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Fluid mechanics

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LOKESH KOLHE
LOKESH KOLHE

This document discusses several topics related to fluid mechanics including: 1. Definitions of specific gravity, density, and atmospheric pressure. 2. Explanations of absolute and gauge pressure. 3. Descriptions of viscosity, surface tension, manometers, and different types of fluid flow. 4. Explanations of the equation of continuity, Bernoulli's equation, and their applications. 5. Discussions of venturi meters, orifices, pumps, hydroelectric power plants, and pump-storage systems.

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Fluid mechanics
FLUID MECHANICS 3 m kg V m = kg m m V = 3 3 m KN 1000 g 1000V mg V W = ==粒
Its specific gravity (relative density) is equal to the ratio of its density to that of water at standard temperature and pressure. W = 粒 粒L W L L =S 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. ah G 粒 粒 = ah G G =S where: At standard condition W = 1000 kg/m3 W = 9.81 KN/m3
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
Atmospheric Pressure Atmospheric pressure is normally about 100,000 Pa Differences in atmospheric pressure cause winds to blow Low atmospheric pressure inside a hurricanes eye contributes to the severe winds and the development of the storm surge
x dx v+dv v moving plate Fixed plate v 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
r h Where: - surface tension, N/m - specific weight of liquid, N/m3 r radius, m h capillary rise, m C 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 粒 慮
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. Pressure Head: where: p - pressure in KPa - specific weight of a fluid, KN/m3 h - pressure head in meters of fluid h P 粒
In steady flow the 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 fluids:
More types of fluid flow Fluid flow can be compressible or incompressible. Most liquids are nearly incompressible. Fluid flow can be viscous or nonviscous.
When the flow is steady, streamlines are often used to represent the trajectories of the fluid particles.
222 2 vA t m 111 1 vA t m Vm The Equation of Continuity distance tvA
222111 vAvA EQUATION 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
Open Type Manometer Open Manometer Fluid Fluid A Differential Type Manometer Fluid B Manometer Fluid Fluid A
Determination of S using a U - Tube x y Open Open Fluid A Fluid B SAx = SBy
Energy and Head Bernoullis Energy equation: Reference Datum (Datum Line) 1 2 z1 Z2 HL = U - Q
BERNOULLIS EQUATION In steady flow of a nonviscous, incompressible fluid, the pressure, the fluid speed, and the elevation at two points are related by:
1. Without Energy head 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 + 粒 P =h+Z+ 2g v + 粒 P L2 2 22 1 2 11 H+Z+ 2g v + 粒 P =Z+ 2g v + 粒 P h+H+Z+ 2g v + 粒 P =+Z+ 2g v + 粒 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 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
Ventury Meter A. Without considering Head loss flowltheoreticaQ vAvAQ Z g2 vP Z g2 vP 2211 2 2 22 1 2 11 粒粒 Manometer 1 2 B. Considering Head loss flowactual'Q vAvA'Q HZ g2 vP Z g2 vP 2211 L2 2 22 1 2 11 粒粒 Meter Coefficient Q 'Q C
Orifice: An orifice is an 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 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
velocityltheoretica velocityactual v C t v v' Cv orificetheofarea contractavena@jetofarea Cc A a Cc 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
Lower Reservoir Upper Reservoir Suction Gauge Discharge Gauge Gate Valve Gate Valve
metersHZZ 2g vvPP H L12 2 1 2 212 t 粒 Q = Asvs = Advd m3/sec WP = Q Ht KW KW 60,000 TN2 BP
HYDRO ELECTRIC POWER PLANT Headrace Tailrace Y Gross Head Penstock turbine 1 2
Headrace Tailrace Y Gross Head Penstock ZB 1 2 Draft Tube B Generator B turbine inlet
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 pool (headrace). Turbine-Pump
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Fluid mechanics

  • 3. Its specific gravity (relative density) is equal to the ratio of its density to that of water at standard temperature and pressure. W = 粒 粒L W L L =S 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. ah G 粒 粒 = ah G G =S where: At standard condition W = 1000 kg/m3 W = 9.81 KN/m3
  • 4. 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
  • 5. Atmospheric Pressure Atmospheric pressure is normally about 100,000 Pa Differences in atmospheric pressure cause winds to blow Low atmospheric pressure inside a hurricanes eye contributes to the severe winds and the development of the storm surge
  • 6. x dx v+dv v moving plate Fixed plate v 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
  • 7. r h Where: - surface tension, N/m - specific weight of liquid, N/m3 r radius, m h capillary rise, m C 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 粒 慮
  • 8. 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. Pressure Head: where: p - pressure in KPa - specific weight of a fluid, KN/m3 h - pressure head in meters of fluid h P 粒
  • 9. In steady flow the 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 fluids:
  • 10. More types of fluid flow Fluid flow can be compressible or incompressible. Most liquids are nearly incompressible. Fluid flow can be viscous or nonviscous.
  • 11. When the flow is steady, streamlines are often used to represent the trajectories of the fluid particles.
  • 13. 222111 vAvA EQUATION 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 Manometer Open Manometer Fluid Fluid A Differential Type Manometer Fluid B Manometer Fluid Fluid A
  • 15. Determination of S using a U - Tube x y Open Open Fluid A Fluid B SAx = SBy
  • 16. Energy and Head Bernoullis Energy equation: Reference Datum (Datum Line) 1 2 z1 Z2 HL = U - Q
  • 17. BERNOULLIS EQUATION In steady flow of a nonviscous, incompressible fluid, the pressure, the fluid speed, and the elevation at two points are related by:
  • 18. 1. Without Energy head 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 + 粒 P =h+Z+ 2g v + 粒 P L2 2 22 1 2 11 H+Z+ 2g v + 粒 P =Z+ 2g v + 粒 P h+H+Z+ 2g v + 粒 P =+Z+ 2g v + 粒 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 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
  • 19. Ventury Meter A. Without considering Head loss flowltheoreticaQ vAvAQ Z g2 vP Z g2 vP 2211 2 2 22 1 2 11 粒粒 Manometer 1 2 B. Considering Head loss flowactual'Q vAvA'Q HZ g2 vP Z g2 vP 2211 L2 2 22 1 2 11 粒粒 Meter Coefficient Q 'Q C
  • 20. Orifice: An orifice is an 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 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
  • 21. velocityltheoretica velocityactual v C t v v' Cv orificetheofarea contractavena@jetofarea Cc A a Cc 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
  • 23. metersHZZ 2g vvPP H L12 2 1 2 212 t 粒 Q = Asvs = Advd m3/sec WP = Q Ht KW KW 60,000 TN2 BP
  • 24. HYDRO ELECTRIC POWER PLANT Headrace Tailrace Y Gross Head Penstock turbine 1 2
  • 25. Headrace Tailrace Y Gross Head Penstock ZB 1 2 Draft Tube B Generator B turbine inlet
  • 26. 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 pool (headrace). Turbine-Pump