Pharos UniversityFluid Mechanics For Electrical

Students

Dr. A. Shibl

Fluid Mechanics

• Is the study of the behavior of fluids at rest or in motion

• Fluids can be either liquids or gases• Liquids flow freely and conform to their

containers • Gases completely fill their containers

Importance Of Fluid Mechanics

• Utilization of Fluid around us; Air, Water… • Prediction of Fluid flow behavior • Sizing or specifying equipment• Estimate the related energy costs• Estimating the system performance under

different conditions

Example

Example

Fluid Properties:Liquid or Gas

• Liquids are:– Incompressible, DV ≠ f(DP)– Viscous (high viscosity)– Viscosity decreases with temperature

• Gases are:– Compressible, DV = f(DP)– Low viscosity– Viscosity increases with temperature

PRESSURE

• Pressure:– Force exerted on a unit area– P = Force/Area– Pressure acts uniformly in all directions and

perpendicular to the boundaries in the container– Example: Piston Force

Area= p/4*D2

Pressure=Force/AreaUnit: Psi or Pa (SI)

P

Density & Sp. Volume

• Density (r) : mass per unit volumer = mass/volume kg/m3, g/cm3, lb/ft3

– Density is a fluid property and slightly dependent on temperature

• Specific Volume (n): Inverse of densityn = 1/r m3/kg

• Specific Gravity ( SG): SG=r/rwater

At same Temp.

Specific Weight

• Specific Weight = Weight/Volumeg = w/V

• Examples– Calculate the weight of a reservoir of oil if it has a

mass of 825 kg– If the volume is 0.917 m3, compute density,

specific weight, specific gravity

Equations for Fluid Property

• Circular Area: • Weight: w = m*g Newton• Density: r = m/V Kg/m3

• Specific Weight: g = w/V N/m3

• Specific gravity: SG=r/rwater

Area = p/4*D2

Viscosity• Dynamic Viscosity

m = Shear Stress/Slope of velocity profile

• Kinematic Viscosity cS (centistokes) or m2/Sec.

yvAF//

Slope = v/y

vn

y

F

cP (centipoise) or Pa-sec

rm

Newtonian and Non-Newtonian Fluids

• Two types of fluids: Newtonian and Non-Newtonian:

• Newtonian: – Ex.: Water, Oil, Gasoline

DD

D

D

vy

yvyv

AF //

DD

vyf

Non-Newtonian Fluids

• Time-independent Fluids– Pseudoplastic (Blood Plasma, syrups, inks)– Dilatant (Starch in water)– Bingham (catsup, mustard, toothpaste)

• Time-dependent Fluids– Electrorheological (behavior changes due to

electric field, particles are present)– Magnetorheological (iron powders in fluid)

Viscosity MeasurementFalling Ball Viscometer

• Viscosity is determined by noting the amount of time a ball takes to travel between two lines

W

Fb Fd

( ) 2

18s f D

V

g gm

Viscosity MeasurementSaybolt Universal Viscometer

• Measurement is not based on definition of viscosity

• Results are relative, so a standard sample is used for calibration

• Fast and easy

Saybolt Viscosity– Saybolt Equations:

n (cS) = 0.226t - 195/t, t< 100 SUSn (cS) = 0.220t – 135/t, t> 100 SUSt, amount of time (seconds, SUS, Saybolt Universal

Seconds) it takes for 60 cm3 to flow through orifice (Saybolt viscometer)

– Example:• An oil has a viscosity of 230 SUS at 150° F. Compute

the viscosity in cS and cP. Specific gravity is 0.9.

Approximate Viscosities of Common Materials(At Room Temperature: 70°F)

Material Viscosity in CentipoiseWater 1 cps

Milk 3 cps SAE 10 Motor Oil 85-140 cps

SAE 20 Motor Oil 140-420 cps

SAE 30 Motor Oil 420-650 cps SAE 40 Motor Oil 650-900 cps

Castrol Oil 1,000 cps Karo Syrup 5,000 cps

Honey 10,000 cps Chocolate 25,000 cps

Ketchup 50,000 cps

Mustard 70,000 cps Sour Cream 100,000 cps

Peanut Butter 250,000 cps

http://www.liquidcontrol.com/etoolbox/viscosity.aspx

Viscosity ChartTemp. ° F

Temp. C

rm

http://www.klassenhydraulics.com/Reference/viscositychart.htm

m Force

Hydraulics Fluids for Fluid Power Systems

• Fluid Power– Pneumatics: air-type systems– Hydraulics: liquid-type systems

• Hydraulic Fluids:– Petroleum oils– Water-glycol fluids– High water based fluids (HWBF)– Silicone fluids– Synthetic oils

Characteristics of Hydraulic Fluids

• Adequate viscosity• Lubricating capability• Cleanliness• Chemical stability• Non-corrosiveness• Ability to resist growth of bacteria• Ecologically acceptable• Low compressibility

Hydraulic Fluids

• HWBF– Fire resistant– ~40% oil in water

• Water-glycol fluids– Fire resistant– 35 to 50% water

Hydraulic Fluids

• Petroleum Oils– SAE 10 W, SAE 20-20W (W means rated at

maximum viscosity and cold temperatures)– Engine oils– Additives are required to avoid growth of bacteria

• Silicone Fluids– For high temperature applications

Pressure

• Pressure:–Absolute = Gage + Atmospheric*–psia = psig + 14.7 psia–*14.7 psia at sea level

Pressure Scale

Units of Pressure

• 1 bar = 105 Pa = 0.1 MPa = 100 kPa• 1 atm = 101,325 Pa = 101.325 kPa • 1 atm = 1.012325 bars• 1 mm Hg = 0.13333 kPa• 1 atm = 14.696 psi

Pressure and Elevation

• Change in pressure in homogeneous liquid at rest due to a change in elevation

DP = ghWhere,DP = change in pressure, kPag = specific weight, N/m3

h = change in elevation, m

Pressure-Elevation Relationship

• Valid for homogeneous fluids at rest (static)

Free Surface Free Surface

P1

P2

P1 > P2

P2 = Patm + rgh

Static Fluids: Same elevation and same fluid → same pressure

P2 = Patm + rgh

Manometers

• Used to measure pressure• DP = gh

Example: Manometer

• Calculate pressure (psig) or kPa (gage) at Point A. Open end is at atmospheric pressure.

A

Hg: SG = 13.54

Water

0.4 m

0.15 m

Pressure Measurement Devices

Highly sensitive inclined manometers for systems demanding precise measurement of low pressures

Manometers

Pressure Measurement DevicesGages

Transducer:

Barometer and Atmospheric Pressure

Patm = rgh

Patm = 14.psi, 1 atm