PRINCIPLES OF FLUID

PRINCIPLES OF FLUIDLECTURER: MADAM NOR AMANI FILZAH BT. MOHD KAMILROOM: PROF MADYA 4, LEVEL 3, SOUTH TOWER 0137705583

1.1Introduction to Fluid Mechanics

1.2Thermodynamic Properties of a FluidContentsIntroduction to Fluid MechanicsThis subject is focus on scientific study related to fluid flow in closed conduit (e.g pipe) and open channel (e.g river).FLUID MECHANICSBehavior of fluidFLUID STATIC (at rest)FLUID DYNAMIC (in motion)

APPLICATION OF FLUID ENGINEERINGBlood flow

Pump

Pipes

Filters

Ship

Ability of substance to resist an applied shear (or tangential) stress that tends to change its shape.Solid: molecules can be fictitiously linked to each other with springs. Difference between fluid and solidF

LiquidSolidFHigh abilityLow abilityRequired supporting walls to eliminate shear stressIf walls are remove, shear develops in the liquid and resulted in a big splash.

LiquidGasThermodynamic Properties of a FluidDefinition: mass per unit volume, = mass/volume = m/ Units: kg/mTypical values:Water = 1000 kg/m; Air = 1.23 kg/m1. Density, slightly affected by changes in temperature and pressure. E.g., Water: Increase 1% if the pressure increase by factor of 220. In liquid, density is nearly constant.

1. Density, Temperature (C)Density (kg/m)0999.810999.220998.230995.740992.350988.0100958.4Density of water changes at 4.14% - can be neglected in engineering analysesA ratio of the density of a liquid to the density of water at standard temperature and pressure (20C, 1 atm)

Unit: dimensionlessSpecific Gravity, SG (or relative density)

v = V = 1 m Unit: m/kg Specific Volume, vSpecific weight, ss = g= density 9.81 Example 1 :A reservoir of glycerin as a mass of 1200 kg and a volume of 0.952 m3. Find the glycerins weight (W), density (), specific weight ( ) and specific gravity (s.g)

Answer 1 :

Weight, W = mg = (1200)(9.81) = 11770N or 11.77kN

Density, = m/V = 1200/0.952 = 1261 kg/m3

Specific weight, = g = (1261)(9.81) = 12.37 kN/m3 (atau W/V)

Specific gravity, SG substance / water at 4oC = 12.37k/9.81k = 1.26

Change in volume of liquid that subjected to change in pressure to characterize compressibility of fluid)E = - dpdV/VBulk Modulus, E (or Compressibility)Pressure changesInitial volumevolume changesA liquid compressed in a cylinder has a volume of 1000 cm3 at 1 MN/m2 and a volume of 995 cm3 at 2 MN/m2. What is its bulk modulus (E)?

16Example 2 :

Answer 2:Represents the internal resistance of fluid flow. The force a flowing fluid exerts on a body in the flow direction is called drag force. Fluid with a high viscosity such as syrup deforms more slowly than fluid with a low viscosity such as waterDrag force increase with densityViscosity,

Drag forceExample:AirWaterOilGasolineAlcoholKeroseneBenzeneGlycerineFluidNewtons lawof viscosityNewtonian fluids obeyreferNewtons law of viscosity is given by;

= shear stress = viscosity of fluiddu/dy = shear rate, rate of strain or velocity gradientNewtonian and Non-Newtonian FluidFluidNewtons lawof viscosityNon- NewtonianfluidsDo not obeyNewtonian and Non-Newtonian FluidThe 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

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

Newtonian and Non-Newtonian Fluid

Units: N.s/m, kg ms, Poise (P)

Dynamic Viscosity, TemperatureLiquidGasesviscosity of liquids with temperature,

viscosity of gases with in temperature

Example 3 :A plate separated by 0.5 mm from a fixed plate moves at 0.5 m/s under a force per unit area of 4.0 N/m2. Determine the viscosity of fluid between the plates.

4.0 N/m20.0005 m

0.5 m/sDefinition: is the ratio of the viscosity to the density;

Units: m2/s

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

Surface Tension, sWater droplets from leaves.Behave like small spherical balloon filled with water.Surface of water acts like a stretched elastic membrane under tension. Pulling force that cause this tension acts parallel to the surface and is due to the attractive forces between molecules in the water. Magnitude force/length = surface tension

Unit: N/ms = F 2bHow surface tension arises?Interior molecule balance each other due to symmetrySurface molecule not symmetry, force from gas molecule smaller than liquid molecule. Therefore, tend to pull molecule on surface toward the interior of the liquid. Force is balance by repulsive force from bottom moleculesResulting compression effect causes the liquid to minimize its surface area tendency liquid dropletsto spherical shape .

Surface Tension, s

For interior of liquid cylinder,

A spherical droplet,

The pressure difference between 2 surfaces of soap bubbles,26Surface Tension, s

R=radiusAn atomizer forms water droplets 45m in diameter. Find the excess pressure within these droplets for water at 30oC.

Answer 4:

= 0.0712 N/m for air-water interface = 0.480 N/m for air -mercury interface

27Example 4 :

Rise or fall of liquid in small diameter tube inserted into the liquid

Cohesive forces: forces between molecules (water & water)Adhesive forces: forces between water & glass. cohesion forces > adhesion forces - waterCapillary effectWet the surface < 90Not wet the surface > 90Increasing of liquids level in tube can be estimated if angle, which is between wall and liquid are known. W = mg = Vg = (Rh)gW = Fsurface = 2Rs cos

h = 2s cos gR

Capillary effect

Find the capillary rise in the tube for a mercury-air-glass interface with 130oC if the tube radius is 1mm and the temperature is 20oC.

30Example 5 :Answer 5 :

31Next slides (pg 32- pg 36) are show the properties of air, water and common gases at standard sea-level atmosphere pressure.

Table A.1: Properties of air at standard sea-level atmosphere pressure

32Temperature oCDensity, kg/m3Specific weight, N/m3Dynamic viscosity, Ns/m2Kinematic Viscosity, m2/s01.2912.71.72 10-513.3 10-6101.2512.21.77 10-514.2 10-6201.2011.81.81 10-515.1 10-6301.1611.41.86 10-516.0 10-6401.1311.01.91 10-516.9 10-6501.0910.71.95 10-517.9 10-6601.0610.41.99 10-518.9 10-6701.0310.12.04 10-519.9 10-6801.009.802.09 10-520.9 10-6900.9729.532.19 10-521.9 10-61000.9469.282.30 10-523.0 10-6TemperatureoCDensity, kg/m3Specific weight, N/m3Dynamic viscosity, Ns/m2Surface tension*, N/m0100098101.75 10-30.075610100098101.30 10-30.07422099897901.02 10-30.07283099697708.00 10-40.07124099297306.51 10-40.06965098896905.41 10-40.06796098496504.60 10-40.06627097895904.02 10-40.06448097195303.50 10-40.06269096594703.11 10-40.060810095894002.82 10-40.058933

Table A.2: Properties of water at standard sea-level atmosphere pressure

* Contact with airFluidTempDensity, Specific gravity, sgViscosity, Surface tension, Bulk Modulus,KoCkg/m310 3 Ns/m2N/m106 N/m2Benzene20oC8760.880.650.0291030Tetrachloride Carbon20oC15881.5940.970.0261100Raw oil20oC8560.867.20.03Gasoline20oC6800.680.29Glycerine20oC12581.26 14940.0634344Hydrogen257oC 73.70.0740.0210.0029 34

Table A.3: Properties of fluid at standard sea-level atmosphere pressure

FluidTempDensity,Specific weight, sgviscosity,Surface tension,Bulk Modulus, KoCkg/m310 3 Ns/m2N/m106N/m2Kerosene20oC8080.811.920.028Mercury20oC13550 13.561.560.5126200Oxygen195oC12061.210.2780.015SAE 10 oil20oC9180.92 820.037SAE 30 oil20oC9180.92 4400.036Water20oC9980.9991.000.0732171Sea water20oC10231.0241.070.073230035

Table A.3: Properties of fluid at standard sea-level atmosphere pressure

36

Table A.4: Physical properties of common gases at standard sea-level atmosphere pressure

GasChemical formulaMolar Mass, MDensity, Viscosity,Gas Constant, Rkg/ kg-molkg/m3106 Ns/m2m2/(s2K)Air28.961.20518.0287Carbon dioxideCO244.011.8414.8188Carbon monoxideCO28.011.1618.2297HeliumHe 4.0030.16619.72077HydrogenH2 2.0160.08399.04120MethaneCH416.040.66813.4520NitrogenN228.021.1617.6297OxygenO232.001.3320.0260Water VapourH2O18.020.74710.1462371.3Summary of Fluids PropertiesValue of fluid properties are vary in different temperatures