
f =
∆p D
1
2
2 ρV L
=⇒
∆p = f
1
2L
ρV
2
D
(4)
Combine Equation (3) and Equation (4) from preceding slide to get
∆p
1 1
V2L
2L
hL =
= f ρV
=f
γ
γ 2
D
2g D
This is the Darcy-Weisbach equation
LV2
hL = f
D 2g
Head Loss in Pipe Flow: January 23, 2007
(5)
page 4
Head Loss in an Inclined Pipe
The Darcy-Weisbach equation gives hL when f is known
LV2
hL = f
D 2g
(5)
This formula was derived for horizontal flow in a pipe, but it applies to flow on an incline.
2
z2
1
z1
L
D
2
V
L
to compute hL
• Use hL = f D
2g
• Substitute hL into Energy equation to
compute ∆p
Q
Head Loss in Pipe Flow: January 23, 2007
page 5
Formulas for Head Loss in a Horizontal Pipe
ReD
flam
64
=
ReD
»
ρV D
=
µ
«
„
1
2.51
ε/D
+
√ = −2 log10
√
3.7
f
Re f
or
V2
p
+
+z
γ
2g
Q
V =
A
–
»
=
out
p
V2
+
+z
γ
2g
–
+ hs − hL
in
LV2
hL = f
D 2g
Head Loss in Pipe Flow: January 23, 2007
page 6
Basic Head Loss Calculation
Given L, D , Q (or V )
1. Look up fluid properties ρ, µ
2. Compute ReD to determine whether the flow is laminar or turbulent
3. If turbulent, look up ε for the pipe material
4. Use the Colebrook equation or the Moody chart to find f
5. Use the Darcy-Weisbach equation to compute hL
6. Use the steady-flow energy equation to find other terms, e.g. pressure drop
Head Loss in Pipe Flow: January 23, 2007
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