Question

(b) A Newtonian liquid of viscosity 0.1 N s m2 is flowing through a pipe of 25 mm diameter and 20 m in length, and the pressure drop is 105 Nm2. As a result of a process change a small quantity of polymer is added to the liquid and this causes the liquid to exhibit non-Newtonian characteristics; its rheology is described adequately by the power-law model and the flow index is 0.33. The apparent viscosity of the modified fluid is equal to the viscosity of the original liquid at a shear rate of 1000 sh. (0) Calculate the consistency coefficient of the liquid when it behaves as a power fluid [4 MARKS] (11) Calculate the flowrate of the liquid when it behaves as a power law non- Newtonian fluid. [4 MARKS] (ili) If the pressure drop is not altered, what will be ratio of the volumetric flow rates of the two liquids? [5 MARKS]

Answer 1

( ) For Newtonian Fluidit the velocity through prize by Higen porsellic - can Coluntake equation as - APXD² 32 4XL - poput 0.0252 m2 32xood Pipe 20 m. - 0.97 65 m larec for sume Prosure drop velocity calculated is hence ratio of volm flow rak= tit. similar Ay. previouy Calculation as it is calcucked Kindly Igone the Bud on 3x105 pq.

tak = 31.25 N = K. (1000 st] 0:33. hence R = 31.25 m sets) Ik= 3.1977 m2 See on Auwerin. 2 1000 0.33 Speis, since we know that I tak (GE) = K Celery Abperut Ahority Given in Quertim Abparent viricity = Uiscoity af fluide Hence for a finit length Pipe the avove equation will be reduced cy) paund. u sv which is similar to newhanan T = M. av [ 0.tx Nosee x 1000 see = 100 N

Punts) for scheal Fluid Hence for this velue Prenuse drop will bet AP= 45 L = 4x100 m 2 x 20 - 0.025 = 312X10 IN Now Applying Alagen poneullie equation. I since Laminas Flow . I since leave to be verything APDL = 3.2X10 y 0,0252 m2 V= MXA2 32x o.1 N. X 20 m 32 Hence = 3125 mm flow ruke - Areax Velocity a 7 x D 2 x v - Tx 0.0252 x 3.125 m3 = m3 see

ratio 3.125 2117 Hence of volumerie Plow in a Viched Upower 0.9765 - 3. 20 Treatio of volmetric Flow = 3.20 Ayarin

We were unable to transcribe this image

tak = 31.25 N = K. (1000 st] 0:33. hence R = 31.25 m sets) Ik= 3.1977 m2 See on Auwerin. 2 1000 0.33 Speis, since we know that I tak (GE) = K Celery Abperut Ahority Given in Quertim Abparent viricity = Uiscoity af fluide Hence for a finit length Pipe the avove equation will be reduced cy) paund. u sv which is similar to newhanan T = M. av [ 0.tx Nosee x 1000 see = 100 N

We were unable to transcribe this image

Punts) for scheal Fluid Hence for this velue Prenuse drop will bet AP= 45 L = 4x100 m 2 x 20 - 0.025 = 312X10 IN Now Applying Alagen poneullie equation. I since Laminas Flow . I since leave to be verything APDL = 3.2X10 y 0,0252 m2 V= MXA2 32x o.1 N. X 20 m 32 Hence = 3125 mm flow ruke - Areax Velocity a 7 x D 2 x v - Tx 0.0252 x 3.125 m3 = m3 see

We were unable to transcribe this image

ratio 3.125 2117 Hence of volumerie Plow in a Viched Upower 0.9765 - 3. 20 Treatio of volmetric Flow = 3.20 Ayarin