《流体力学》课程教学资源：（英文版）Fluid Flow Concepts

Fluid Flow Concepts Flow Classification Ideal fluid flow Frictionless(zero viscosity ● Incompressible Can be solved mathematically Real fluid flow Shear stress develops where there is velocity gradient Fluid in contact with wall has zero velocity Pipe wall Ideal fluid Real fluid Uniform velocity Non-uniform velocity Shear stress Zero shear stress eXIstS Fluid close to wall has zero velocity

Fluid Flow Concepts Flow Classification : Ideal Fluid Flow • Frictionless (zero viscosity) • Incompressible • Can be solved mathematically Real Fluid Flow • Shear stress develops where there is velocity gradient • Fluid in contact with wall has zero velocity Pipe Wall Ideal Fluid : Uniform velocity Zero shear stress Real Fluid : Non-uniform velocity Shear stress exists Fluid close to wall has zero velocity

Flow Classification Laminar flow Occurs at low reynolds number Fluid moves along smooth layers Motion governed by newton's law of viscosity Turbulent flow e Occurs at high reynolds number o Fluid moves along irregular, fluctuating and random paths

Flow Classification Laminar Flow • Occurs at low Reynolds number • Fluid moves along smooth layers • Motion governed by Newton’s law of viscosity Turbulent Flow • Occurs at high Reynolds number • Fluid moves along irregular, fluctuating and random paths

Flow Classification Rotational (vortex) flow Fluid undergoes net rotation about some axis Irrotational flow Fluid has no net rotation, only linear translation e All ideal fluid flows are irrotational flows Variation of fluid properties(velocity, pressure density, temperature etc) Temporal variation Steady flow -Properties at a point not changing with flow Unsteady flow- changing with time Spatial variation Uniform- Properties at an instant do not change with space Non-uniform flow-changing from point to point Four possible flow types · Steady uniform flow Steady non-uniform flow Unsteady uniform flow Unsteady non-uniform flow

Flow Classification Rotational (vortex) flow • Fluid undergoes net rotation about some axis Irrotational flow • Fluid has no net rotation, only linear translation • All ideal fluid flows are irrotational flows Variation of fluid properties (velocity, pressure, density, temperature etc) Temporal Variation : • Steady flow –Properties at a point not changing with flow • Unsteady flow – changing with time Spatial Variation : • Uniform flow – Properties at an instant do not change with space • Non-uniform flow – changing from point to point Four possible flow types : • Steady uniform flow • Steady non-uniform flow • Unsteady uniform flow • Unsteady non-uniform flow

Flow Classification One-dimensional flow Flow properties are function of time(t) and one space coordinate(e.g X) Two-dimensional flow Flow properties are function of time(t) and two space coordinates(e.g. x, y) TThree-dimensional flow Flow properties are function of time(t) and three space coordinates(x, y, 2)

Flow Classification One-dimensional flow • Flow properties are function of time (t) and one space coordinate (e.g. x) Two-dimensional flow • Flow properties are function of time (t) and two space coordinates (e.g. x, y) Three-dimensional flow • Flow properties are function of time (t) and three space coordinates (x, y, z) x x y

Engineering Simplification Many engineering problems are simplified as one dimensional problems Pipe flow: Actual Assumed 1-D VdA= al V=0/A Open Channel Actua Assumed 1-D Q/A

Engineering Simplification Many engineering problems are simplified as one￾dimensional problems Pipe Flow : Open Channel : Vm = Q/A v Vm Actual Assumed 1-D Actual Assumed 1-D V Vm V Q A VdA AV m A m = / = 

Engineering Simplification Axi-Symmetric Flow through Circular pipe 6 R r A=TI 6A=2πror Elemental discharge through elemental area δQ=v.SA=v.2πrδr Total Q through pipe section given by integration Q=vdA= 2nrvdr Mean velocity Vm=Q/a=Q/(TR2)

Engineering Simplification Axi-Symmetric Flow through Circular Pipe Elemental discharge through elemental area : Q = v . A = v . 2rr Total Q through pipe section given by integration : Mean velocity Vm = Q/A = Q/(R2 ) r r R A = 2rr v A =r 2 Vm Q   = = A R Q vdA rvdr 0 2

Fluid kinematics Under the 'continuum hypothesis a fluid body is considered to be made up of infinitesimal fluid ' particles tightly packed together and interact with each other Each fluid" contains numerous molecules Fluid motion is described in terms of velocity and acceleration of fluid'particles', and not individual molecules Fluid Kinematics Study of the motion of fluid(position, velocity and acceleration) without consideration offorces producing the motion Fluid dynamics Analyses of fluid motion in relation to forces producing the motion

Fluid kinematics • Under the ‘continuum’ hypothesis, a fluid body is considered to be made up of infinitesimal fluid ‘particles’ tightly packed together and interact with each other • Each fluid ‘particle’ contains numerous molecules • Fluid motion is described in terms of velocity and acceleration of fluid ‘particles’, and not individual molecules Fluid Kinematics Study of the motion of fluid (position, velocity and acceleration) without consideration of forces producing the motion Fluid Dynamics Analyses of fluid motion in relation to forces producing the motion

Fluid kinematics Inflow CV-I Fixed control surface and system System boundary at time r System boundary at time t+ or o A definite mass of matter which distinguishes it from its surrounding matter e Has constant mass System boundary moves Used in bernoulli's equation Control volume(c v) Definite region in space enclosed by control surfaces, fixed relative to observer Control Volume boundary is fixed e Mass can flow in or out of c. v Used in Continuity and momentum equations

Fluid kinematics System • A definite mass of matter which distinguishes it from its surrounding matter • Has constant mass • System boundary moves • Used in Bernoulli’s equation Control Volume (C.V.) • Definite region in space enclosed by control surfaces, fixed relative to observer • Control Volume boundary is fixed • Mass can flow in or out of C.V. • Used in Continuity and Momentum equations

Flow Analyses Eulerian method Fluid motion and properties(pressure, density, velocity etc)are described as functions of space and time Lagrangian Method Follows the motion of individual fluid particles determines how the fluid properties of the particles change with time Location o: T=7(xo, yo, r) Particle A I、=T(t)

Flow Analyses Eulerian Method Fluid motion and properties (pressure, density, velocity etc) are described as functions of space and time Lagrangian Method Follows the motion of individual fluid particles determines how the fluid properties of the particles change with time

Flow kinematics Streamline Imaginary line through fluid such that at an instant, velocity of ever particle on the line is tangent to it Stream-tube Imaginary tube formed by all streamlines passing through a closed curve no fluid can enter or leave a stream tube except through its ends Used in continuity equation

Flow kinematics Streamline : Imaginary line through fluid such that at an instant, velocity of ever particle on the line is tangent to it Stream-tube Imaginary tube formed by all streamlines passing through a closed curve. No fluid can enter or leave a stream tube except through its ends Used in continuity equation