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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

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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:

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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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Bernoullis Equation

Unit: L

(Energy per unit weight)

Basic assumptions:

Inviscid & incompressible fluid

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)