Drag ratio definition

One of the most important functions in the description of fluidization is the drag function which measures the ratio of pressure gradient to gas volume flux. The definition of this drag function is discussed in (14) through recourse to the correlation of Richardson (22). 

The electromechanical analogy provides for simple equivalents of a resistor, an inductance, and a capacitance, which are the dashpot (quantified by the drag coefficient, p), the point mass (quantified by the mass, mp), and the spring (quantified by the spring constant, /cp). The ratio of force and speed is the mechanical impedance, Z - For a dashpot, the impedance by definition is... 

To illustrate this point, one must look at the derivative of drag with respect to chord length. We wish to treat velocity, area, and lift coefficient as constants, so the span must be a function of aspect ratio. Using the definition for aspect ratio and defining the average chord length c =A/b, we obtain... 

As shown in Eqn. (6), the drag coefficient of a cylindrical fiber imder cross flow condition is a function of the Reynolds Number, which is generally expressed as Re = pUp,hd/p (i.e. the ratio of inertial force to viscous force). This definition holds true for Newtonian fluids, where shear stress < shear rate. However, the fluids that are often utilized in fiber sweep applications are non-Newtonian. Hence, the Reynolds Number must be redefined using the apparent viscosity function as Re = pUp>d/papp. The viscosity for Newtonian fluids is independent of the shear rate. However, for non-Newtonian fluids, the apparent viscosity varies with shear rate. Applying the Yield Power Law (YPL) rheology model, the apparent viscosity is expressed as ... 

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