Description of Fluid in Motion

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Lecture 4

Mechanics of Fluids 1: Lecture 4: Descriptions of Fluid in MotionDepartment of Mechanical Engineering MEHB223

Description of Description of Fluid in MotionFluid in Motion

Fluid in MotionMechanics of Fluids 1: Lecture 4: Descriptions of Fluid in MotionDepartment of Mechanical Engineering MEHB223

Isabel Loop Isabel Loop –– Vortex MotionVortex Motion

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Chapter Summary

• Introduction


• Introduction

• Steady and Unsteady Flows

• Pathline, Streakline and Streamline

• Real and Ideal Fluids

• Laminar and Turbulent Flows

• Flow Dimensionality

• Frame of Reference

• Lagrangian Vs Eulerian Viewpoint

4.1 Introduction

Fl id ti b 3 ti


• Fluid motions are govern by 3 conservation laws ‐mass, momentum and energy conservation

• Basic concepts will be introduced as a basis for analyzing fluid motionf y g f

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4.2. Steady and Unsteady Flow

• Steady and Unsteady Flow : ‐


S eady a d U s eady o– If flow parameters is not changing with time the flow field is said to be STEADY FLOW

– If it is changing with time => UNSTEADY FLOW

Steady-Flow Unsteady-Flow

0u=

∂ 0u≠

∂

Time, t

u

Time, t

u

Probe 0t=

∂0

t≠

∂

4.2. Steady and Unsteady Flow

• Steady and Unsteady Flow : ‐


S eady a d U s eady o

Steady-FlowUnsteady-FlowHarrier VTOL Fighter Plane

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4.3. Pathline, Steakline & Streamline

• Physical Observations of Flow Pattern : ‐


ys ca Obse a o s of o a e– A few techniques are available to describe flow pattern

– Pathline ~ Lines traced out by individual particles of fluids, Can be observed by following the path of a marker as it moves in the fluid

Path of markerA

B

Pathline through APathline through B

If further markers were inserted at A & B and pathlines were coincident, flow is STEADY


• Physical Observations of Flow Pattern : ‐


ys ca Obse a o s of o a e– Streakline ~ Traced observed when a dye or smoke is continuously injected at a fixed point or points within a flow field

Fluid FlowStreaklines

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Streaklines : ‐


Physical Observations of Flow Pattern : -

4.3. Pathline, Steakline & Streamline4.3. Pathline, Steakline & Streamline


Streamline ~ Lines representing the direction of velocity throughout the flowfield at any instant in time. Thus there is no flow across streamlines. Snapshot of streaklines

Uniform flow

0u=

∂

Tangent = velocity

Non-uniform flow

s∂

0su≠

∂∂

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Physical Observations of Flow Pattern : -



Physical Observations of Flow Pattern : Properties of Streamlines : ~

• velocity components normal to streamlines is zero• In unsteady flow, shape changes with time• In steady flow, unchanging with time and coincident with pathlines

and streaklines• They vary in spacing - indicates the velocity variation• Follows shape of solid boundaries except when separation occurs• They cannot intersect

Stream-surface - A surface formed of streamlinesStream-tube - Stream surface wrap around to form a tube

Pathlines Vs Streaklines Vs Streamlines: -



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Pathlines Vs Streaklines Vs Streamlines : -4.3. Pathline, Steakline & Streamline4.3. Pathline, Steakline & Streamline


((a) t = 4 s.(b) t = 7 s. (c) t = 10 s.a) t = 4 s.(b) t = 7 s. (c) t = 10 s.

Real Vs Ideal Fluid : -

4.4.44. . Real and Ideal FluidReal and Ideal Fluid


Ideal fluid - fluid with no viscosity and incompressible. Fluid ‘slip’ at solid boundary. Velocity exist at the wall.Real fluid -

No slip condition at the wall. No tangential velocity at the wallBoundary Layer exists near the wallVelocity profile developed - varies in traverse direction

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Real Vs Ideal Fluid : -

4.4.44. . Real and Ideal FluidReal and Ideal Fluid


Laminar and Turbulent Flow: -Laminar Flow - steady no mixing smooth appearance E g

4.4.55. . Laminar and Turbulent FlowsLaminar and Turbulent Flows


Laminar Flow steady, no mixing, smooth appearance. E.g. Flow of fluid with high viscosity, honey, lubrication oilTurbulent Flow - with mixing action throughout the flow-field with formation of eddies : characterized by statistical fluctuation about mean valueGovern by Reynolds number , Re =ρud/μ

Laminar flowRe < Recrit

Turbulent flowRe > Recrit

'_

uuu +=

∫Δ+

Δ=

Tt

t

_

udtT

1u

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Laminar and Turbulent Flow (Reynolds Experiment): -4.4.55. . Laminar and Turbulent FlowsLaminar and Turbulent Flows


Flow Dimensionality : -

4.4.66. . Flow DimensionalityFlow Dimensionality


ythe minimum number of space coordinates required to specify itOne-Dimensional Flow - Velocity profile is uniform at any station - e.g. Ideal fluid flow in pipe or duct.Two-Dimensional Flow - Flow of real fluid in duct with infinite width in cartesian x-y coordinates - Axi-symmetricinfinite width in cartesian x-y coordinates - Axi-symmetric flow in circular pipe in cylindrical x-r coordinatesThree-Dimensional Flow - Flow of real fluid in duct with end effects in x-y-z cartesian coordinates

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Flow Dimensionality : -

4.4.66. . Flow DimensionalityFlow Dimensionality


y

1D Flow - uniform vel profile 2D Flow - velocity varies in x & y

2D Axi-symmetric flow General 3D Flow

Frame of Reference –

4.4.77. . Frame of ReferenceFrame of Reference


f fThe laws of mechanics are still applicable if the frame of reference is moving at a constant velocity in straight lineIt is easier to analyze Steady flow cf. Unsteady flowSometimes convenient to change frame of reference from a fixed coordinates to moving coordinates (relative frame)

STEADYUNSTEADY

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Analyzing Fluid Flow - LAGRANGIAN Vs EULERIAN

4.4.88. . LagrangianLagrangian Vs Vs EulerianEulerian


y gLAGRANGIAN Viewpoint : -Following the movement of individual fluid particle with time. Many particles followed and interaction considered.Control mass Approach (as in Thermodynamics 1)velocity description : u = u(t) = uxi + uyj + uzk : tangent to streamlinestreamline

LAGRANGIAN APPROACH

EULERIAN Viewpoint : -

4.4.88. . LagrangianLagrangian Vs Vs EulerianEulerian


pFocus on certain point in space and describe the motion of fluid particles that pass this point as time goes on.Control Volume Approach (as in Thermodynamics 1)velocity description : u = u(x,y,z,t) = function of position along a streamline and time

EULERIAN APPROACH

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End of End of Lecture Lecture 44

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Description of Fluid in Motion