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• 1. Hydraulics
By: Engr. Yuri G. Melliza
• 2. FLUID MECHANICS
Properties of Fluids
1. Density ()
2.Specific Volume ()
3.Specific Weight ()
• 3. 4. Specific Gravity or Relative Density
For Liquids: Its specific gravity (relative density) is equal to the ratio of its density to that of water at standard temperature and pressure.
For Gases:Its specific gravity (relative density) is equal to the ratio of its density to that of either air or hydrogen at some specified temperature and pressure.
where: At standard condition
W = 1000 kg/m3
W = 9.81 KN/m3
• 4. 5. Temperature
6. Pressure
If a force dF acts on an infinitesimal area dA, the intensity of pressure is,
where: F - normal force, KN
A - area, m2
• 5. PASCAL’S LAW: At any point in a homogeneous fluid at rest the pressures are
the same in all directions.
y
P3 A3
A
P1 A1
x

B
C
z
P2 A2
Eq. 3 to Eq. 1
P1 = P3
Eq. 4 to Eq. 2
P2 = P3
Therefore:
P1 = P2 = P3
Fx = 0 and Fy = 0
P1A1 – P3A3 sin  = 0  1
P2A2 – P3A3cos = 0  2
From Figure:
A1 = A3sin   3
A2 = A3cos   4
• 6. Atmospheric pressure:The pressure exerted by the atmosphere.
At sea level condition:
Pa = 101.325 KPa
= .101325 Mpa
= 1.01325Bar
= 760 mm Hg
= 10.33 m H2O
= 1.133 kg/cm2
= 14.7 psi
= 29.921 in Hg
= 33.878 ft H2O
Absolute and Gage Pressure
Absolute Pressure:is the pressure measured referred to absolute zero and using absolute zero as the base.
Gage Pressure:is the pressure measured referred to atmospheric pressure, and using atmospheric pressure as the base
• 7. Pgage
Atmospheric pressure
Pvacuum
Pabs
Pabs
Absolute Zero
Pabs = Pa+ Pgage
Pabs = Pa - Pvacuum
• 8. 7. Viscosity: A property that determines the amount of its resistance to
shearing stress.
moving plate
v
v+dv
dx
x
v
Fixed plate
S dv/dx
S = (dv/dx)
S = (v/x)
 = S/(v/x)
where:
 - absolute or dynamic viscosity
in Pa-sec
S - shearing stress in Pascal
v - velocity in m/sec
x -distance in meters
• 9. 8. Kinematic Viscosity: It is the ratio of the absolute or dynamic viscosity to
mass density.
 = / m2/sec
9. Elasticity: If the pressure is applied to a fluid, it contracts,ifthe pressure is
released it expands, the elasticity of a fluid is related to the amount of deformat-
ion (contraction or expansion) for a given pressure change. Quantitatively, the
degree of elasticity is equal to;
Ev = - dP/(dV/V)
Where negative sign is used because dV/V is negative for a positive dP.
Ev = dP/(d/)
because -dV/V = d/
where:
Ev - bulk modulus of elasticity, KPa
dV - is the incremental volume change
V - is the original volume
dP - is the incremental pressure change
• 10.

r
h
10. Surface Tension: Capillarity
Where:
 - surface tension, N/m
 - specific weight of liquid, N/m3
h – capillary rise, m
Surface Tension of Water
• 11. FREE SURFACE
h1
1•
h2
h
2•
Variation of Pressure with Elevation
dP = - dh
Note:Negative sign is used because pressure decreases as elevation increases and pressure
increases as elevation decreases.
where:
p - pressure in KPa
 - specific weight of a fluid, KN/m3
h - pressure head in meters of fluid
MANOMETERS
Manometer is an instrument used in measuring gage pressure in length of some liquid
column.
• Open Type Manometer : It has an atmospheric surface and is capable in measuring
gage pressure.
• Differential Type Manometer : It has no atmospheric surface and is capable in
measuring differences of pressure.
• 13. Fluid A
Fluid A
Open
Fluid B
Manometer Fluid
Manometer Fluid
Open Type Manometer
Differential Type Manometer
• 14. Open
Open
Fluid A
x
y
Fluid B
Determination of S using a U - Tube
SAx = SBy
• 15. S
S
S
Free Surface

M
M
hp
F
•C.G.
•C.G.
•C.P.
•C.P.
yp
e
N
N
Forces Acting on Plane Surfaces
F - total hydrostatic force exerted by the fluid on any plane surface MN
C.G. - center of gravity
C.P. - center of pressure
• 16. where:
Ig- moment of inertia of any plane surface MN with respect to the axis at its centroids
Ss - statical moment of inertia of any plane surface MN with respect to the axis SS not
lying on its plane
e - perpendicular distance between CG and CP
• 17. Forces Acting on Curved Surfaces
FV
Free Surface
D
E
Vertical Projection of AB
F
C’
L
C
C
A
C.G.
Fh
C.P.
B
B
B’
• 18. A = BC x L
A - area of the vertical projection of AB, m2
L - length of AB perpendicular to the screen, m
V = AABCDEA x L, m3
• 19. D
h
1 m
D
P = h
T
T
F
F
1 m
T
t
T
Hoop Tension
F = 0
2T = F
T = F/2  1
S = T/A
A = 1t  2
• 20. S = F/2(1t)  3
From figure, on the vertical projection the pressure P;
P = F/A
A = 1D
F = P(1D)  4
substituting eq, 4 to eq. 3
S = P(1D)/2(1t)
where:
S - Bursting Stress KPa
P - pressure, KPa
D -inside diameter, m
t - thickness, m
• 21. Laws of BuoyancyAny body partly or wholly submerged in a liquid is subjected to a buoyant or upward force which is equal to the weight of the liquid displaced.
1.
W
where:
W - weight of body, kg, KN
BF - buoyant force, kg, KN
 - specific weight, KN/m3
 - density, kg/m3
V - volume, m3
Subscript:
B - refers to the body
L - refers to the liquid
s - submerged portion
Vs
BF
W = BF
W = BVB
BF = LVs
W = BF
W = BVB KN
BF = LVs KN
• 22. 2.
BF
T
Vs
W
where:
W - weight of body, kg, KN
BF - buoyant force, kg, KN
T - external force T, kg, KN
 - specific weight, KN/m3
 - density, kg/m3
V - volume, m3
Subscript:
B - refers to the body
L - refers to the liquid
s - submerged portion
W = BF - T
W = BVB KN
BF = LVs KN
W = BF - T
W = BVB
BF = LVs
• 23. T
W
BF
Vs
3.
where:
W - weight of body, kg, KN
BF - buoyant force, kg, KN
T - external force T, kg, KN
 - specific weight, KN/m3
 - density, kg/m3
V - volume, m3
Subscript:
B - refers to the body
L - refers to the liquid
s - submerged portion
W = BF + T
W = BVB g
BF = LVs g
W = BF + T
W = BVB g
BF = LVs g
• 24. W
T
Vs
BF
4.
VB = Vs
W = BF + T
W = BVB g
BF = LVs g
W = BF + T
W = BVB
BF = LVs
• 25. W
Vs
BF
T
5.
VB = Vs
W = BF - T
W = BVB g
BF = LVs g
W = BF - T
W = BVB
BF = LVs
Bernoullis Energy equation:
2
HL = U - Q
Z2
1
z1
Reference Datum (Datum Line)
• 27. 1. Without Energy head added or given up by the fluid (No work done by
the system or on the system:
2. With Energy head added to the Fluid: (Work done on the system)
3. With Energy head added given up by the Fluid: (Work done by the system)
Where:
P – pressure, KPa - specific weight, KN/m3
v – velocity in m/sec g – gravitational acceleration
Z – elevation, meters m/sec2
+ if above datum H – head loss, meters
- if below datum
• 28. APPLICATION OF THE BERNOULLI&apos;S ENERGY THEOREM
Nozzle
Base
Tip
Q
Jet
where: Cv - velocity coefficient
• 29. Venturi Meter
inlet
1
throat
exit
2
Meter Coefficient
Manometer
• 30. Orifice: An orifice is an any opening with a closed perimeter
and from figure: Z1 - Z2 = h, therefore
1
a
h
Vena Contracta
By applying Bernoulli&apos;s Energy theorem:
Let v2 = vt
2
a
where:
vt - theoretical velocity, m/sec
h - head producing the flow, meters
g - gravitational acceleration, m/sec2
But P1 = P2 = Pa and v1is negligible, then
• 31. COEFFICIENT OF DISCHARGE(Cd)
COEFFICIENT OF VELOCITY (Cv)
COEFFICIENT OF CONTRACTION (Cc)
where:
v&apos; - actual velocity
vt - theoretical velocity
a - area of jet at vena contracta
A - area of orifice
Q&apos; - actual flow
Q - theoretical flow
Cv - coefficient of velocity
Cc - coefficient of contraction
Cd - coefficient of discharge
• 32. Jet Trajctory
2
d
v sin
v

1
3
v cos
R = v cos (2t)
If the jet is flowing from a vertical orifice and the jet is initially horizontal where
vx = v.
v = vx
y
x
• 33. Upper
Reservoir
Suction Gauge
Discharge Gauge
Lower
Reservoir
Gate Valve
Gate
Valve
PUMPS: It is a steady-state, steady-flow machine in which mechanical work is added to the fluid in order
to transport the liquid from one point to another point of higher pressure.
• 34. 1. TOTAL DYNAMIC HEAD
4. BRAKE or SHAFT POWER
FUNDAMENTAL EQUATIONS
2. DISCHARGE or CAPACITY
3. WATER POWER or FLUID POWER
WP = QHtKW
• 35. 5. PUMP EFFICIENCY
6. MOTOR EFFICIENCY
7. COMBINED PUMP-MOTOR EFFICIENCY
• 36. 8. MOTOR POWER
• For Single Phase Motor
• 37. For 3 Phase Motor
where: P - pressure in KPa T - brake torque, N-m
v - velocity, m/sec N - no. of RPM
 - specific weight of liquid, KN/m3 WP - fluid power, KW
Z - elevation, meters BP - brake power, KW
g - gravitational acceleration, m/sec2 MP - power input to
HL - total head loss, meters motor, KW
E - energy, Volts
I - current, amperes
(cos) - power factor
• 38. Penstock
turbine
Tailrace
HYDRO ELECTRIC POWER PLANT
A. Impulse Type turbine (Pelton Type)
1
2
• 39. 1
Generator
Penstock
B
ZB
Draft Tube
2
B – turbine inlet
Tailrace
B. Reaction Type turbine (Francis Type)
• 40. Fundamental Equations
Where:
PB – Pressure at turbine inlet, KPa
vB – velocity at inlet, m/sec
ZB – turbine setting, m
 - specific weight of water, KN/m3
Impulse Type
h = Y – HL
Y = Z1 – Z2
Where:
Z1 – head water elevation, m
Z2 – tail water elevation, m
B. Reaction Type
h = Y – HL
Y = Z1 –Z2
• 41. 2. Water Power (Fluid Power)
FP = Qh KW
Where:
Q – discharge, m3/sec
3. Brake or Shaft Power
Where:
T – Brake torque, N-m
N – number of RPM
Where:
eh – hydraulic efficiency
ev – volumetric efficiency
em – mechanical efficiency
4. Turbine Efficiency
• 42. 5. Generator Efficency
6. Generator Speed
Where:
N – speed, RPM
f – frequency in cps or Hertz
n – no. of generator poles (usually divisible by four)
• 43. Turbine-Pump
Pump-Storage Hydroelectric power plant: During power generation the turbine-pump acts as a turbine and
during off-peak period it acts as a pump, pumping water from the lower pool (tailrace) back to the upper