CE 204 FLUID MECHANICS
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1 CE 204 FLUID MECHANICS Onur AKAY Assistant Professor Okan University Department of Civil Engineering Akfırat Campus Tuzla-Istanbul/TURKEY Phone: ext.1974 Fax: Onur Akay, Ph.D. CE 204 Fluid Mechanics 1
2 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
3 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
4 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
5 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
6 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
7 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
8 Pathlines and Streaklines: Onur Akay, Ph.D. CE 204 Fluid Mechanics 8
9 Pathlines and Streaklines: Examples: MOVIE Onur Akay, Ph.D. CE 204 Fluid Mechanics 9
10 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
11 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
12 Acceleration: local convective centripetal Onur Akay, Ph.D. CE 204 Fluid Mechanics 12
13 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
14 Onur Akay, Ph.D. CE 204 Fluid Mechanics 14
15 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
16 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
17 Euler s Equation: Onur Akay, Ph.D. CE 204 Fluid Mechanics 17
18 Euler s Equation: Euler s Equation: For an incompressible flow, γ is constant Onur Akay, Ph.D. CE 204 Fluid Mechanics 18
19 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
20 Onur Akay, Ph.D. CE 204 Fluid Mechanics 20
21 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
22 Onur Akay, Ph.D. CE 204 Fluid Mechanics 22
23 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
24 Bernoulli Equation: Onur Akay, Ph.D. CE 204 Fluid Mechanics 24
25 Onur Akay, Ph.D. CE 204 Fluid Mechanics 25
26 Onur Akay, Ph.D. CE 204 Fluid Mechanics 26
CE 204 FLUID MECHANICS
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:
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