CE 204 FLUID MECHANICS - Okan University · Chapter 4Kinematics of Fluids Descriptions of Fluid...

of 26 /26
Chapter 4 Kinematics of Fluids Descriptions of Fluid Flow, Euler’s Equation, Bernoulli Equation CE 204 FLUID MECHANICS Onur AKAY Assistant Professor Onur Akay, Ph.D. CE 204 Fluid Mechanics 1 Okan University Department of Civil Engineering Akfırat Campus 34959 Tuzla-Istanbul/TURKEY Phone: +90-216-677-1630 ext.1974 Fax: +90-216-677-1486 E-mail: [email protected]

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 Tuzla-Istanbul/TURKEY

    Phone: +90-216-677-1630 ext.1974

    Fax: +90-216-677-1486

    E-mail: [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: Well-ordered 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 cross-stream 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

    One-Dimensional and Multi-Dimensional Flows:

    The dimensionality is characterized by the number of spatial dimensions needed to

    describe the velocity field.

    One-dimensional

    Onur Akay, Ph.D. CE 204 Fluid Mechanics 10

    Two-dimensional

    Three-dimensional

  • 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