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    INS 306 HYDRAULICS

    Review of Basic Fluid Mechanics Concepts

    http://th.physik.uni-frankfurt.de/~jr/physstamps.html

    Dr. A. Ozan Celik Thursday, Feb. 7, 2013

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    71 DIMENSIONS AND UNITS

    A dimension is a measure of a physical quantity without numerical values, while a unit is a way to assign a number to the dimension. For example, length is a dimension, but centimeter is a unit.

    Dimension: A measure of a physical quantity (without numerical values).

    Unit: A way to assign a number to that dimension.

    There are seven primary dimensions (also called fundamental or basic dimensions): mass, length, time, temperature, electric current, amount of light, and amount of matter.

    All nonprimary dimensions can be formed by some combination of the seven primary dimensions.

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    The water strider is an insect that can walk on water due to surface tension.

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    72 DIMENSIONAL HOMOGENEITY

    You cant add apples and oranges!

    Total energy of a system at state 1 and at state 2.

    The law of dimensional homogeneity: Every additive term in an equation must have the same dimensions.

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    An equation that is not dimensionally homogeneous is a sure sign of an error.

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    The Bernoulli equation is a good example of a dimensionally homogeneous equation. All additive terms, including the constant, have the same dimensions, namely that of pressure. In terms of primary dimensions, each term has dimensions {m/(t2L)}.

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    Basics of fluid flow

    Types of flow

    Fluid Ideal/Real Compressible/Incompressible

    Flow Steady/Unsteady Uniform/Non-uniform Laminar/Turbulent Pressure/Gravity (free surface)

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    Basics of fluid flow

    One -, two -, and three- dimensional flows

    This is the most general 3-D flow:

    The flow is classified as 2-D if: The flow can be viewed as 1-D if:

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    Basics of fluid flow

    Velocity and Acceleration

    This is the most general 3-D flow:

    For steady 1-D flow:

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    Basics of fluid flow

    Velocity and Acceleration

    Convective (spatial)

    acceleration

    at

    Local (temporal)

    acceleration

    an

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    Basics of fluid flow

    Reynolds Transport Theorem & Continuity

    QVAVA 2211

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    Energy in Steady Flow

    Bernoullis Equation

    Unit: L

    (Energy per unit weight)

    Basic assumptions:

    Inviscid & incompressible fluid

    Steady flow

    Applies along a streamline

    No energy added or removed from the fluid along the streamline

    Piezometric pressure

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    Energy in Steady Flow, Pipe Flow

    V

    p/ p/

    V2/2g

    Bring moving water to a halt, and it'll drive a column of water up to exactly the height from which water would flow to gain that velocity.

    Pitot Tube (Measures stagnation pressure)

    Free stream dynamic pressure

    Free stream static pressure

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    Energy in Steady Flow, Free surface flow

    V

    V2/2g

    Bring moving water to a halt, and it'll drive a column of water up to exactly the height from which water would flow to gain that velocity.

    Pitot Tube (Measures stagnation pressure)

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    Energy in Steady Flow

    Motion of a real fluid no friction only pressure forces exist (normal to the surfaces)

    -Tangential (shearing forces exist between the fluid layers as well as between the fluid and solid boundary

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