*Fluid PropertiesThe properties outlines below are general properties of fluids which are of interest in engineering.

DensityThe density of a substance is the quantity of matter contained in a unit volume of the substance. It can be expressed in three different ways.Mass Densitythe mass of substance per unit volume.Specific Weightthe weight of substance per unit volume.Relative Density the ratio of mass density of a substance to some standard mass density.

Viscosityis the property of a fluid, due to cohesion and interaction between molecules, which offers resistance to sheer deformation. Coefficient of Dynamic Viscosity is defined as the shear force, per unit area.Kinematic Viscosity is defined as the ratio of dynamic viscosity to mass density.

Pressure and Velocity

*Forces in FluidsIn general, fluids exert both normal and shearing forces on surfaces that are in contact with them. Fluids with velocity gradients produce shearing forces. For fluids at rest, only normal forces exist. These normal forces in fluids are called pressure forces.Two important properties in the study of fluid mechanics are: Pressure and Velocity.The direction of pressure forces will always be perpendicular to the surface of interest.The rate of change of position in a flow field is called velocity. It is used not only to specify flow field characteristics but also to specify flow rate, momentum and viscous effects for a fluid in motion.

*Fluid StaticsDefinition of PressureAt every point in a static fluid a certain pressure intensity exists. Specifically, this pressure intensity called pressure, is defined as follows:Where F is the normal force acting over the area A.Pressure intensity is a scalar quantity, that is, it has magnitude only and acts equally in all directions.Pressure TransmissionIn a closed system a pressure change produced at one point in the system will be transmitted throughout the entire system. The principle is known as Pascals law after Blaise Pascal, the French scientist who first stated it in 1653.This phenomenon of pressure transmission has led to the widespread development of hydraulic controls for operating equipments.

*Basic Differential EquationConsider the differential element (dx, dy, dz) of static fluid of constant density as shown in figure.Assume that the pressure at the center of the element is p. The forces acting on the fluid element in the vertical direction are:The body force, the action of gravity on the mass within the elementThe surface forces, transmitted from the surrounding fluid and acting at right angles against the top, bottom, and sides of the element.At rest, the summation of forces in any direction must be zero. To satisfy Fx= 0 and Fy = 0, the pressures on the opposite vertical faces must be equal. Thus p/x = p/y = 0

*dzdxdyxyzdxdydzBDEPDifferential Element of Fluid

*Taylors SeriesTopBottomWhich indicates that pressure is independent of coordinates x and y; it depends on z alone. Thus since p is a function of a single variable, a total derivative may be used instead of a partial derivative.The minus sign indicates that as z gets larger (increasing elevation), the pressure gets smaller. BDEor

*Pressure Variation for a Uniform-density FluidWith constant specific weight, integration of above equation resultThe sum of the terms p/ and z is called the Piezometric head.We can relate the pressure and elevation at one point to the pressure and elevation at another point in the fluid as:BDEorDatum

*Flow ClassificationIdeal or Real FlowLaminar or Turbulent FlowCompressible or Incompressible flowSteady or Unsteady FlowUniform or Non-uniformOne, two or three dimensional

*Possible Classification of Continuum Fluid MechanicsContinuum Fluid MechanicsIn viscidViscousLaminarTurbulentInternalExternalCompressibleIncompressible

*Compressible or IncompressibleAll fluids are compressible -even water- their density will change as pressure changes. Under steady conditions, and provided that the changes in pressure are small, it is usually possible to simplify analysis of the flow by assuming it is incompressible and has constant density. As you will appreciate, liquids are quite difficult to compress - so under most steady conditions they are treated as incompressible. In some unsteady conditions very high pressure differences can occur and it is necessary to take these into account - even for liquids. Gasses, on the contrary, are very easily compressed, it is essential in most cases to treat these as compressible, taking changes in pressure into account.

*Steady and Uniform FlowSteady FlowSteady flow means steady with respect to time. Thus all properties of the flow at every point remain constant with respect to time.Unsteady FlowThe flow properties at a point change with time.Uniform FlowIn which the velocity is the same in both magnitude and direction at a given point in the field.Non-uniform Flow

*ExamplesCombining the above we can classify any flow in to one of four type:

Steady uniform flow. Conditions do not change with position in the stream or with time. An example is the flow of water in a pipe of constant diameter at constant velocity.Steady non-uniform flow. Conditions change from point to point in the stream but do not change with time. An example is flow in a tapering pipe with constant velocity at the inlet - velocity will change as you move along the length of the pipe toward the exit.Unsteady uniform flow. At a given instant in time the conditions at every point are the same, but will change with time. An example is a pipe of constant diameter connected to a pump pumping at a constant rate which is then switched off.Unsteady non-uniform flow. Every condition of the flow may change from point to point and with time at every point. For example waves in a channel.

*Flow PatternsUniform flow in open channel 1. Streamlines must be straight and parallelUniform flow in pipe2. If Streamlines are not parallel, there will be a change of speed along the streamlines. If they are not straight, there will be directional change of velocity.Vortex flowNon-uniform flow, converging flow

*Visualization of Fluid FlowThree basic types of lines used to illustrate fluid flow patterns:Streamline: a line that is everywhere tangent to the local velocity vector at a given instant.Pathline: a line that represents the actual path traversed by a single fluid particle.Streakline: a line that represents the locus of fluid particles at a given instant that have earlier passed through a prescribed point.

*Flow PathsStreamlines are useful in fluid flow analysis, but are difficult to observe experimentally for unsteady flows.

The pathline is a Lagrangian concept that can be visualized in the laboratory by marking a fluid particle and taking a time exposure photograph of its trajectory.

The streakline can be visualized in the laboratory by continuously marking all fluid particles passing through a fixed point and taking an instantaneous photograph.

Streamlines, pathlines, and streak-lines are identical for steady flows.

*Velocity-description1. Lagrangian Approach:Consider an individual fluid particle for all time. Using the Cartesian coordinate system, the particles position vector is expressed asr(t) = xi + yj +zk(1)Where i. j and k are the unit vectors in the X, Y and Z directions.Differentiating Equation #1 with respect to time, we obtain the velocity of the fluid particle and acceleration:We can use Newtons law of motion (F=ma) on the body to determine the acceleration and thus, the velocity and position. However, in fluid mechanics, it is difficult to track a single fluid particle. But in the lab we can observe many particles passing by one single location.Where u, v and w are the component velocities in their respective coordinates directions.

*2. Eulerian ApproachIn this case, the fluid particle velocity depends on the point in space and timeu = f1(x,y,z,t)v = f2(x,y,z,t)w = f3(x,y,z,t)(1)In order to describe the entire flow field, we must know the fluid motion at all points in the field. Equation (1) give the component velocities as a function of space and time in the Cartesian coordinate system,

But there is another useful way of expressing velocity by using the Eulerian viewpoint to describe the total velocity as function of position along a streamline and time. This is given as:V = V(s,t)

*AccelerationThe acceleration of a fluid particle is the rate of change of a particles velocity with time. It is a vector quantity, it can be caused due to change in magnitude or direction (or both) of the velocity vector.By the Eulerian approach, the velocity components are function of space and timeV = u i + v j + w ku = f1(x,y,z,t)v = f2(x,y,z,t)w = f3(x,y,z,t)(1)The acceleration of a fluid particle in the x-direction is given by ax = du/dtBy using the chain rule for differentiation of a multivariable function u= f1(x, y, z, t)

*AccelerationIn time dt, the fluid particle moves in the x-direction a distance dx = u dt, sou = dx /dt and similarly v = dy/dt and w = dz/dtLocal AccelerationConvective Acceleration

*AccelerationConvective AccelerationChange of velocity with respect to positionIt occurs when the flow is non-uniform that is, when the velocity changes along a streamline.

Local AccelerationChange of velocity with respect to time at a given pointLocal acceleration results when the flow is unsteadyIt is acceleration component tangential to the streamline

FM-1-PropertiesProf. Dr. Taj Ali Khan, UET Peshawar*Prof. Dr. Taj Ali Khan, UET PeshawarFM-1-PropertiesProf. Dr. Taj Ali Khan, UET Peshawar*Prof. Dr. Taj Ali Khan, UET PeshawarFM-1-PropertiesProf. Dr. Taj Ali Khan, UET Peshawar*Prof. Dr. Taj Ali Khan, UET PeshawarFM-1-PropertiesProf. Dr. Taj Ali Khan, UET Peshawar*Prof. Dr. Taj Ali Khan, UET PeshawarFM-1-PropertiesProf. Dr. Taj Ali Khan, UET Peshawar*Prof. Dr. Taj Ali Khan, UET PeshawarFM-1-PropertiesProf. Dr. Taj Ali Khan, UET Peshawar*Prof. Dr. Taj Ali Khan, UET Peshawar