HYDRAULICS Fundamental Properties of Fluids

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    FUNDAMENTAL PROPERTIES OF FLUIDS

    THE SCIENCE OF HYDRAULICS Branch of science which treats of water or other fluid

    in motion.

    Hydrostatics study of pressure exerted by fluids at rest

    Hydrodynamics study of forces exerted by or upon

    fluids in motion

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    FLUIDS Substances capable of f lowing, having particles which

    easily move and change their relative position withouta separation of the mass.

    No resistance to change of form

    Conform to the shape of the solid body with whichthey come in contact.

    May be a liquid or a gas

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    Differences of liquids and gasesA liquid has a free surface, and a given mass of a liquid

    occupies only a given volume in a container, whereas agas does not have a free surface, and a given massoccupies all portions of any container regardless of itssize

    Liquids are practically incompressible while gases are

    compressible

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    Distinctions between a solid and a

    fluidA solid is deformed by a shearing stress, the amount of

    unit deformation up to a certain point beingproportional to the unit stress; a fluid is also deformedby a shearing stress but at a time rate of deformationwhich is proportional to the stress

    If the elastic limit is not exceeded, the application of a

    given unit shearing stress to a solid produces a certainunit deformation which is independent of the time ofapplication of the force, and when the stress isremoved the solid returns to its original form

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    If a given shearing stress is applied to a fluid,deformation continues to take place at a uniform ratewith time, and when the stress is removed the fluiddoes not, through forces contained within itself, return

    to its original form.

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    Units used in Hydraulics Fundamental equation relating force F, massM, and

    acceleration a F = kMa

    kis a proportionality factorValue ofkis made equal to 1 by two different systems

    of defining units

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    1. Gravitational system, in which kis made equal to 1 bydefining the unit of mass. If a body of unit weight fallsfreely, unit force is acting and the acceleration isg.Thus for unit force to produce unit acceleration theunit of mass must consist ofg units of weight.

    a) Foot-pound-second system: 1 lb force=1 slug mass x 1 ftper second per second, in which 1 slug mass=g pounds

    weight divided byg feet per second per second,g is32.2 ft per sec per sec.

    b) Metric system: 1 gram force= 1 unit of mass x 1 cm persecond per second, in which a unit of mass=g grams

    weight divided byg centimeters per second persecond,g is 981 cm per second per second

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    2. Absolute system, in which kis made equal to 1 bydefining the unit of force.

    a) Foot-pound-second system: Unit force is that forcewhich, acting on a body of 1 lb mass, gives it an

    acceleration of 1 ft per second per second, and is calleda poundal, 1 poundal force= 1 lb mass x 1 ft per secondper second

    b) Metric system: Unit force is that force which, acting on

    a body of 1 gram mass, gives it an acceleration of 1 cmper second per second, and is called a dyne. 1 dyneforce=1 gram mass x 1 cm per second per second

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    The metric and foot-pound-second systems are related

    by the following units of length and weight:

    1 meter = 3.2808 ft

    1 kilogram = 2.2046 lb

    Example:

    How many dynes force are equivalent to 1lb force?

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    General Properties of Fluids Unit weight w: the weight of a unit volume of a f luid,

    in foot-pound-second expressed as pounds per cubicfoot

    Mass Densityr (rho): the mass per unit of volume, ingravitational unitsr = w/g or w=rg ,where g is the acceleration due togravity

    in foot-pound-second units mass density is slugs percubic foot

    in metric system density is measured in grams percubic centimeter

    Specific gravitys: the ratio of the unit weight of a fluidto the unit weight of water at 4C

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