The objective of this section is to give an essential idea about Fluid Mechanics that students need to know before they start to perform an experiment. This section will be divided into three major
subsections which is ‘Fluid Properties’, ‘Fluid Visualization’ and ‘Basic Governing Equation for Fluid Flow’. The way it is written is very brief so that students may need to refer to their reference book(s) in order to get more explanation. The suggested references are given at ‘References’.
Fluid Properties
1. Measure of Fluid Mass and Weight 1.1. Density,
1.1.1. Is defined as mass per unit volume
1.1.2. Liquid have small effects of pressure and temperature while gaseous are strongly influenced by the change of pressure and temperature
1.1.3. For ideal gas, we can relate density with pressure and temperature by using ideal gas law
1.2. Specific Weight, γ
1.2.1. Is defined as weight per unit volume
1.3. Specific Gravity, SG
1.3.1. Is ratio of the density of the fluid to the density of water at some specified temperature (usually at 4°C)
2. Viscosity
2.1. Describe the “fluidity” of the fluid
2.2. It also indicates the internal resistance of the fluid to a motion
2.3. Also shows tendency of a fluid to stick to other substance or other fluid
2.4. Fluid that the shearing stresses are linearly related to the rate of shearing strains is called as Newtonian Fluid while fluid behave oppositely is known as Non-Newtonian Fluid
2.5. Non-Newtonian fluid can generally be classified to three type which is Bingham Plastic (e.g.
toothpaste), shear thickening fluid (e.g. starch) and shear thinning fluid (e.g. paint) 2.6. Dynamic viscosity usually referred to as viscosity only
2.7. Kinematic viscosity is the ratio of viscosity (dynamic viscosity) to the density of the fluid.
3. Pressure
3.1. Is defined as force per unit area.
3.2. Pressure at a point in a fluid at rest, or in motion, is independent of direction as long as there are no shearing stresses present.
3.3. Pressure decreases as we move vertically upward in a fluid at rest.
3.4. For incompressible fluid
3.4.1. Pressure variation in an incompressible fluid is shown as
3.4.2. Pressure head is a height of a column of fluid of specific weight, γ required to give pressure, P or pressure difference P1-P2.
3.5. For compressible fluid
3.5.1. Integrate equation of motion for fluid at rest to obtain pressure variation within compressible fluid.
3.5.2. In integrating this equation, we need to know how the density, thus specific weight, changes with elevation change.
3.6. Manometer 3.6.1. Piezometer
3.6.2. U-tube manometer
3.6.3. Inclined tube manometer
3.7. Designation of pressure 3.7.1. Absolute pressure
3.7.1.1. Measured pressure relative to the perfect vacuum pressure (absolute zero pressure)
3.7.1.2. Have only positive value 3.7.2. Gage pressure
3.7.2.1. Measured pressure relative to the local atmospheric pressure
3.7.2.2. Have positive or negative value which indicates either larger or smaller than local atmospheric pressure.
Fundamental of Fluid Visualizations 1. Streamline
1.1. A streamline is a curve that is everywhere tangent to the instantaneous local velocity vector.
1.2. Streamlines (solid black curves) for the steady, incompressible, two-dimensional velocity field; where the velocity given by
and velocity vectors (pink arrows) are superimposed for comparison.
2. Streak Line
2.1. A streakline is the locus of fluid particles that have passed sequentially through a prescribed point in the flow.
2.2. A streakline is formed by continuous introduction of dye or smoke from a point in the flow.
Labeled tracer particles (1 through 8) were introduced sequentially.
3. Timeline
3.1. A timeline is a set of adjacent fluid particles that were marked at the same (earlier) instant in time.
3.2. Timelines are formed by marking a line of fluid particles, and then watching that line move (and deform) through the flow field; timelines are shown at t = 0, t1, t2, and t3.
4. Path Line
4.1. A pathline is the actual path traveled by an individual fluid particle over some time period.
4.2. A pathline is formed by following the actual path of a fluid particle.
5. Streamlines, Streaklines and Pathlines for steady flow
Basic Governing Equation for Fluid Flow 1. Control mass
1.1. mass of matters chosen for analysis
1.2. mass is absolutely not allow to move across the boundary but energy maybe move across 1.3. if the energy also not allow to move across then we call it as isolated control mass 2. Control volume
2.1. region in space that been chosen for analysis purpose
2.2. mass and energy allowed to move across it boundary or control surface.
3. Conservation of Mass
3.1. For a mass of a system, conservation of mass states that the time rate of change of mass of system is equal to zero.
3.2. For a control volume, it states that the time rate of change of the mass of the contents of the control volume plus the net rate of mass flow through the control surface must equal zero.
3.3. For steady, incompressible flow, the equation reduced to A1V1 = A2V2, where A is the cross section area and V is the flow velocity.
4. Conservation of Linear Momentum (Newton’s 2nd Law)
4.1. For a system, the conservation of linear momentum follows the Newton 2nd Law which states that time rate of change of the linear momentum of the system is equal to the sum of external forces acting on the system
4.2. For a fixed and non deforming control volume, the conservation of linear momentum states that the sum of external forces acting on the control volume is equal to the sum of the two control volume quantities: the time rate of change of the linear momentum of the contents of the control volume, and the net rate of linear momentum flow through the control surface.
5. Conservation of Energy (First Law of Thermodynamics)
5.1. The first law of thermodynamics for a system, in words, stated that the time rate of increase of the total stored energy of the system is equal to sum of the net time rate of energy addition by heat transfer into the system and the net time rate of energy addition by work transfer into the system.
where e is energy per unit mass.
5.2. For a control volume it states that, the sum of the time rate of the total stored energy of the contents of the control volume and the net rate of flow of the total stored energy out of the control volume through the control surface is equal to the sum of the net time rate of energy addition by heat transfer into the control volume and the net time rate of energy addition by work transfer into the control volume.
5.3. In application of this equation, it needs careful interpretation and consideration of each term.
5.4. Work can be transferred by 5.4.1. moving shaft or shaft work
5.4.2. force associated with fluid normal stress 5.4.3. force associated with fluid tangential stress 5.5. For flow where the work by tangential force is zero,
5.6. Extended Bernoulli Equation (steady-in-the mean-flow, one dimensional flow)
or
where
and
5.7. Modified Bernoulli equation where no shaft work involves in the steady one dimensional flow.
or
with
5.8. Bernoulli equation
6. Bernoulli equation 6.1. Restriction
6.1.1. One dimensional flow or applicable along a streamline 6.1.2. Incompressible flow
6.1.3. Inviscid flow or frictionless flow 6.1.4. Steady flow
6.1.5. No shaft work involves
6.2. Pressure terms
6.2.1. The first term is called static pressure or the actual thermodynamics pressure 6.2.2. Second term is called dynamic pressure
6.2.3. Third term is called hydrostatic pressure 6.2.4. The fourth term is the total pressure
6.2.5. The summation of dynamic and static pressure is called stagnation pressure where the velocity at that point is equal to zero