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Fluids ### Properties

The difference between Fluids and other Substances.

Matter is primarily found in three forms: solids, liquids and gases. Gases and liquids together are called fluids. The molecules of a solid are usually mutually closer than those of a fluid. The attractive forces between the molecules of a solid are so large that a solid tends to retain its shape. This is not the case for a fluid, where the attractive forces between the molecules are smaller. There are plastic solids, which flow under the proper circumstances, and even metals may flow under high pressures. On the other hand there are certain viscous fluids liquids that do not flow readily and is easy to confuse them with plastic solids. The distinction is that any fluid, no matter how viscous will yield in time to the slightest stress. But a solid, no matter how plastic, requires a certain magnitude of stress to be exerted before it will flow. Also when the shape of a solid is altered by external forces, the tangential stresses between adjacent particles tend to restore the body to its original configuration. With a fluid, these tangential stresses depend on the velocity of deformation and vanish as the velocity approaches zero. When motion ceases, the tangential stresses disappear and the fluid does not regain its original shape.

Properties of fluids:

• Density, Specific weight, specific volume and specific gravity: The density of a fluid is its mass per unit volume, while the specific weight is the weight per unit volume. They are related as g = r g. The specific volume n is the volume occupied by a unit mass of fluid. Specific volume is the reciprocal of density. n = 1/ r. Specific gravity s of a liquid is the ratio of its density to the density of water at a standard temperature. Engineers use 600F as this temperature. Specific gravity of a gas is the ratio of its density to the density of hydrogen or air at some specified temperature and pressure.
• Compressible and incompressible fluids: Fluids may be either of a constant or variable density. There is nothing like an incompressible fluid, but the term is applied to those fluids whose density changes negligibly with pressure. Liquids are ordinarily considered incompressible fluids, but sound travels through them demonstrating that they are elastic.
• Compressibility: This is defined as the change in volume due to change in pressure. It is inversely proportional to its volume modulus of elasticity, also known as bulk modulus. The bulk modulus is analogous to the modulus of elasticity of solids; however for fluids it is defined on a volume basis.
• Vapour pressure of liquids: As all liquids tends to evaporate or vaporize, which they do by projecting molecules into the space above their surfaces. The pressure exerted by the molecules increases till some of the molecules start re-entering the liquid. This pressure is called the vapour pressure.

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### Viscosity

Viscosity: The viscosity of a fluid is a measure of its resistance to shear or angular deformation. In other words, viscosity of a fluid is that property which determines the amount of resistance to a shearing force. It is due primarily to interaction between fluid molecules. The friction forces in fluid flow result from cohesion and momentum interchange between molecules in the fluid. This decides that as temperature increases the viscosities of all liquids decrease and those of all gases increase. Viscosity of a fluid can be expressed in two ways:
• Kinematic viscosity
• Dynamic viscosity
Viscosities of liquids decrease with temperature increases but are unaffected by pressure changes.

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### Fluid flow in a pipe

The fluid flow in a pipe is governed by the following equation:

dp + r vdv + dZ = 0
where P is the pressure, r is the density and Z is the head of the fluid.

Integrating the equation,

P + (1/2)r v2 + Z = C
C is any arbitrary constant.

This can also be written as

P1 + (1/2) r v12 + Z1 = P2 + (1/2) r v22 + Z2
where the subscripts 1 and 2 denote any two positions.

This equation is called Euler's equation and it implies that at different points in the pipe the energy of the fluid is constant. This equation does not take the frictional losses in the pipe into account.

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### Static Pressure, Dynamic Pressure and Total Pressure

Static pressure is that which would be measured by an instrument moving with the flow. However, it is rather difficult to make this measurement in a practical situation. Stagnation pressure is obtained when the flowing fluid is decelerated to zero speed by a friction less process. This is also called the total pressure and

P0 = P + (1/2) r v2
Where P0 = stagnation pressure or total pressure
P = static pressure
r = density of the fluid
v = velocity of flow.

The term (1/2) r v2 has the dimensions of pressure and is called the dynamic pressure of the fluid.

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Head loss is defined as the loss of energy per unit mass of the fluid. It represents the irreversible conversion of mechanical energy to an unwanted thermal energy and loss of this energy via heat transfer. Head loss can be regarded as a sum of ‘major losses’, which are due to frictional effects in fully developed flow in constant area tubes and minor losses due to entrances, fittings, area changes and so on.

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### Fluid Hammer

When a valve in a pipe with a flowing fluid is suddenly closed, a fluid hammer pressure wave is set up. The very high pressures generated by such waves can damage the pipe. The maximum pressure generated by the fluid hammer ph is a function of the fluid density r , initial flow speed u0 and the velocity of the pressure wave set up in the pipe cp.

ph = f (r , u0, cp ).

The fluid hammer causes pressure fluctuations in the fluid in the pipe because of which the pipe expands and contracts. This is a critical problem in case of power plants, where the flow of water must be varied rapidly in proportion to the load changes on the turbine. Incidentally, the pressure wave is always set up as a result of abrupt decrease in velocity.

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### Reynolds Number

The Reynolds number is a dimension less constant which determines the type of flow in a pipe. It represents the ratio of inertial forces to the viscous forces.

For circular pipes flowing full, Reynolds number

Re = (VDr /m ) = (VD/n )
where V = mean velocity of fluid
D = diameter of the pipe
n = kinematic viscosity f the fluid
r = mass density of the fluid
m = absolute viscosity of the fluid.

For non circular cross sections, the ratio of the cross sectional area to the wetted perimeter is used as the Reynolds number.

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### Laminar & Turbulent Flow

In laminar flow fluid particles move along straight, parallel paths in layers or laminae. The magnitudes of velocities of adjacent laminae are not the same. Shear stress and rate of angular deformation govern this type of flow. The viscosity of the fluid is dominant and thus suppresses any tendency to turbulent conditions. The Reynolds number determined for this type of flow is less than 2000. At a given cross section the velocity distribution follows a parabolic law of variation for a laminar flow. The maximum velocity at the centre of the pipe is twice the average velocity.
In turbulent flow the particles of the fluid move in a haphazard fashion in all directions. It is impossible to trace the motion of an individual particle. There is more uniform distribution of velocity. The Reynolds number determined for a turbulent flow is greater than 2000.

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### Critical Velocity

The critical velocity of practical interest to engineers is the velocity below which all turbulence is damped out is damped out by the viscosity of the fluid. The Reynolds number for upper limit of laminar flow is about 2000.

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