ins 306 hydraulics review of basic fluid mechanics · pdf filetypes of flow fluid ideal/real...

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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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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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Velocity and Acceleration
This is the most general 3-D flow:
For steady 1-D flow:

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Velocity and Acceleration
Convective (spatial)
acceleration
at
Local (temporal)
acceleration
an

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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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ins 306 hydraulics review of basic fluid mechanics · pdf filetypes of flow fluid ideal/real...

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