CE 204 FLUID MECHANICS  Okan University · Chapter 4Kinematics of Fluids Descriptions of Fluid...
Embed Size (px)
Transcript of CE 204 FLUID MECHANICS  Okan University · Chapter 4Kinematics of Fluids Descriptions of Fluid...

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 TuzlaIstanbul/TURKEY
Phone: +902166771630 ext.1974
Fax: +902166771486
Email: [email protected]

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.

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.
Onur Akay, Ph.D. CE 204 Fluid Mechanics 3
The flow pattern provided by the streamlines
represent an instantaneous visualization of the
flow field.MOVIES

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
Onur Akay, Ph.D. CE 204 Fluid Mechanics 4

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
Onur Akay, Ph.D. CE 204 Fluid Mechanics 5

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.
Onur Akay, Ph.D. CE 204 Fluid Mechanics 6
Streamlines give no indication of the steadiness or unsteadiness of the flow!!!
Steady or unsteady?

Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Laminar Flow: Wellordered state of flow in which adjacent flow layers move smoothly with
respect to each other..
Onur Akay, Ph.D. CE 204 Fluid Mechanics 7
MOVIETurbulent Flow: Unsteady flow characterized by intense crossstream mixing.
Instantaneous
velocity profile

Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Pathlines and Streaklines:
Onur Akay, Ph.D. CE 204 Fluid Mechanics 8

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
Onur Akay, Ph.D. CE 204 Fluid Mechanics 9
MOVIE

Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
OneDimensional and MultiDimensional Flows:
The dimensionality is characterized by the number of spatial dimensions needed to
describe the velocity field.
Onedimensional
Onur Akay, Ph.D. CE 204 Fluid Mechanics 10
Twodimensional
Threedimensional

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
Onur Akay, Ph.D. CE 204 Fluid Mechanics 11
Velocity
Acceleration
an : normal component of acceleration
(centripetal)
at : tangential component of acceleration

Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Acceleration:
Onur Akay, Ph.D. CE 204 Fluid Mechanics 12
convective
local
centripetal

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.
Onur Akay, Ph.D. CE 204 Fluid Mechanics 13
In steady flow the local acceleration is zero.
In uniform flow the convective acceleration is zero.

Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Onur Akay, Ph.D. CE 204 Fluid Mechanics 14

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.
Onur Akay, Ph.D. CE 204 Fluid Mechanics 15

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
Onur Akay, Ph.D. CE 204 Fluid Mechanics 16
Same ideas are applied to a moving fluid, but now we are executing Newtons second law.

Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Eulers Equation:
Onur Akay, Ph.D. CE 204 Fluid Mechanics 17

Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Eulers Equation:
Onur Akay, Ph.D. CE 204 Fluid Mechanics 18
For an incompressible flow, is constant
Eulers Equation:

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)
Onur Akay, Ph.D. CE 204 Fluid Mechanics 19
REMEMBER

Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Onur Akay, Ph.D. CE 204 Fluid Mechanics 20

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:
Onur Akay, Ph.D. CE 204 Fluid Mechanics 21
Uniform or nonuniform?

Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Onur Akay, Ph.D. CE 204 Fluid Mechanics 22

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
Onur Akay, Ph.D. CE 204 Fluid Mechanics 23
For steady flow:
piezometric kinetic pressure

Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Bernoulli Equation:
Onur Akay, Ph.D. CE 204 Fluid Mechanics 24

Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Onur Akay, Ph.D. CE 204 Fluid Mechanics 25

Chapter 4 Kinematics of Fluids
Descriptions of Fluid Flow, Eulers Equation, Bernoulli Equation
Onur Akay, Ph.D. CE 204 Fluid Mechanics 26