Hydraulics Lesson 2

7/30/2019 Hydraulics Lesson 2

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g.Dep.-Hydraulic

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s

g.Dep.-H

ydraulic

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g.Dep.-Hydraulic

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s

g.Dep.-H

ydraulic

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g.Dep.-Hydraulic

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s

g.Dep.-H

ydraulic

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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

s

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.

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observable pattern and no definite layers.

s

Laminar and Turbulent Flow

g.Dep.-H

ydraulic

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REYNOLDS Reynoldsapparatus

g.Dep.-Hydraulic

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s

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

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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 .

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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

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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:

-

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.

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s

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 :

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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?

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EntranceRegionandFully

DevelopedFlow

g.Dep.-Hydraulic

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s

FrictionHeadLossinCircularConduits

g.Dep.-H

ydraulic

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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

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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

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VgD

LV

D

Lhf 22 3232

s

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.

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EXAMPLE5:LaminarFlowExamples

g.Dep.-Hydraulic

distance from the pipe entrance to the first

point at which the flow is established?

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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,

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(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

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(a) horizontal

(b)inclined 15 upward

(c) inclined 15 downward

also verify that flow through the pipe is laminar?

Hydraulics Lesson 2

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