HYDRAULICS 1HYDRAULICS 1HYDRAULICS 1HYDRAULICS 1

HYDRAULICS 1HYDRAULICS 1HYDRAULICS 1HYDRAULICS 1

F L UID PRE S S UREPRE S S URE M E A S URE M E NT S

HYD RO S T A T IC F O RC E S on PL A NE ST HRUS T C URV E D S URF A C E

S T A BIL IT Y O F F L O A T ING BO D IE S

FLUID STATICS

F L O W S IN PIPE L INE SL A M INA R F L O W

T URBUL E NT F L O WPIPE S YS T E M S

O PE N C HA NNE L F L O WUNIF O RM F L O W

E NE RG YE Q UA T IO NHYD RA UL IC JUM P

C O NT INUIT Y E Q UA T IO NBE RNO UL L IS ´ E Q UA T IO NM O M E NT UM E Q UA T IO N

E NE RG Y E Q UA T IO N

F L UID A C C E L E RA T IO NF L O W PA T T E RN

F L O W RA T E

D IMEN SIO N AL AN ALYSIS

FLUID DYNAMICS

FLUID PROPERTIES

HYDRAULICS 1

HYDRAULICS 1HYDRAULICS 1HYDRAULICS 1HYDRAULICS 1

DEFINITION OF PRESSURE

DEFINITION OF PRESSURE

PRESSURE; P= lim F/A A 0

FORCE; F (N)AREA; A (m2)

P=F/A (N/m2) = (Pascal)

1 bar = 105 N/m2 = 1 atmosphere

A

F

A

F

DEFINITION OF DEFINITION OF PRESSURE PRESSURE

DEFINITION OF DEFINITION OF PRESSURE PRESSURE

P1

P2

P3

Q

W

B

A C x

y

P1 , P2 , P3 = average-pressure on the surfaces AB,AC, BC.

=arbitrary angle

W =weight of the body ABC.

LENGTH OF BODY = 1m

PRESSURE VARIATIONPRESSURE VARIATION PRESSURE VARIATIONPRESSURE VARIATION

z (m)

Patm.A

(kN)

P.A (kN)

z.A. (kN)

Patm =Atmospheric pressure(kPa)Pabs = Absolute pressure (kPa)

Pabs=.z + Patm

PRESSURE VARIATIONPRESSURE VARIATION

l

p . A

(p+p) . A

A . l . z

lz

ABSOLUTE-, GAGE PRESSURE

ABSOLUTE-, GAGE PRESSURE

GAGE PRESSURE : Pgage

ABSOLUTE PRESSURE Pabs

ATMOSPHERIC PRESSURE Patm

Pgage= Pabs-Patm

Pgage=z Pabs=z+Patm

z

ABSOLUTE- ,GAGE PRESSURE

ABSOLUTE- ,GAGE PRESSURE

Vacuum: 0 N/m2 (Pa)Atmospheric pressure (Patm): 1.013 . 105 N/m2

(Pa)Gage pressure (Pgage): Pressure reading at gageAbsolute Pressure (Pabs): Pabs=Patm+Pgage

Patm=101 kPa

Ex Pabs=151 kPa Pabs=51 kPa

Pabs=151

Pgage=50 kPa

Pabs =51 kPa

Pgage= -50 kPa

Pabs=0

Pgage=0Patm=gage reference

Pabs=0

PIEZOMETRIC HEADPIEZOMETRIC HEADPressure head h=P/ (m) h

Piezometric headThe sum of the elevation abovean arbitrary datum plus thepressure head.H= h + z = P/ + z

h

P

z z

P

PROPERTY OF PROPERTY OF PRESSUREPRESSURE

PROPERTY OF PROPERTY OF PRESSUREPRESSURE

z (m)

Pressure the same inall directions P=gz

Pressure always perpendicular to a surface.

A B

Pressure the same at A and B.

ExampleExample

5.5 m

What is the water pressure at the bottom under the peer?

3.5 m