Lecture 05: STKM3212

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Lecture 05: STKM3212

  1. 1. LECTURE NOTES 05/07 STKM3212: FOOD PROCESSING TECHNOLOGY FLUIDS MECHANIC: VISCOSITY OF FLUIDS (MEKANIK BENDALIR: KELIKATAN BENDALIR) SAIFUL IRWAN ZUBAIRI PMIFT, Grad B.E.M. B. Eng. (Chemical-Bioprocess) (Hons.), UTM M. Eng. (Bioprocess), UTM ROOM NO.: 2166, CHEMISTRY BUILDING, TEL. (OFF.): 03-89215828, FOOD SCIENCE PROGRAMME, CENTRE OF CHEMICAL SCIENCES AND FOOD TECHNOLOGY, UKM BANGI, SELANGOR
  2. 2. 1.1 OUTLINES <ul><li>1.2 NEWTON’S LAW AND VISCOSITY. </li></ul><ul><li>1.3 VISCOSITIES OF NEWTONIAN FLUIDS. </li></ul><ul><li>1.4 VISCOSITIES OF NON-NEWTONIAN FLUIDS. </li></ul><ul><li>1.5 IDENTIFICATION OF FLUIDS RHEOLOGY USING VISCOMETER . </li></ul><ul><li>1.6 LAMINAR AND TURBULENT FLOW. </li></ul><ul><li>1.8 REYNOLDS NUMBER (Re). </li></ul>
  3. 3. 1.2 NEWTON’S LAW AND VISCOSITY <ul><li>Some of the food substances are in the form of LIQUID. </li></ul><ul><li>One of the PHYSICAL PROPERTIES FOR LIQUID FOOD  VISCOSITY (Kelikatan) . </li></ul><ul><li>REASON FOR APPLYING THE SCIENCE OF VISCOSITY: </li></ul><ul><li>(1) Will influence the perception of consumer: </li></ul><ul><li>(a) e.g.: ‘KAYA’  Cannot be too dilute, viscose is the best. </li></ul><ul><li>(b) e.g.: SAUCE  Must be in certain value of viscosity. </li></ul><ul><li>(c) e.g.: JUICES  Need to be diluted, not viscose. </li></ul><ul><li>(2) Easy to transport: </li></ul><ul><li>(a) e.g.: For transporting the liquid food to the other location in the factory. </li></ul><ul><li>(3) Easy for gripping (adhesion) : </li></ul><ul><li>(a) e.g.: Adhesion of coated flour to the chicken meat. </li></ul><ul><li>(b) e.g.: Adhesion to the container or wrapper. </li></ul>
  4. 4. CONTINUE: <ul><li>Movement of FLUID will occur if the STRESS (TEGASAN) is given. </li></ul><ul><li>STRESS/PRESSURE = Force (N)/Area (m 2 ) </li></ul><ul><li>If the FORCE (N) is perpendicular (at 90 o angle) with surface  It is called NORMAL STRESS (Tegasan Normal). </li></ul><ul><li>Normally, it is called = PRESSURE (P) </li></ul><ul><li>If the FORCE is HORIZONTAL/PARALLEL (180 0 ) with the surface  It is called SHEAR STRESS (Tegasan Ricihan) . </li></ul><ul><li>Different materials will give different effect of the SHEAR STRESS. </li></ul>P 3 P 2 P 1 (Force) F 1 = N ( V 0 to A ) V 0 = m/s Fluid  r (distance of the fluid movement), m Viscosity (  ) = Pa.s OR kg/m.s V A = m/s
  5. 5. CONTINUE: <ul><li>VISCOSITY,  (Kelikatan) = “resistance (rintangan) of GASSES OR FLUIDS towards the flow of the SHEAR STRESS” . </li></ul><ul><li>When STRESS is applied  Fluids will move. </li></ul><ul><li>SO,  STRESS (F/A);  VELOCITY (m/s). </li></ul><ul><li>Fluids is assumed to be combination of FLUID LAYERS. </li></ul><ul><li>When the lower layer is given the STRESS, it will effect the upper layer. </li></ul><ul><li>USUALLY, viscosity of lower layer > upper layer. </li></ul><ul><li>Each layer will move at different velocity (m/s). </li></ul><ul><li>The far the layer from the source of STRESS, the  velocity (m/s) of that layer. </li></ul><ul><li>Upper layer has < velocity (m/s). </li></ul><ul><li>The subsequent layer has > velocity (m/s). </li></ul>
  6. 6. CONTINUE: <ul><li>The English unit for VISCOSITY  are called “ Poise” or “centipoise” (cp) = g/cm.s </li></ul><ul><li>The SI UNIT for VISCOSITY  Pa.s ( N.s/m 2 OR kg/m.s) </li></ul><ul><li>1 cp = 1 × 10 -3 kg/m.s = </li></ul><ul><li>1 × 10 -3 Pa.s = 1 × 10 -3 N.s/m 2 (SI Unit) </li></ul><ul><li>1 cp = 0.01 poise = 0.01 g/cm.s (English Unit) </li></ul>
  7. 7. CONTINUE: <ul><li>THEREFORE: ------- NEWTON’S LAW  SHEAR STRESS (  ) (shear stress) is shear force (N) per area (m 2 ) </li></ul><ul><li>  (tau) = F/A = -  .dv/dr -------- (N/m 2 ) </li></ul><ul><li>SHEAR RATE (  )  is defined as velocity gradient (m/s) at the r distances (m) : </li></ul><ul><li> (gamma) = d v /dr = ( v 1 - v 2 )/(r 2 -r 1 ) -------- (s -1 ) </li></ul><ul><li>Where: r = distance at velocity zero, v = velocity at distance r </li></ul><ul><li>RELATIONSHIP BETWEEN: VISCOSITY (  ) VS  VS  are : </li></ul><ul><li>  =  /  -------- (N.s/m 2 ) </li></ul>
  8. 8. CONTINUE: <ul><li>(1) For ELASTIC SOLID  when the shear stress is applied, it will change accordingly to the flow of the stress. </li></ul><ul><li>The material will RETURN BACK to its normal size when the stress is removed.  e.g.: rubber materials. </li></ul><ul><li>(2) For SOLID that have a plastic properties  when the SHEAR STRESS is applied, it will change accordingly to the flow of the stress. </li></ul><ul><li>BUT = it will not come back to its original shape right after the stress is removed.  e.g.: jelly (agar-agar). </li></ul><ul><li>(3) For FLUIDS  when the SHEAR STRESS is applied, it will change accordingly to the flow of the stress. </li></ul><ul><li>This material will not come back to its original shape & will moving towards the flow of the stress. </li></ul>
  9. 9. 1.3 VISCOSITIES OF NEWTONIAN FLUIDS <ul><li>FLUIDS  show LINEAR relationship between SHEAR STRESS (  ) & SHEAR RATE (  ) = “NEWTONIAN FLUIDS” </li></ul><ul><li>SLOPE = Viscosity (  ) . </li></ul><ul><li>Viscosity (  ) for the NEWTONIAN FLUIDS are not influenced by the SHEAR RATE (  ) . </li></ul><ul><li>The “VISCOSITY” TERMS is ONLY SUITABLE  “NEWTONIAN FLUIDS” . </li></ul>(  ) = slope (  ) (  )
  10. 10. CONTINUE: <ul><li>Examples of NEWTONIAN FLUIDS AND GASESS : (1 atm = 101.32 Kpa) </li></ul>COMMON SENSE:  T ( O C);  viscosity (  ) ---- WHY? = when the temperature is increases, the molecules of substance will evaporate thus resulted in decreases of mass (mg). So, less shear force (  ) is needed to measure its viscosity. REFER TO THE EQUATION -----  =  / 
  11. 11. 1.4 VISCOSITIES OF NON-NEWTONIAN FLUIDS <ul><li>For “NON-NEWTONIAN FLUIDS” = The term of APPARENT VISCOSITY (kelikatan tampak) is usually used.  </li></ul><ul><li>Examples of NON-NEWTONIAN FLUIDS : “pastes (perekat), slurries (lumpur lembik), high polymers, emulsions, etc” . </li></ul><ul><li>NON-NEWTONIAN FLUIDS = it has: </li></ul><ul><li>(1) ‘SHEAR-THINNING’ (ricihan-kekurangan)  Pseudoplastic </li></ul><ul><li>(2) ‘SHEAR-THICKENING’ (ricihan-tambahan)  Dilatant </li></ul><ul><li>(3) ‘YIELD STRESS’ (Tegasan berian)  Bingham plastic </li></ul><ul><li>REMEMBER  “Most of the non-newtonian fluids are TIME INDEPENDENT & EXHIBIT (pamerkan) elastic (rubberlike) behavior” ---- it is called “VISCOELASTICS FLUIDS” </li></ul>
  12. 12. CONTINUE: <ul><li>(1) ‘SHEAR-THINNING’ (ricihan-kekurangan)  it has dispersed phase (fasa terserak) which tends to COMBINE with the flow that has the minimum resistances. </li></ul><ul><li>Its particle will form a position at the minimum resistances flow. </li></ul><ul><li>e.g.: mayonnaise/biological fluids/paints/greases/detergent slurries. </li></ul><ul><li>(2) ‘ SHEAR-THICKENING ’ (ricihan-tambahan)  it has dispersed phase (fasa terserak) which tends to EXPAND OR its molecule will make a cross bonding with each others. </li></ul><ul><li>e.g.: wet beach sand/starch in water/high conc. of powder in water. </li></ul><ul><li>(3) ‘YIELD STRESS’ (Tegasan berian)  These are the simplest because they differ from newtonian only in that the linear relationship does not go through origin (Figure 3.5-1)  A SET YEILD STRESS (shear) in N/m 2 is needed to INITIATE FLOW . </li></ul><ul><li>e.g.: drilling muds/peat slurries/margarine/chocalate mix/soap/sewage sludge/toothpaste. </li></ul><ul><li>  </li></ul>
  13. 13. CONTINUE: <ul><li>There are 2 equation that represent the “NON-NEWTONIAN FLUIDS”: </li></ul><ul><li>  = K(  ) n ------------ (1) </li></ul><ul><li> </li></ul><ul><li>Where: </li></ul><ul><li>  n = flow behavior index (dimensionless) - (n < 1.0: Pseudoplastic) OR (n > 1.0: Dilatant) . </li></ul><ul><li> n = will shows whether it is “shear-thinning(pseudoplastic)” OR “shear-thickening (dilatant) . </li></ul><ul><li>  K = consistency index (N.s n /m 2 ). </li></ul><ul><li> [Generally, the more viscose of fluids, the higher K values] . </li></ul>
  14. 14. CONTINUE: (A) (B) (C) SLOPE: (A) > (B) > (C) = APPARENT VISCOSITY (  app ) ----   app with  SHEAR RATE (  ) (n > 1.0) (n < 1.0) (n = 1.0)
  15. 15. CONTINUE: <ul><li>APPARENT VISCOSITY (Kelikatan tampak): </li></ul><ul><li>  app =  /  = K(  ) n-1 ------- (2) </li></ul><ul><li>Calculation of APPARENT VISCOSITY is done by assuming that the NON-NEWTONIAN FLUIDS is behave like NEWTONIAN FLUIDS . </li></ul><ul><li>Referring to Figure 3.5-1: </li></ul><ul><li>(1)   app with  SHEAR RATE (  ) ----- PSEUDOPLASTIC </li></ul><ul><li>(2)   app with  SHEAR RATE (  ) ----- DILATANT </li></ul><ul><li>“ Disebabkan kelikatan tampak (apparent viscosity) berubah dengan kadar ricihan (shear rate), maka perlu apabila melaporkan kelikatan tampak untuk melaporkan juga kadar ricihan yang digunakan </li></ul>
  16. 16. 1.5 IDENTIFICATION OF FLUIDS RHEOLOGY USING VISCOMETER <ul><li>RHEOLOGY  “The science of the flow and deformation (pembentukan) of fluids” . </li></ul><ul><li>2 types of measurement equipment : </li></ul><ul><li>(1) Rotational Type Viscometer (Viskometer Jenis Putaran): </li></ul><ul><li>  Concentric cylinder (silinder konsentrik/berpusat sama). UKM: known as ---- “Wide-gap rotational viscometer with </li></ul><ul><li> spindle cylinder” </li></ul><ul><li>  Parallel plate (plat selari). </li></ul><ul><li>  Cone & plate (kon & plat). </li></ul><ul><li>  Mixer (pengacau). </li></ul><ul><li>(2) Tube Type Viscometer (Viskometer Jenis Tiub): </li></ul><ul><li>  Glass capillary (kapillari kaca). </li></ul><ul><li>  Pipe (paip). </li></ul><ul><li>  High pressure capillary (kapilari tekanan tinggi). </li></ul>
  17. 17. CONTINUE: Tube Type Viscometer: High pressure capillary (kapilari tekanan tinggi) <ul><li>NON-NEWTONIAN SUBTANCES: </li></ul><ul><li>Lubricating oil </li></ul><ul><li>Polymer solutions </li></ul><ul><li>Fuel oil </li></ul><ul><li>Emulsions </li></ul><ul><li>Fat melts </li></ul><ul><li>Suspensions </li></ul><ul><li>Printing inks </li></ul><ul><li>Liquid detergents </li></ul><ul><li>Latex </li></ul><ul><li>Adhesives </li></ul><ul><li>Lacquers </li></ul><ul><li>Glues </li></ul>
  18. 18. CONTINUE: Rotational Type Viscometer Concentric cylinder (silinder konsentrik) <ul><li>NON-NEWTONIAN SUBSTANCES : </li></ul><ul><li>suspensions </li></ul><ul><li>diary products </li></ul><ul><li>lacquers or varnishes </li></ul><ul><li>printing inks </li></ul><ul><li>emulsion paints </li></ul><ul><li>lubricants </li></ul><ul><li>latex </li></ul><ul><li>polymer solutions </li></ul><ul><li>coal suspensions </li></ul><ul><li>glues or adhesives </li></ul><ul><li>resins </li></ul><ul><li>coating slips </li></ul><ul><li>chocolate suspensions </li></ul><ul><li>sealing compounds </li></ul><ul><li>fruit mash or preparations </li></ul><ul><li>vegetable mash </li></ul><ul><li>coating colours </li></ul><ul><li>cosmetics </li></ul><ul><li>solutions </li></ul><ul><li>emulsions </li></ul><ul><li>mud </li></ul>
  19. 19. CONTINUE:
  20. 20. CONTINUE: Rotational Type Viscometer: Mixer (pengacau)
  21. 21. CONTINUE: <ul><li>The most common type of equipment  concentric cylinder viscometer (viskometer silinder konsentrik) . </li></ul><ul><li>Consisted with 2 concentric cylinder (silinder berpusat sama). </li></ul><ul><li>Fluid substances is put between 2 cylinders (INTERNAL & EXTERNAL CYLINDER) . </li></ul><ul><li>INTERNAL CYLINDER (spindle)  will spin & gives SHEAR FORCE to the fluid substances. </li></ul><ul><li>There are particular sizes of SPINDLE can be found  depending on the viscosity of the fluid substances (make a visual interpretation before selecting the sizes of spindle) . </li></ul><ul><li>Resistance towards the flow will be experienced by SPINDLE & it will measured the resistance. </li></ul><ul><li>The measured values will be multiply with CERTAIN CONVERSION FACTOR for obtaining the  “ACTUAL VISCOSITY” . </li></ul>
  22. 22. CONTINUE: <ul><li>The CONVERSION FACTOR  is different according to the SIZE of the SPINDLE & SPIN SPEED . </li></ul><ul><li>The example of viscometer brand: “Brookefield Viscometer” </li></ul><ul><li>CALCULATION EXAMPLES: </li></ul><ul><li>  Spindle = No. 2 </li></ul><ul><li>  Spindle speed (N) = 60 rpm </li></ul><ul><li>  CF = 5 </li></ul><ul><li>  Reading from the device = 64 </li></ul><ul><li>  Viscosity (  app:Non-newtonian OR  Newtonian ) : 64 x 5 = 320 cp </li></ul><ul><li>  Spindle : No. 3 ; Spindle speed (N) = 6 rpm; CF = 200 </li></ul><ul><li>  Reading from the device = 64.4 </li></ul><ul><li>  (  app:Non-newtonian OR  Newtonian ) : 64.4 x 200 </li></ul><ul><li> = 12,880 cp </li></ul>
  23. 23. NEWTONIAN FLUIDS: ROTATIONAL VISCOMETER <ul><li>For NEWTONIAN FLUID  it will give actual value of viscosity (  ). </li></ul><ul><li>n (flow behavior index) for NEWTONIAN = 1.0 and  Plot graph Log  vs. Log  . </li></ul><ul><li>PLOT FROM ORIGIN (0,0) ------ SLOPE = Actual viscosity (  ) </li></ul><ul><li>SHEAR STRESS;  (N.m 2 )  torque (N.m) ------- (1) </li></ul><ul><li>SHEAR RATE;  (s -1 )  N (spindle speed, rpm) ------------- (2) </li></ul>(  ) = slope (  ) (  )
  24. 24. CONTINUE: <ul><ul><li>The SHEAR RATE (  ) at the surface of the spindle for NEWTONIAN FLUIDS is as follows with n = 1 : </li></ul></ul><ul><ul><li>4  N/1 - ( R b / R c ) 2 </li></ul></ul><ul><ul><li>Where: (a) R b - radius of the spindle, m </li></ul></ul><ul><ul><li>(b) R c - radius of the outer cylinder or container, m </li></ul></ul><ul><ul><li>(c)  - angular velocity of the spindle, rad/s </li></ul></ul><ul><ul><li> = 2  N/60 ,when N is the RPM </li></ul></ul><ul><ul><li>The SHEAR STRESS (  ) at the wall of the spindle: </li></ul></ul><ul><ul><ul><ul><li>  = A/2  L R b 2 </li></ul></ul></ul></ul> = Where: A = Torque (N.m) L = Height of the spindle, m R b = radius of the spindle, m =
  25. 25. EXAMPLE 1 (NEWTONIAN): Rotational Type Viscometer Concentric cylinder (Wide-gap rotational viscometer with spindle): A wide-gap rotational viscometer with a spring constant of 7,187 dynes.cm are used to measure a viscosity (cps; %) of RO-H 2 O. The outer radius (R c ), spindle radius (R b ), and height (L) of the cylindrical spindle are 2.75 cm, 1.50 cm and 5.0 cm respectively. Determine the viscosity (  ) in N.s/m 2 of RO-H 2 O. Measurement values are given below: Spindle speed (N) Device reading; cps (% scale) 20 rpm 16 50 rpm 22 100 rpm 45
  26. 26. CONTINUE: Spindle cylinder Test fluid - RO-H 2 O Beaker “ Wide-gap rotational viscometer with spindle cylinder” L R c R b
  27. 27. CONTINUE: <ul><li>ANS: </li></ul><ul><li>(1) RO-H 2 O = NEWTONIAN FLUIDS </li></ul><ul><li>(2) Firstly, we ONLY construct a graph of ----  vs.  </li></ul><ul><li>(3) The SLOPE = viscosity (  ) in N.s/m 2 </li></ul><ul><li>(3) Convert: Device reading; cps (%)  Torque (dynes.cm) </li></ul><ul><li>Torque (dynes.cm) = Device reading; cps (%) × spring constant </li></ul><ul><li>(7,187 dynes.cm) </li></ul><ul><li>e.g.: Torque (dynes.cm) = 16/100 × 7187 = 1,149.92 </li></ul><ul><li>(4) Convert: {dynes.cm}  {N.m} by using the conversion factor: </li></ul><ul><li> CONVERSION FACTOR: (1 dynes = 10 -5 Newton) </li></ul><ul><li>e.g.: 1149.92 dynes.cm 10 -5 N 1 m = 0.000115 N.m </li></ul><ul><li> 1 dynes 100 cm </li></ul>
  28. 28. CONTINUE: <ul><li>(5) Convert: Torque (N.m)   (N/m 2 ) by using the formula: </li></ul><ul><li>  = A/2  LR b 2 ; A = Torque (N.m) </li></ul><ul><li>e.g.:  = 0.000115/[2 × 3.14 × 5.0/100 × (1.5/100) 2 ] = 1.62 N/m 2 </li></ul><ul><li>(6) Convert: N (rpm)   (s -1 ) by using the formula: </li></ul><ul><li>  = 4  N/1 - ( R b / R c ) 2 </li></ul><ul><li>e.g.:  = [4 × 3.14 × (20 rpm/60 s)]/1 - (0.015/0.0275) 2 = 5.98 s -1 </li></ul>N (rpm)  (s -1 ) Torque (dynes.cm) Torque (N.m)  (N/m 2 ) 20 rpm 5.98 1149.92 0.000115 1.62 50 rpm 14.95 1581.14 0.000158 2.24 100 rpm 29.90 3234.15 0.000323 4.57
  29. 29. CONTINUE:  You should get a LINEAR EQUATION WITH ‘0’ INTERCEPT The equation: y = 0.16x ----- so; the SLOPE = viscosity (  ) in N.s/m 2  Viscosity (  ) of RO-H 2 O = 0.16 N.s/m 2
  30. 30. NON-NEWTONIAN FLUIDS: ROTATIONAL VISCOMETER <ul><li>For NON-NEWTONIAN FLUID  it will give apparent viscosity (  app ). </li></ul><ul><li>Besides viscosity value, n (flow behavior index) and K [consistency index (N.s n /m 2 )] can also be calculated using the graph of  (Log torque vs. Log N) & (Log  vs. Log  ). </li></ul><ul><li>(1) Log torque vs. Log N ------ To get the n value: SLOPE: n </li></ul><ul><li>(2) Log  vs. Log  --------- To get the K value: INTERCEPT: y-axis = log K </li></ul><ul><li>SHEAR STRESS (  ); N.m 2  torque (N.m) ------- (1) </li></ul><ul><li>SHEAR RATE (  ); s -1  N (spindle speed, rpm) ------------- (2) </li></ul>
  31. 31. CONTINUE: <ul><ul><li>The SHEAR RATE (  ) at the surface of the spindle for NON-NEWTONIAN FLUIDS is as follows for 0.5 < Rb/Rc < 0.99: </li></ul></ul><ul><ul><li>--------------- (1) </li></ul></ul><ul><ul><li>Where: (a) R b - radius of the spindle, m </li></ul></ul><ul><ul><li>(b) R c - radius of the outer cylinder or container, m </li></ul></ul><ul><ul><li>(c) n - flow behavior index (dimensionless) </li></ul></ul><ul><ul><li>(d)  - angular velocity of the spindle, rad/s </li></ul></ul><ul><ul><li> = 2  N/60 ,when N is the RPM </li></ul></ul><ul><ul><li>The SHEAR STRESS (  ) at the wall of the spindle: </li></ul></ul><ul><ul><ul><ul><li>  = A/2  L R b 2 </li></ul></ul></ul></ul> = Where: A = Torque (N.m) L = Height of the spindle, m R b = radius of the spindle, m
  32. 32. CONTINUE: <ul><li>VARIOUS SPECIAL CASES CAN BE DERIVED FROM EQUATION (1): </li></ul><ul><li>(1) VERY LARGE GAP ( R b /R c < 0.1) = This is the case of a spindle immersed in a large beaker of test fluid. [  = 2  N/60 ,when N is the RPM] </li></ul> = = 4  N/n Test fluid R b R c Spindle Container or cylinder
  33. 33. CONTINUE: <ul><li>VARIOUS SPECIAL CASES CAN BE DERIVED FROM EQUATION (1): </li></ul><ul><li>(1) VERY NARROW GAP ( R b /R c > 0.99) = This is similar to flow parallel plates. Taking the shear rate at radius ( R b + R c )/2 . </li></ul><ul><li>[  = 2  N/60 ,when N is the RPM] </li></ul>Test fluid R b R c Spindle Container or cylinder  =
  34. 34. EXAMPLE 2 (NON-NEWTONIAN): <ul><li>Rotational Type Viscometer Concentric cylinder (Wide-gap rotational viscometer with spindle): </li></ul><ul><li>A wide-gap rotational viscometer with a spring constant of 7,187 dynes.cm are used to measure a viscosity (cps; %) of a tomato sauce. The outer radius (R c ), spindle radius (R b ) and height (L) of cylindrical spindle are 2.70 cm, 0.15 cm and 5.0 cm respectively. Determine the K and n? Calculate also the apparent viscosity (  app ) of tomato sauce in N.s/m 2 at spindle speed of 35 rpm. Measurement values are given below: </li></ul>Spindle speed (N) Device reading; cps (% scale) 20 rpm 29 50 rpm 44 100 rpm 60
  35. 35. CONTINUE: Spindle cylinder Test fluid - Tomato sauce Beaker “ Wide-gap rotational viscometer with spindle cylinder” L R c R b
  36. 36. CONTINUE: <ul><li>ANS: </li></ul><ul><li>R b / R c = 0.15 cm/2.7 cm = 0.055 < 0.1 --- So, equation very large gap is used </li></ul><ul><li>n value determination : </li></ul><ul><li>(1) Sauce tomato = NON-NEWTONIAN FLUIDS </li></ul><ul><li>(2) Firstly, we have to construct a graph of ---- Log torque vs. Log N </li></ul><ul><li>(3) Convert: Device reading; cps (%)  Torque (dynes.cm) </li></ul><ul><li>Torque (dynes.cm) = Device reading; cps (%) × spring constant </li></ul><ul><li>(7,187 dynes.cm) </li></ul><ul><li>e.g.: Torque (dynes.cm) = 29/100 × 7187 = 2,084.23 </li></ul><ul><li>(4) Convert: {dynes.cm}  {N.m} by using the conversion factor: </li></ul><ul><li> CONVERSION FACTOR: (1 dynes = 10 -5 Newton) </li></ul><ul><li>e.g.: 2084.23 dynes.cm 10 -5 N 1 m = 0.000208 N.m </li></ul><ul><li> 1 dynes 100 cm </li></ul><ul><li>(5) Log (N) rpm ---- “see table” </li></ul>
  37. 37. CONTINUE: <ul><li>(6) Plot the graph: </li></ul>N (rpm) Log N Cps (%) Torque (dynes.cm) Torque (N.m) Log Torque 20 rpm 1.30 29 2084.23 0.000208 -3.68 50 rpm 1.70 44 3162.28 0.000316 -3.50 100 rpm 2.00 60 4312.20 0.000431 -3.37
  38. 38. CONTINUE: <ul><li>(7) So, we have the LINEAR equation: </li></ul><ul><li>y = 0.451x - 4.268 -------- n value is the SLOPE </li></ul><ul><li> n = 0.451 (n < 1.0 = PSEUDOPLASTICS FLUIDS) </li></ul><ul><li>K value determination : </li></ul><ul><li>(1) Convert: Torque (N.m)   (N/m 2 ) by using the formula: </li></ul><ul><li>  = A/2  LR b 2 ; A = Torque (N.m) </li></ul><ul><li>e.g.:  = 0.000208/[2 × 3.14 × 5.0/100 × (0.15/100) 2 ] = 294.62 N/m 2 </li></ul><ul><li>(2) Log  ------- ‘see table’ </li></ul><ul><li>(3) Convert: N (rpm)   (s -1 ) by using the formula: </li></ul><ul><li>  = 4  N/n </li></ul><ul><li>e.g.:  = [4 × 3.14 × (20 rpm/60 s)]/0.451 = 9.26 s -1 </li></ul>
  39. 39. CONTINUE: <ul><li>(3) Plot the graph: </li></ul>N (rpm)  (s -1 ) Log  Torque (N.m)  (N/m 2 ) Log  20 rpm 9.26 0.97 0.000208 294.62 2.47 50 rpm 23.16 1.36 0.000316 447.60 2.65 100 rpm 46.32 1.67 0.000431 610.36 2.79
  40. 40. CONTINUE: <ul><li>(4) So, we have the LINEAR equation: </li></ul><ul><li>y = 0.451x + 2.033 ---------- intercept (c) = K </li></ul><ul><li> c = Log  ---- Antilog (c): Antilog [2.033] = K = 107.89 N.s 0.451 /m 2 </li></ul><ul><li>Apparent viscosity (  app ) in N.s/m 2 at spindle speed of 35 rpm : </li></ul><ul><li>Convert: N (rpm)   (s -1 ) by using the formula: </li></ul><ul><li> = 4  N/n </li></ul><ul><li> = [4 × 3.14 × (35 rpm/60 s)]/0.451 = 16.25 s -1 </li></ul><ul><li>Log [16.25] = 1.21 </li></ul><ul><li>Based on the equation: y = 0.451x +2.033; </li></ul><ul><li>y = 0.451( 1.21) + 2.033 = 2.58 </li></ul><ul><li>Antilog (y) =  = 380.19 N/m 2 ---- SO; </li></ul><ul><li> (  app ) =  /  = 380.19/16.25 = 23.40 N.s/m 2 </li></ul>OR ALTERNATIVELY using equation:  app =  /  = K(  ) n-1 = 107.89[(16.25) 0.451-1 ]  app = 107.89  16.25 -0.549 = 23.40 N.s/m 2
  41. 41. 1.6 LAMINAR AND TURBULENT FLOW <ul><li>These 2 types of flow can commonly seen in a open stream or RIVER. </li></ul><ul><li>When velocity (m/s) of flow is SLOW  the FLOW PATTERNS are SMOOTH. </li></ul><ul><li>When velocity (m/s) of flow is HIGH  unstable PATTERN IS OBSERVED in which EDDIES (small packets of fluids particles) are present moving in all directions and at all angles to the normal line of flow. </li></ul><ul><li>(1) “LAMINAR FLOW” = flow at low velocities where layers of fluids seem to slide by one another without eddies/swirls (pusaran) being present. </li></ul><ul><li>(2) “TURBULENT FLOW” = flow at higher velocities where eddies are present giving the fluid a fluctuating nature. </li></ul>
  42. 42. CONTINUE: “ The was no mixing in any parts of the tube and the fluid flowed in straight parallel lines”  LAMINAR/VISCOUS FLOW “ As the velocity increased, it was found that a definite velocity the thread of dye became dispersed and the pattern was very erratic/inconsistent”  TURBULENT/CRITICAL VELOCITY
  43. 43. 1.7 REYNOLDS NUMBER (Re) <ul><li>FLUID FLOWS  can be as LAMINAR or TURBULENT . </li></ul><ul><li>(Re) is important to identify whether the flow is LAMINAR or TURBULENT. </li></ul><ul><li>Studies has shown that the transition from LAMINAR to TURBULENT flow in the tubes is not only a function of velocity (m/s), but also density, viscosity & tube diameter . </li></ul><ul><li>  </li></ul><ul><li> Re = Dv  /  ----------- (1) [DIMENSIONLESS] </li></ul><ul><li>  D = tube diameter (m) </li></ul><ul><li> v = average velocity (m/s) - volumetric flow rate (m 3 /s)/cross sectional area of the pipe (m 2 ) </li></ul><ul><li>  = density of the fluid (kg/m 3 ) </li></ul><ul><li>  = viscosity of the fluid (Pa.s) </li></ul><ul><li>IF, Re  2100 ------------- LAMINAR FLOW </li></ul><ul><li>IF, Re > 4000 ------------- TURBULENT FLOW </li></ul>In between the 2100 & 4000 = the flow will be TURBULENT or VISCOUS, depending upon the apparatus details, which can not be predicted. It is called “TRANSITION REGION”
  44. 44. EXAMPLE 1:
  45. 45. CONTINUE:

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