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Fluid fundamentals
The document discusses fundamental concepts in fluid mechanics, including properties of fluids such as density, viscosity, and pressure types. It covers instruments like manometers for pressure measurement, flow types, Bernoulli's equation, and energy considerations in fluid systems. Additionally, it explores the functioning of pumps and turbines in hydroelectric power plants.
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Fundamentals of fluid mechanics introduce basic concepts.
Density, specific volume, specific weight, and specific gravity are discussed along with formulas.
Atmospheric pressure and its impact, along with absolute and gauge pressure definitions.
Viscosity as a resistance factor in fluids and surface tension properties, including water tension data.
Manometers' types (open and differential) are explained, along with pressure measurement concepts.
Bernoulli's energy equation relates pressure, elevation, and fluid speed in steady flow scenarios.
Venturi meter and orifice flow measurement principles, including coefficients of velocity and discharge.
Pumps' functions in fluid transport and power generation in hydroelectric systems are discussed.
Reaction-type (Francis type) turbine operations and dual uses in pump-storage systems.
Conclusion slide for the presentation, marking the end of the discussion.
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Fluid fundamentals
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- 2. FLUID MECHANICSFLUID MECHANICS 1.Density (1. Density (ρρ)) 3 m kg V m =ρ 2.Specific Volume (υ) kg m m V = 3 υ 3.Specific Weight3.Specific Weight ((γγ)) 3 m KN 1000 g 1000V mg V W = ρ ==γ Properties of FluidsProperties of Fluids
- 3. Specific Gravity orRelative DensitySpecific Gravity or Relative Density For Liquids: Its specific gravityIts specific gravity (relative density) is equal to(relative density) is equal to the ratio of its density to thatthe ratio of its density to that of water at standardof water at standard temperature and pressure.temperature and pressure. W = γ γL W L L ρ ρ =S ah G γ γ = ah G G ρ ρ =S Where, At standard condition ρW = 1000 kg/m3 γW = 9.81 KN/m3
- 4. Atmospheric pressure:Atmospheric pressure: Thepressure 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: the pressure measured referred to absolute zero and using absolute zero as the base. Gage Pressure: the pressure measured referred to atmospheric pressure, and using atmospheric pressure as the base
- 5. Atmospheric PressureAtmospheric Pressure •Atmospheric pressure is normally about 100,000 Pa • Differences in atmospheric pressure cause winds to blow • Low atmospheric pressure inside a hurricane’s eye contributes to the severe winds and the development of the storm surge
- 6. Viscosity:Viscosity: A propertyAproperty that determines thethat determines the amount of its resistanceamount of its resistance to shearing stressto shearing stress xx dxdx v+dvv+dv vv moving platemoving plate Fixed plateFixed plate vv S∞ dv/dx S = µ(dv/dx) S = µ(v/x) µ = S/(v/x) where: µ - absolute or dynamic viscosity in Pa-sec S - shearing stress in Pascal v - velocity in m/sec x -distance in meters
- 7. θ θ r h σσ SurfaceSurface TTension: Capillarityension: Capillarity Where: σ - surface tension, N/m γ - specific weight of liquid, N/m3 r – radius, m h – capillary rise, m °C σ 0 0.0756 10 0.0742 20 0.0728 30 0.0712 40 0.0696 60 0.0662 80 0.0626 100 0.0589 Surface Tension of Water r cos2 h γ θσ =
- 8. MANOMETERS Manometer is aninstrument 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. Pressure Head: where: p - pressure in KPa γ - specific weight of a fluid, KN/m3 h - pressure head in meters of fluid h P = γ
- 9. In steady flowthe velocity of the fluid particles at any point is constant as time passes. Unsteady flow exists whenever the velocity of the fluid particles at a point changes as time passes. Turbulent flow is an extreme kind of unsteady flow in which the velocity of the fluid particles at a point change erratically in both magnitude and direction. Types of flowing fluidsTypes of flowing fluids
- 10. More types offluid flowMore types of fluid flow • Fluid flow can be compressible or incompressible. • Most liquids are nearly incompressible. • Fluid flow can be viscous or nonviscous. • An incompressible, nonviscous fluid is called an ideal fluid.
- 11. When the flowis steady, streamlines are often used to represent the trajectories of the fluid particles.
- 12. 222 2 vA t m ρ= ∆ 111 1 vA t m ρ= ∆ Vm ρ= Equationof ContinuityEquation of Continuity distance tvA ∆= ρ
- 13. 222111 vAvA ρρ= EQUATION OF CONTINUITYEQUATION OF CONTINUITY The mass flow rate has the same value at every position along a tube that has a single entry and a single exit for fluid flow. SI Unit of Mass Flow Rate: kg/s
- 14. Open Type ManometerOpenType Manometer Open Manometer Fluid Fluid A Differential Type ManometerDifferential Type Manometer Fluid B Manometer Fluid Fluid A
- 15. Determination of Susing a U - TubeDetermination of S using a U - Tube x y Open Open Fluid A Fluid B SAx = SBy
- 16. Energy and HeadBernoullis Energy equation:Energy and Head Bernoullis Energy equation: Reference Datum (Datum Line) 1 2 z1 Z2 HL = ∆U - Q
- 17. BERNOULLI’S EQUATIONBERNOULLI’S EQUATION Insteady flow of a nonviscous, incompressible fluid, the pressure, the fluid speed, and the elevation at two points are related by:
- 18. 1. Without Energyhead added or given up by the fluid (No work done by the system or on the system) L2 2 22 t1 2 11 H+Z+ 2g v + γ P =h+Z+ 2g v + γ P L2 2 22 1 2 11 H+Z+ 2g v + γ P =Z+ 2g v + γ P h+H+Z+ 2g v + γ P =+Z+ 2g v + γ P L2 2 22 1 2 11 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 γ - 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
- 19. Ventury MeterVentury Meter A.Without considering Head loss flowltheoreticaQ vAvAQ Z g2 vP Z g2 vP 2211 2 2 22 1 2 11 − == ++=++ γγ inlet throat exit Manometer 1 2 B. Considering Head loss flowactual'Q vAvA'Q HZ g2 vP Z g2 vP 2211 L2 2 22 1 2 11 − == ++=++ + γγ Meter Coefficient Q 'Q C =
- 20. An orifice isan any opening with a closed perimeter without considering Head Loss 1 2 a a Vena Contractah By applying Bernoulli's Energy theorem: 2 2 22 1 2 11 Z g2 vP Z g2 vP ++ γ =++ γ But P1 = P2 = Pa and v1is negligible, then 21 2 2 ZZ g2 v −= and from figure: Z1 - Z2 = h, therefore h g2 v 2 2 = gh2v2 = Let v2 = vt gh2vt = where: vt - theoretical velocity, m/sec h - head producing the flow, meters g - gravitational acceleration, m/sec2 OrificeOrifice
- 21. COEFFICIENT OF VELOCITY(Cv)COEFFICIENT OF VELOCITY (Cv) velocityltheoretica velocityactual v C = t v v' Cv = COEFFICIENT OF CONTRACTION (Cc)COEFFICIENT OF CONTRACTION (Cc) orificetheofarea contractavena@jetofarea Cc = A a Cc = COEFFICIENT OF DISCHARGE(Cd)COEFFICIENT OF DISCHARGE(Cd) dischargeltheoretica dischargeactual v C = Q Q' Cd = vcd CCC = where: v' - actual velocity vt - theoretical velocity a - area of jet at vena contracta A - area of orifice Q' - actual flow Q - theoretical flow Cv - coefficient of velocity Cc - coefficient of contraction Cd - coefficient of discharge
- 22. It is asteady-state, steady-flowIt is a steady-state, steady-flow machine in which mechanical workmachine in which mechanical work is added to the fluid in orderis added to the fluid in order to transport the liquid from oneto transport the liquid from one point to another point of higherpoint to another point of higher pressure.pressure. Lower Reservoir Upper Reservoir Suction Gauge Discharge Gauge Gate Valve Gate Valve PUMPSPUMPS
- 23. FUNDAMENTAL EQUATIONSFUNDAMENTAL EQUATIONS 1.TOTAL DYNAMIC HEAD1. TOTAL DYNAMIC HEAD metersHZZ 2g vvPP H L12 2 1 2 212 t +−+ − + − = γ KW 60,000 TN2 BP π =
- 24. HYDRO ELECTRIC POWERPLANTHYDRO ELECTRIC POWER PLANT Headrace Tailrace Y – Gross Head Penstock turbine 1 2
- 25. B. Reaction Typeturbine (Francis Type)B. Reaction Type turbine (Francis Type) Headrace Tailrace Y – Gross Head Penstock ZB 1 2 Draft Tube B Generator B – turbine inlet
- 26. During power generationthe 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 pool (headrace). Turbine-Pump Pump-Storage Hydroelectric power plantPump-Storage Hydroelectric power plant
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