HYDRAULICS 1
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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
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
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.