Fluid Mechanics 230

Fluid Mechanics 230Dr. Law Ming Chiat

Semester 1, 2015

2 x Lectures per weekClashes?1 x Tutorial per weekCivil (GP3:101, Monday, 12-1 pm)Questions?2 lab work per semester Lab registration starts at 10 am todayBe punctual Read before you attend the lab sessionAppropriate attire ConsultationConsultation: Go to your respective tutor Make appointment before you come

Unit Learning Outcomes (ULO)Recognize fluid phenomena and understand their causes, especially with regards to viscous and inviscid flow

Characterize fluid behavior and its effects using non-dimensional groups

Apply basic conservation principles in Fluid Mechanics

Model simple flow situations to make estimate of fluid forces

Perform design calculations for engineering applications that involve fluid flowCHAPTER ONE The Characterization of Fluid FlowsWhat is a FLUID?3 states of matter: Solid, Liquid, GasTo classify FLUIDS or Non FLUIDS: based on how they respond to a SHEAR FORCESolid: can resist shear force Fluid: deforms continuously

Fluids Vs SolidsFluids (liquid and gas) is lacking the ability of solids to offer permanent resistance to a deforming force, F acting tangentially to the surfacesFBBCCADFE xyA fluid is a substance which deforms continuously under the action of shearing forceIf a fluid is at rest, there can be no shearing force acting and, therefore, allforces in the fluid must be perpendicular to the plane upon which they actFluid MechanicsA study of conservation laws (mass, momentum, energy) with respect to fluids

To use this understanding in wide range of applications such as:aircraft flight, the pipe work system in an oil processing plant, or the design of buildings able to withstand hurricane-force winds Flow Fields (1)Describes the motion of fluid in a given region

Example 1:Uniform flow, occurring in an infinite region

streamlinesFlow velocity is constant, u

Flow Fields (2)Example 2:Uniform flow (inviscid) passes an object (a cylinder) Spatial dependence (i.e. on x and y) of flow velocity is now evident flow velocity and speed can change along a streamline

Streamline Equations Two-dimensional and steady flows

Case 1: Uniform flow

Case 2: Fluid flow past a particle

General Streamline EquationThree dimensional and unsteady flows

Flow velocity

Flow speed

Effect of ViscosityWhat is viscosity?Can be thought of as producing friction (or shear stress) between lumps of fluids as they pass by each otherThat makes the fluid cling to a rigid boundary in the flow fields

Fluid at boundary moves at same velocity as boundaryUw(y=0) = 0Uw(y=D) = UwVelocity must change from 0 to Uw going from bottom to TopIf D is small, Uw varies linearly with y-axis.Uw(y) = yUw/D

No Slip ConditionNo-slip Condition

Flow velocity:There are shear forces in the flowNewtonian Fluid

Newtons law of viscositydynamic viscosity (Ns/m2)

kinematic viscosity (m2/s)

Newtons law of viscosityInternal Pipe Flows

LaminarTurbulent

Laminar and Turbulent FlowsLaminar Flow:The flow is well ordered and stratified with a quadratic (in y) velocity profile. Note that the flow is also steady (time independent). It is the velocity which ensures that the flow is well ordered with its effect influencing all of the flow from the wall to the centre-line

Turbulent Flow:The laminar flow has broken down to give random fluctuations in the core region of the flow. This is unsteady flow (time dependent) although the random behavior of the fluid allows us to use time averaged values the velocity profile shown is a time averaged characterization.At the higher flow speeds associated with turbulent flow in pipes, the effect of viscosity only penetrates a small region close to the wall. External Uniform flow over the plate

Reynolds NumberFor pipe flow

For flow over a plate

What Reynolds number means for us?A measure of the importance of viscosity in the flow

When Re number is very large, the flow can be regarded as inviscid (viscous effects are negligible)

In Internal/external flows, the viscous effects are confined to a small layer at and close to the solid surface this thin layer is called the boundary layer, where the shear stress is only significant within this layer and at the surface. Beyond the boundary layer, the flow is essentially inviscid.Other Examples of Laminar/Turbulent Flows

SummaryYou have learnt different characteristics of fluid flows

In many instances (i.e. aircraft design), we want to avoid a turbulence flow

In other applications (i.e. heat transfer and mixing), turbulent flow is encouraged

The job of engineer is to manipulate fluid flows to suit a particular purpose (or application)