hydraulics lesson 2
TRANSCRIPT
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g.Dep.-Hydraulic
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g.Dep.-H
ydraulic
EnvironmentalE
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g.Dep.-Hydraulic
EnvironmentalE
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g.Dep.-H
ydraulic
EnvironmentalE
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g.Dep.-Hydraulic
EnvironmentalE
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g.Dep.-H
ydraulic
EnvironmentalE
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s Flow Regimes
Laminar and Turbulent Flow
g.Dep.-Hydraulic
Laminar Flow
Turbulent Flow
The amount of fluid friction, whichdetermines the amount of energy required
EnvironmentalE o ma n a n e es re ow, epen s
upon the mode of flow
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Laminar Flow
Laminar flow is also referred to as streamline
g.Dep.-H
ydraulic or v scous ow.
layers of water flowing over one another at
different speeds with virtually no mixingbetween layers
fluid particles move in definite and observable
EnvironmentalE paths or streamlines, and
the flow is characteristic of viscous (thick) fluid.
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Turbulent flow is characterized by the irregularmovement of articles of the fluid.
Turbulent Flow
g.Dep.-Hydraulic
There is no definite frequency as there isin wave motion.
EnvironmentalE
observable pattern and no definite layers.
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Laminar and Turbulent Flow
g.Dep.-H
ydraulic
EnvironmentalE
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REYNOLDS Reynoldsapparatus
g.Dep.-Hydraulic
EnvironmentalE
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Reynolds Number
The Reynolds Number is important in analyzing
g.Dep.-H
ydraulic
gradient - shear force.
The Reynolds Number indicates the relativesignificance of the viscous effect compared to theinertia effect.
The Reynolds number is defined as the ratio of the
EnvironmentalE inertial force and the viscous force.
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REYNOLDS Reynolds Number can be expressed as:
g.Dep.-Hydraulic
velocityV
lengthcticcharacteriL
R
:
:
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ityviskinematic
ityvisobsoluteorityvisdynamic
cos:
coscos:
s
Kinematic Viscosity is the ratio of absolute ordynamic viscosity to the density, a quantity in which
Kinematic Viscosity
g.Dep.-H
ydraulic no orce s nvo ve .
EnvironmentalE
For the SI system the theoretical unit is m2/s orcommon used Stoke (St)St = 10-4 m2/s.
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The flow is:
g.Dep.-Hydraulic
laminar if Re < 2300transient if 2300 < Re < 4000turbulent if Re > 4000
EnvironmentalE
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EXAMPLE1:-
LaminarFlowExamples
g.Dep.-H
ydraulic
Isthe flow Laminar or Turbulent?
n o w = . m s ows n a
10 cm diameter pipe at 0.5 L/s
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LaminarFlowExamplesEXAMPLE2:
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g.Dep.-Hydraulic
Below what velocity will the flow belaminar?
w a nema c v scos y o . x m s
is flowing through a 0.00762 m diameter pipe.
EnvironmentalE
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Rh = A/P
Hydraulic Radius
g.Dep.-H
ydraulic h = y rau c ra us
A = the cross sectional data
P = wetted perimeter
Forfull pipe flow with a circular conduit :
EnvironmentalE Rh = D/4
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s In dealing with a non-circular
Hydraulic Diameter
g.Dep.-Hydraulic con u
Dh = Hydraulic Diameter = 4Rh For example, when using Reynolds
number to evaluate the flow in a
non-circular conduit, we have to
substitute 4Rh for D.
EnvironmentalE This is known as equivalent
diameter.
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EXAMPLE3:LaminarFlowExamples
g.Dep.-H
ydraulic
the hydraulic radius of a 300 mm diameter
pipe and 300 mm square-duct?
EnvironmentalE
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EntranceRegionandFully
DevelopedFlow
g.Dep.-Hydraulic
EnvironmentalE
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FrictionHeadLossinCircularConduits
g.Dep.-H
ydraulic
EnvironmentalE
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FrictionHeadLossinCircularConduits
g.Dep.-Hydraulic
2f
EnvironmentalE roug e mens ona ana ys s
Friction head loss
0 8
2
2L
L vh f
D g
s
FrictionLossinNoncircularConduits
g.Dep.-H
ydraulic
g
V
R
Lf
g
V
D
Lfh
h
f
242
22
EnvironmentalE
VRVRR hh
)4()4(
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EfforttoLinkingfandR
g.Dep.-Hydraulic
HazonPoiseuillelaw
g
V
R
Lf
g
V
D
Lfh
h
f242
22
)2300(64
RR
f
EnvironmentalE
VgD
LV
D
Lhf 22 3232
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EXAMPLE4:2
LaminarFlowExamples
g.Dep.-H
ydraulic . .
in a 100 mm diameter pipe at a rate of 0.64
L/s. Find (a) the head loss per unit length (b)the shear stress at the pipe wall.
EnvironmentalE
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EXAMPLE5:LaminarFlowExamples
g.Dep.-Hydraulic
distance from the pipe entrance to the first
point at which the flow is established?
EnvironmentalE
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EXAMPLE6:Water at 4C(=1000kg/m3 and
LaminarFlowExamples
g.Dep.-H
ydraulic
=0.001545kg/ms) is flowing through a 0.305
cm diameter 9.14 m long horizontal pipe
steadily at an average velocity of 0.914 m/s.
Determine,
EnvironmentalE
(b)The pressure drop
(c) The pumping power requirement to
overcome this pressure drop.
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EXAMPLE7:Oil at 20(=888kg/m3 and =0.800kg/ms) is
LaminarFlowExamples
g.Dep.-Hydraulic
flowing steadily through a 5 cm diameter 40 m
long pipe. The pressure at the pipe inlet and outlet
are measured to be 745 and 97 kPa, respectively.
Determine the flow rate of oil through the pipe
EnvironmentalE
(a) horizontal
(b)inclined 15 upward
(c) inclined 15 downward
also verify that flow through the pipe is laminar?