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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
CE 204
FLUID MECHANICS
Onur AKAY
Assistant Professor
Onur Akay, Ph.D. CE 204 Fluid Mechanics 1
Assistant Professor
Okan University
Department of Civil Engineering
Akfrat Campus
34959 Tuzla-Istanbul/TURKEY
Phone: +90-216-677-1630 ext.1974
Fax: +90-216-677-1486
E-mail: [email protected]
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Kinematics of Fluids:
The relationship between pressure and flow velocity is important in many engineering
applications.
- Blood pressure (flow of blood through veins and arteries.
- Weather forecasts (pressure readings of atmospheric flow patterns)
Onur Akay, Ph.D. CE 204 Fluid Mechanics 2
- Stirring a cup of coffee (pressure variations enhance mixing)
- Design of tall structures (pressure forces from the wind)
- Aircraft design (lift and drag)
- Flow systems (heating and air conditioning)
The eye of a
hurricane.
The space
shuttle during
liftoff.
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Streamlines and Flow Patterns:
- Flow pattern shows the flow direction.
- Streamlines are drawn tangent to local velocity vectors.
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The flow pattern provided by the streamlines
represent an instantaneous visualization of the
flow field.MOVIES
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Uniform Flow: The velocity does not change along a fluid path.
s: the distance traveled by a fluid particle along a path.
t: time
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Nonuniform Flow: The velocity changes along a fluid path.
s: the distance traveled by a fluid particle along a path.
t: time
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Steady Flow: The velocity at a given point on a fluid path does not change with time.
Unsteady Flow: The velocity at a given point on a fluid path changes with time.
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Streamlines give no indication of the steadiness or unsteadiness of the flow!!!
Steady or unsteady?
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Laminar Flow: Well-ordered state of flow in which adjacent flow layers move smoothly with
respect to each other..
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MOVIETurbulent Flow: Unsteady flow characterized by intense cross-stream mixing.
Instantaneous
velocity profile
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Pathlines and Streaklines:
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Pathlines and Streaklines:
Examples:
http://www.tecplot.com/showcase/contours/article.aspx?issue=35&article=2
http://en.wikipedia.org/wiki/Streamlines,_streaklines,_and_pathlines
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MOVIE
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
One-Dimensional and Multi-Dimensional Flows:
The dimensionality is characterized by the number of spatial dimensions needed to
describe the velocity field.
One-dimensional
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Two-dimensional
Three-dimensional
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Acceleration:
Acceleration is the rate of change of the particles velocity with time.
Velocity
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Velocity
Acceleration
an : normal component of acceleration
(centripetal)
at : tangential component of acceleration
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Acceleration:
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convective
local
centripetal
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Acceleration:
convective
local
centripetal
In steady flow the local acceleration is zero.
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In steady flow the local acceleration is zero.
In uniform flow the convective acceleration is zero.
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Lagrangian and Eulerian Approach:
Objective: To determine the pressure and velocities at arbitrary locations in a flow field.
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Eulers Equation:
Hydrostatic equations were derived by equating the
sum of forces on a fluid element equal to zero.
Leonhard Euler
Born: 15 April 1707, Basel, Switzerland
Died: 18 September 1783, St. Petersburg, Russia
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Same ideas are applied to a moving fluid, but now we are executing Newtons second law.
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Eulers Equation:
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Eulers Equation:
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For an incompressible flow, is constant
Eulers Equation:
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Eulers Equation:
In a static body of fluid, Eulers equation reduces to:
(Hydrostatic Equation)
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REMEMBER
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Pressure Distribution in Rotating Flows: Eulers Equation
Apply Eulers equation outward from the center of rotation.
Since the flow is steady, the partial derivative has been
replaced by an ordinary derivative:
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Uniform or nonuniform?
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Bernoulli Equation:
Bernoulli equation is developed by applying Eulers
equation along a pathline:
Daniel Bernoulli
Born: 8 February 1700, Groningen, Netherlands
Died: 8 March 1782, Basel, Switzerland
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For steady flow:
piezometric kinetic pressure
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Bernoulli Equation:
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
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Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
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