CE 204 FLUID MECHANICS Onur AKAY Assistant Professor 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: onur.akay@okan.edu.tr Onur Akay, Ph.D. CE 204 Fluid Mechanics 1
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) - Stirring a cup of coffee (pressure variations enhance mixing) - Design of tall structures (pressure forces from the wind) The eye of a hurricane. - Aircraft design (lift and drag) - Flow systems (heating and air conditioning) The space shuttle during liftoff. Onur Akay, Ph.D. CE 204 Fluid Mechanics 2
Streamlines and Flow Patterns: - Flow pattern shows the flow direction. -Streamlinesare drawn tangent to local velocity vectors. The flow pattern provided by the streamlines represent an instantaneous visualization of the flow field. MOVIES Onur Akay, Ph.D. CE 204 Fluid Mechanics 3
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
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
Steady Flow:The velocity at a given pointon a fluid path does not change with time. Unsteady Flow:The velocity at a given pointon a fluid path changes with time. Streamlines give no indication of the steadiness or unsteadiness of the flow!!! Steady or unsteady? Onur Akay, Ph.D. CE 204 Fluid Mechanics 6
Laminar Flow:Well-ordered state of flow in which adjacent flow layers move smoothly with respect to each other.. Turbulent Flow: Unsteady flow characterized by intense cross-stream mixing. MOVIE Instantaneous velocity profile Onur Akay, Ph.D. CE 204 Fluid Mechanics 7
Pathlines and Streaklines: Onur Akay, Ph.D. CE 204 Fluid Mechanics 8
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 MOVIE Onur Akay, Ph.D. CE 204 Fluid Mechanics 9
One-Dimensional and Multi-Dimensional Flows: The dimensionality is characterized by the number of spatial dimensions needed to describe the velocity field. One-dimensional Two-dimensional Three-dimensional Onur Akay, Ph.D. CE 204 Fluid Mechanics 10
Acceleration: Acceleration is the rate of change of the particle s velocity with time. Velocity Acceleration a n : normal component of acceleration (centripetal) a t : tangential component of acceleration Onur Akay, Ph.D. CE 204 Fluid Mechanics 11
Acceleration: local convective centripetal Onur Akay, Ph.D. CE 204 Fluid Mechanics 12
Acceleration: local convective centripetal In steady flow the local acceleration is zero. In uniform flow the convective acceleration is zero. Onur Akay, Ph.D. CE 204 Fluid Mechanics 13
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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
Euler s Equation: Leonhard Euler Hydrostatic equations were derived by equating the sum of forces on a fluid element equal to zero. Born: 15 April 1707, Basel, Switzerland Died: 18 September 1783, St. Petersburg, Russia Same ideas are applied to a moving fluid, but now we are executing Newton s second law. Onur Akay, Ph.D. CE 204 Fluid Mechanics 16
Euler s Equation: Onur Akay, Ph.D. CE 204 Fluid Mechanics 17
Euler s Equation: Euler s Equation: For an incompressible flow, γ is constant Onur Akay, Ph.D. CE 204 Fluid Mechanics 18
Euler s Equation: In a static body of fluid, Euler s equation reduces to: (Hydrostatic Equation) REMEMBER Onur Akay, Ph.D. CE 204 Fluid Mechanics 19
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Pressure Distribution in Rotating Flows: Euler s Equation Apply Euler s equation outward from the center of rotation. Since the flow is steady, the partial derivative has been replaced by an ordinary derivative: Uniform or nonuniform? Onur Akay, Ph.D. CE 204 Fluid Mechanics 21
Onur Akay, Ph.D. CE 204 Fluid Mechanics 22
Bernoulli Equation: Daniel Bernoulli Bernoulli equation is developed by applying Euler s equation along a pathline: Born: 8 February 1700, Groningen, Netherlands Died: 8 March 1782, Basel, Switzerland For steady flow: piezometric kinetic pressure Onur Akay, Ph.D. CE 204 Fluid Mechanics 23
Bernoulli Equation: Onur Akay, Ph.D. CE 204 Fluid Mechanics 24
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