FE 222 FLUID MECHANICS

1. FE 222 FLUID MECHANICS • Transport Processes and Separation Process Principles (Includes Unit Operations)(4th Edition) by Christie John Geankoplis, published by Pearson Education,Inc (Used to be Transport Processes and Unit Operations, 3rd ed…..) • Unit Operations of Chemical Engineering(7th edition)(McGraw Hill Chemical Engineering Series) by Warren McCabe, Julian Smith, and Peter Harriott

2. 2 exams 30 % each final 40 %

3. Fluids essential to life Human body 65% water Earth’s surface is 2/3 water Atmosphere extends 17km above the earth’s surface History shaped by fluid mechanics Geomorphology Human migration and civilization Modern scientific and mathematical theories and methods Warfare Affects every part of our lives

4. History Faces of Fluid Mechanics Archimedes (C. 287-212 BC) Newton (1642-1727) Leibniz (1646-1716) Bernoulli (1667-1748) Euler (1707-1783) Navier (1785-1836) Stokes (1819-1903) Prandtl (1875-1953) Reynolds (1842-1912) Taylor (1886-1975)

5. Weather & Climate Tornadoes Thunderstorm Global Climate Hurricanes

6. Vehicles Surface ships Aircraft Submarines High-speed rail

7. Environment River hydraulics Air pollution

8. Physiology and Medicine Ventricular assist device Blood pump Fluid channels in eye

9. Sports & Recreation Water sports Cycling Offshore racing Auto racing Surfing

10. SPORTS

12. TRAY DRIER PACKED BED PLATE FILTER

13. Shell and tube heat exchanger

15. Themain unitoperationsusuallypresent in a typicalfood-processingline, including: 1. Flow of fluid– when a fluid is movedfromonepointto anotherbypumping, gravity, etc. 2. Heat transfer– in whichheat is eitherremovedoradded (heating; cooling; refrigerationandfreezing). 3. Mass transfer – whetheror not thisrequires a change in state. Processesthatusemass transfer includedrying, distillation, evaporation, crystallization, andmembraneprocesses. 4. Otheroperationsrequiringenergy, such as mechanicalseparation(filtration, centrifugation, sedimentation, andsieving); size adjustmentby size reductions(slicing, dicing, cutting, grinding) or size increase(aggregation, agglomeration, gelation); andmixing, whichmayincludesolubilizingsolids, preparingemulsionsorfoams, anddryblending of drypowders (flour, sugar, etc.).

16. Example of theuse of flotationfor separation of fruitsfromcontainer (bins)

17. Alltheoreticalequations in mechanics (and in otherphysicalsciences) aredimensionallyhomogeneous; i.e., eachadditiveterm in theequation has thesamedimensions. Example is theequationfromphysicsfor a body fallingwithnegligibleairresistance: S =S0+ V0t + ½ gt2 whereS0 is initialposition, V0 is initialvelocity, andg is theacceleration of gravity. Eachterm in thisrelation has dimensions of length {L}.

18. However, manyempiricalformulas in theengineeringliterature, arisingprimarilyfromcorrelations of data, aredimensionallyinconsistent. Referred as dimensionalequations. Definedunitsforeachtermmust be used with it.

19. Three States of Mass

21. Fluids:Statics vs Dynamics

22. Continiummechanics : Branch of engineeringsciencethatstudiesbehavior of solidsandfluids Fluidmechanics: Branch of engineeringsciencethatstudiesbehavior of fluids Fluidstatics: Dealswithfluids in theequilibriumstate of noshearstress (study of fluids at rest) Fluiddynamics: Dealswiththefluidswhenportions of thefluidare in motionrelativetootherparts. (study of fluids in motion)

23. A fluid is a substance that flows under the action of shearing forces. Fluids are gases and liquids. If a fluid is at rest, we know that the forces on it are in balance. (A solid can resist a shear stress, a fluid cannot.)

24. Density The density of a fluid is defined as its mass per unit volume. It is denoted by the Greek symbol, . kg  water= 998 kgm-3 m  = V air =1.2kgm-3 kgm-3 m3 If the density is constant (most liquids), the fluid is incompressible. If the density varies significantly (e.g. some gases), the fluid is compressible. (Although gases are easy to compress, the flow may be treated as incompressible if there are no large pressure fluctuations)

25. Pressure Pressure is the force per unit area, where the force is perpendicular to the area. N F p= Nm-2 (Pa) A m2

26. Pressure Pressure in a fluid acts equally in all directions Pressure in a static liquid increases linearly with depth p= g  h increase in depth (m) pressure increase The pressure at a given depth in a continuous, static body of liquid is constant. p3 p1 = p2 = p3 p1 p2

27. Pressure field • Pressure is a scalar field: p = p(x; y; z; t) • The value of pvaries in space, but pis not associated with a direction. • The pressure at any point in a stationary fluid is independent of direction. • A pressure sensor will not detect different values of pressure when the orientation of the sensor is changed at a fixed measurement point.

28. Atmospheric Pressure Pressure = Force per Unit Area Atmospheric Pressure is the weight of the column of air above a unit area. For example, the atmospheric pressure felt by a man is the weight of the column of air above his body divided by the area the air is resting on P = (Weight of column)/(Area of base) Standard Atmospheric Pressure: 1 atmosphere (atm) = 14.7 lbs/in2 (psi) = 760 Torr (mm Hg) = 1013.25 millibars= 101.3 kPa 1Pa = 1N/m2

29. Equality of pressure at the same level in a static fluid

30. Variation of pressure with elevation

31. General variation of pressure in a static fluid due to gravity

32. General variation of pressure in a static fluid due to gravity for vertical direction: q = 0

33. Variation of pressure in an incompressible fluid (liquid) for liquids: r = const.

34. Variation of pressure in an compressible fluid (gas) r is variable, e.g. for an ideal gas:

35. Variation of pressure in an compressible fluid (gas) need to know T=T(z)

36. Variation of pressure in an compressible fluid (gas) case of uniform temperature: T=To

37. Variation of pressure in an compressible fluid (gas) case of linear temperature variation: T=To+bz at z1=0 (sea level) T=To p1=po

38. What are the z-direction forces? Let Pz and Pz+Dz denote the pressures at the base and top of the cube, where the elevations are z and z+Dz respectively. z y x

39. Pressure distribution for a fluid at rest A force balance in the z direction gives: For an infinitesimal element (Dz0)

40. Incompressible fluid Liquids are incompressible (density is constant): When we have a liquid with a free surface the pressure P at any depth below the free surface is: Po is the pressure at the free surface (Po=Patm)

41. SomePressureLevels 10 Pa - Thepressure at a depth of 1 mm of water 10 kPa - Thepressure at a depth of 1 m of water, orthedrop in airpressurewhengoingfromsealevelto 1000 m elevation 10 MPa - A "highpressure" washerforcesthewaterout of thenozzles at thispressure 10 GPa - Thispressureformsdiamonds

42. SomeAlternativeUnits of Pressure 1 bar - 100,000 Pa 1 millibar - 100 Pa 1 atmosphere - 101,325 Pa 1 mm Hg - 133 Pa 1 inch Hg - 3,386 Pa Thebar is common in theindustry. One bar is 100,000 Pa, andformostpracticalpurposes can be approximatedtooneatmosphereevenif1 Bar = 0.9869 atm

44. BourdonGauge: Thepressureto be measured is appliedto a curvedtube, oval in crosssection. Pressureappliedtothetubetendstocausethetubetostraightenout,andthedeflection of theend of thetube is communicatedthrough a system of leversto a recordingneedle. Thisgauge is widelyusedforsteamandcompressedgases. Thepressureindicated is thedifferencebetweenthatcommunicatedbythesystemtotheexternal (ambient)pressure, and is usuallyreferredtoas thegaugepressure.

45. Pressure scales • Absolute pressure:pabsis measured relative to an absolute vacuum; it is always positive. (The pressure of a fluid is expressed relative to that of vacuum (=0) • Gauge pressure:pgaugeis measured relative to the current pressure of the atmosphere; it can be negative or positive. (Pressure expressed as the difference between the pressure of the fluid and that of the surrounding atmosphere.)Usual pressure gauges record gauge pressure.

48. Measuring Pressure Barometers A barometer is used to measure the pressure of the atmosphere. The simplest type of barometer consists of a column of fluid. vacuum p1 = 0 p2 - p1 = gh h pa = gh p2 = pa examples water: h =10m mercury: h = 760mm

49. Piezometer Piezometers or pressure head taps must be installed with care and with a knowledge of how they perform; otherwise, indicated pressure values can be in error. For example, as shown on figure the four piezometers indicate different pressure readings (water levels) because of the manner in which flow passes the piezometer opening. Piezometer openings are shown larger than they should be constructed in practice. Always use the smallest diameter opening consistent with the possibility of clogging by foreign material. Unless the piezometer is vertical as in Y, the water elevation will be drawn down as in X or increased as in Z. Basically, pressure taps should be perpendicular to the flow boundary, and the flow must be parallel to the boundary.

50. Rough edges or burrs on or near the edges of the piezometer holes deflect the water into or away from the piezometer, causing erroneous indications. The case as in W shows the tube pushed into the flow, causing the flow to curve under the tip which pulls the water level down. Errors caused by faulty piezometer tap installation increase with velocity. By determining the height to which liquid rises and using the relation P = ρgh, gauge pressure of the liquid can be determined. To avoid capillary effects, a piezometer's tube should be about 1/2 inch or greater.