Pharos University Fluid 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

Fluid Properties: Liquid or Gas Liquids are: – Incompressible,  V ≠ f(  P) – Viscous (high viscosity) – Viscosity decreases with temperature Gases are: – Compressible,  V = f(  P) – 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=  /4*D 2 Pressure=Force/Area Unit: Psi or Pa (SI) P

Density & Sp. Volume Density (  : mass per unit volume  = mass/volume kg/m 3, g/cm 3, lb/ft 3 –Density is a fluid property and slightly dependent on temperature Specific Volume  : Inverse of density = 1/  m 3 /kg Specific Gravity ( SG): SG=  /  water At same Temp.

Specific Weight Specific Weight = Weight/Volume  = w/V Examples –Calculate the weight of a reservoir of oil if it has a mass of 825 kg –If the volume is m 3, compute density, specific weight, specific gravity

Equations for Fluid Property Circular Area: Weight: w = m*g Newton Density:  = m/V Kg/m 3 Specific Weight:  = w/V N/m 3 Specific gravity: SG=  /  water Area =  /4*D 2

Viscosity Dynamic Viscosity  = Shear Stress/Slope of velocity profile Kinematic Viscosity cS (centistokes) or m 2 /Sec. Slope = v/y v y F cP (centipoise) or Pa-sec

Newtonian and Non-Newtonian Fluids Two types of fluids: Newtonian and Non- Newtonian: Newtonian: – Ex.: Water, Oil, Gasoline

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 Measurement Falling Ball Viscometer Viscosity is determined by noting the amount of time a ball takes to travel between two lines W F b F d

Viscosity Measurement Saybolt 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: (cS) = 0.226t - 195/t, t< 100 SUS (cS) = 0.220t – 135/t, t> 100 SUS t, amount of time (seconds, SUS, Saybolt Universal Seconds) it takes for 60 cm 3 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) MaterialViscosity in Centipoise Water1 cps Milk3 cps SAE 10 Motor Oil cps SAE 20 Motor Oil cps SAE 30 Motor Oil cps SAE 40 Motor Oil cps Castrol Oil1,000 cps Karo Syrup5,000 cps Honey10,000 cps Chocolate25,000 cps Ketchup50,000 cps Mustard70,000 cps Sour Cream100,000 cps Peanut Butter250,000 cps

Viscosity Chart Temp. ° F Temp.  C  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 psia –*14.7 psia at sea level

Pressure Scale

Units of Pressure 1 bar = 10 5 Pa = 0.1 MPa = 100 kPa 1 atm = 101,325 Pa = kPa 1 atm = bars 1 mm Hg = kPa 1 atm = psi

Pressure and Elevation Change in pressure in homogeneous liquid at rest due to a change in elevation  P =  h Where,  P = change in pressure, kPa  = specific weight, N/m 3 h = change in elevation, m

Pressure-Elevation Relationship Valid for homogeneous fluids at rest (static) Free Surface P1 P2 P1 > P2 P 2 = P atm +  gh

Static Fluids: Same elevation and same fluid → same pressure P 2 = P atm +  gh

Manometers Used to measure pressure  P =  h

Example: Manometer Calculate pressure (psig) or kPa (gage) at Point A. Open end is at atmospheric pressure. A Hg: SG = 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 Devices Gages Transducer:

Barometer and Atmospheric Pressure P atm =  gh P atm = 14.psi, 1 atm