fluid mechanics

FLUID MECHANICS

C.SURESHM140539ME

Fluid Concept• Fluid mechanics is a division in applied mechanics related to

the behaviour of liquid or gas which is either in rest or in motion.

• The study related to a fluid in rest or stationary is referred to fluid static, otherwise it is referred to as fluid dynamic.

• Fluid can be defined as a substance which can deform continuously when being subjected to shear stress at any magnitude. In other words, it can flow continuously as a result of shearing action. This includes any liquid or gas.

SOLID• More Compact Structure• Attractive Forces between the

molecules are larger therefore more closely packed

• Solids can resist tangential stresses in static condition.

• Whenever a solid is subjected to shear stress

a. It undergoes a definite deformation α or breaks

b. α is proportional to shear stress up to some limiting condition

LIQUID• Less Compact Structure• Attractive Forces between the

molecules are smaller therefore more loosely packed

• Fluids cannot resist tangential stresses in static condition

• Whenever a fluid is subjected to shear stress a. No fixed deformation

b. Continuous deformation takes place until the shear stress is applied

Fluid Concept• Thus, with exception to solids, any other matters can be

categorised as fluid. In microscopic point of view, this concept corresponds to loose or very loose bonding between molecules of liquid or gas, respectively.

• Examples of typical fluid used in engineering applications are water, oil and air.

• An analogy of how to understand different bonding in solids and fluids is depicted in Fig. 1.1

1.1 Fluid Concept

Figure 1.1 Comparison Between Solids, Liquids and Gases

• For solid, imagine that the molecules can be fictitiously linked to each other with springs.

(a) Solid (b) Liquid (c) Gas

k

k k

k

Free surface

1.1 Fluid Concept In fluid, the molecules can move freely but are constrained

through a traction force called cohesion. This force is interchangeable from one molecule to another.

For gases, it is very weak which enables the gas to disintegrate and move away from its container.

For liquids, it is stronger which is sufficient enough to hold the molecule together and can withstand high compression, which is suitable for application as hydraulic fluid such as oil.

THE NO-SLIP CONDITION

• It important to understand how the presence of solid surfaces affects fluid flow

• Consider the flow of a fluid in a stationary pipe or over a solid surface that is nonporous. All experimental observations indicate that a fluid in motion comes to a complete stop at the surface and assumes a zero velocity relative to the surface.

• That is, a fluid in direct contact with a solid “sticks” to the surface due to viscous effects, and there is no slip. This is known as the no-slip condition.

THE NO-SLIP CONDITION

CONTINUUM

• The concept of continuum is a kind of idealization of the continuous description of matter where the properties of the matter are considered as continuous functions of space variables.

• Although any matter is composed of several molecules, the concept of continuum assumes a continuous distribution of mass within the matter or system with no empty space, instead of the actual conglomeration of separate molecules.

• In continuum approach, fluid properties such as density, viscosity, thermal conductivity, temperature, etc. can be expressed as continuous functions of space and time.

1.3 Fluid Continuum• Since the fluid flows continuously, any method and technique

developed to analyse flow problems should take into consideration the continuity of the fluid. There are two types of approaches that can be used:

1.Eulerian approach — analysis is performed by defining a control volume to represent fluid domain which allows the fluid to flow across the volume. This approach is more appropriate to be used in fluid mechanics.

• In the eulerian method we compute the pressure field p(x, y, z, t) of the flow pattern, not the pressure changes p(t) that a particle experiences as it moves through the field.

• Lagrangian approach — The second method, which follows an individual particle moving through the flow, is called the lagrangian description. The lagrangian approach, which is more appropriate to solid mechanics

1.3 Fluid Continuum The fluid behaviour in which its properties are continuous field

variables, either scalar or vector, throughout the control volume is known as continuum. From this concept, several fluid or flow definitions can be made as follows:

Steady state flow — A flow is said to be in steady state if its properties is only a function of position (x,y,z) but not time t:

x,y,z), V = V x,y,z)

An example is the velocity of a steady flow of a river where the upstream and downstream velocities are different but their values does not change through time.

1.3 Fluid Continuum• Uniform flow — A flow is said to be uniform if its

velocity and all velocity components is only a function of time t:

• V = V t)An example is the air flow in a constant diameter duct where the velocity is constant throughout the length of the duct but can be increased uniformly by increasing the power of the fan.

• Isotropic fluid — A fluid is said to be isotropic if its density is not a function of position (x,y,z) but may vary with time t:

t) An example is the density of a gas in a closed container where the container is heated. The density is constant inside the container but gradually increases with time as the temperature increases.

Thermodynamic Propertiesof a Fluid

• While the velocity field V is the most important fluid property, it interacts closely with the thermodynamic properties of the fluid. The three most common such properties are

1. Pressure p 2. Density 3. Temperature T• In addition, friction and heat conduction effects are governed

by the two so-called transport properties 8. Coefficient of viscosity 9. Thermal conductivity

PRESSURE

• The pressure p is the most dynamic variable in fluid mechanics. Differences or gradients in pressure often drive a fluid flow, especially in ducts.

• In low-speed flows, the actual magnitude of the pressure is often not important, unless it drops so

• Low as to cause vapor bubbles to form in a liquid. For convenience, we set many such problem assignments at the level of 1 atm = 101,300 Pa.

1.5 Density• Density of a fluid, , • Definition: mass per unit volume, slightly affected by changes in temperature and

pressure. •

• = mass/volume = m/• • Units: kg/m3•

• Typical values:• Water = 1000 kg/m3; Air = 1.23 kg/m3

1.6 Viscosity• Viscosity, , is a measure of resistance to fluid flow as a result

of intermolecular cohesion. In other words, viscosity can be seen as internal friction to fluid motion which can then lead to energy loss.

• Different fluids deform at different rates under the same shear stress. The ease with which a fluid pours is an indication of its viscosity. Fluid with a high viscosity such as syrup deforms more slowly than fluid with a low viscosity such as water. The viscosity is also known as dynamic viscosity.

Units: N.s/m2 or kg/m/s

Typical values: Water = 1.14x10-3 kg/m/s; Air = 1.78x10-5 kg/m/s

Example:AirWaterOilGasolineAlcoholKeroseneBenzeneGlycerine

Fluid Newton’s law

of viscosity

Newtonian fluids obey refer

Newton’s’ law of viscosity is given by;

dy

du

•The viscosity is a function only of the condition of the fluid, particularly its temperature.

•The magnitude of the velocity gradient (du/dy) has no effect on the magnitude of .

= shear stress = viscosity of fluiddu/dy = shear rate, rate of strain or velocity gradient

Newtonian and Non-Newtonian Fluid

Fluid Newton’s law

of viscosity

Non- Newtonianfluids

Do not obey

• The viscosity of the non-Newtonian fluid is dependent on the velocity gradient as well as the condition of the fluid.

Newtonian Fluidsa linear relationship between shear stress and the velocity

gradient (rate of shear), the slope is constant the viscosity is constant

non-Newtonian fluids slope of the curves for non-Newtonian fluids varies


If the gradient m is constant, the fluid is termed as Newtonian fluid. Otherwise, it is known as non-Newtonian fluid. Fig. 1.5 shows several Newtonian and non-Newtonian fluids.


Definition: is the ratio of the viscosity to the density;

• will be found to be important in cases in which significant viscous and gravitational forces exist.

Units: m2/s

Typical values: Water = 1.14x10-6 m2/s; Air = 1.46x10-5 m2/s;

In general, viscosity of liquids with temperature, whereas

viscosity of gases with in temperature.

/

Kinematic viscosity,

Specific WeightSpecific weight of a fluid, • Definition: weight of the fluid per unit volume • Arising from the existence of a gravitational force • The relationship and g can be found using the following:

Since = m/therefore = g (1.3)

Units: N/m3

Typical values:Water = 9814 N/m3; Air = 12.07 N/m3

The specific gravity (or relative density) can be defined as:

Definition 1: A ratio of the density of a liquid to the density of water at (4C, 1 atm), or

Unit: dimensionless.

Specific Gravity

STPwater

liquid

STPwater

liquidSG@@

STPair

gas

STPair

gasSG@@

1.7 Surface Tension• Surface tension coefficient s can be defined as the intensity of

intermolecular traction per unit length along the free surface of a fluid, and its SI unit is N/m.

• The surface tension effect is caused by unbalanced cohesion forces at fluid surfaces which produce a downward resultant force which can physically seen as a membrane.

• The coefficient is inversely proportional to temperature and is also dependent on the type of the solid interface.

• For example, a drop of water on a glass surface will have a different coefficient from the similar amount of water on a wood surface.

1.7 Surface Tension• The effect may be becoming significant for small fluid system

such as liquid level in a capillary, as depicted in Fig. 1.6, where it will decide whether the interaction form by the fluid and the solid surface is wetted or non-wetted.

• If the adhesion of fluid molecules to the adjacent solid surface is stronger than the intermolecular cohesion, the fluid is said to wet on the surface. Otherwise, it is a non-wetted interaction.

1.8 Vapour Pressure• Vapour pressure is the partial pressure produced by fluid

vapour in an open or a closed container, which reaches its saturated condition or the transfer of fluid molecules is at equilibrium along its free surface.

• In a closed container, the vapour pressure is solely dependent on temperature. In a saturated condition, any further reduction in temperature or atmospheric pressure below its dew point will lead to the formation of water droplets.

• On the other hand, boiling occurs when the absolute fluid pressure is reduced until it is lower than the vapour pressure of the fluid at that temperature.

• For a network of pipes, the pressure at a point can be lower than the vapour pressure, for example, at the suction section of a pump. Otherwise, vapour bubbles will start to form and this phenomenon is termed as cavitation.

COMPRESSIBILITY AND BULKMOULUS

• The volume (or density) of a fluid changes with a change in its temperature or pressure. Fluids usually expand as they are heated or depressurized and contract as they are cooled or pressurized.

• But the amount of volume change is different for different fluids, and we need to define properties that relate volume changes to the changes in pressure and temperature.

• Compressibility is the reciprocal of bulk modulus of elasticity K ,Which is defined as ratio of compressive stress to the volumetric strain

SYSTEM AND CONTROL VOLUME

• A system is defined as a quantity of matter or a region in space chosen for study.

• The mass or region outside the system is called the surroundings.

• The real or imaginary surface that separates the system from its surroundings is called the boundary. The boundary of a system can be fixed or movable

• Systems may be considered to be closed or open, depending on whether a fixed mass or a volume in space.

• A closed system (also known as a control mass) consists of a fixed amount of mass, and no mass can cross its boundary. But energy, in the form of heat or work, can cross the boundary, and the volume of a closed system does not have to be fixed.

• control volume it is a volume fixed in a space or moving with constant velocity through which the fluid flows.

• The surface enclosing the control volume is referred to as the control surface.

• Both mass and energy can cross the boundary of a control volume.

fluid mechanics

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