By James Freeman Steffe
Ebook through James Freeman Steffe
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Extra resources for Bioprocessing Pipelines: Rheology and Analysis
Process line between tanker truck and storage tank with control volume located between the fluid level in the truck and a point just outside the pipe exit. 4. Process line between tanker truck and storage tank with control volume located between the inlet and outlet of the pump. 44 Bioprocessing Pipelines Another practical problem is illustrated in Fig. 5 where the control volume is defined between the exit of the pump and the exit to the tank. In this case, W = 0 (there is no pump in the control volume), u2 = 0 (pumping into a large tank), and friction losses occur in the valve, the strainer, two elbows, the exit, and the straight pipe.
1. These constants are strictly empirical and only relate to the specific geometry (impeller and cup) combination tested. Other factors such as the fluid levels during testing, and spacing between the impeller and the cup, must also be maintained. One limitation of mixer viscometry is that low values of k′ restrict the instruments to moderate shear rates that may be below the maximum shear rates found in pipelines. Also, the torque capacity of the instrument may limit the analysis to low shear rates when dealing with thick materials.
5) is used as the basis for determining the rheological properties of fluids. Substituting Eq. 7) into Eq. 9) Substituting Eq. 9) into Eq. 10) where k″ is a constant defined as the mixer coefficient: k″ = A−1d −3 . Newtonian fluids with a known viscosity are used to determine k″. This constant ties together the dynamic relationship between the physical system (mixer, impeller, degree of fill), torque, angular velocity of the impeller, and viscosity. 12) To determine the average shear rate, one must apply the matching viscosity assumption that the Newtonian viscosity and the apparent viscosity are equal at the same shear rate.