Ostwald de Waele model

In this case, p is an arbitrary constant, chosen as the zero shear rate viscosity. The expression for the non-Newtonian viscosity is a constitutive equation for a generalized Newtonian fluid, like the power law or Ostwald-de-Waele model [6]... 

The power law, or Ostwald-de Waele, model is the simplest and most widely used rheologic empiricism. The power law states... 

Several models have been proposed to describe the dependence of viscosity on shear rate. One of the most used in engineering applications is the two-parameter Ostwald-De Waele model given by (45)... 

This equation predicts a straight line on a log-log plot of viscosity and shear rate with a slope of [n-1]. A horizontal line or n s 1 indicates a Newtonian fluid. The fluids that obey the Ostwald-de Waele model are called power-law fluids and n is referred to as the power-law index. 

The laminar flow of a certain aqueous polystyrene sulfonate solution can be represented by the Ostwald-de Waele model with an exponent of 0,500, The solution is contained in a tank that is a vertical cylinder. Solution flows out through a horizontal tube attached to the bottom of the tank, (a) If the time for the height of solution in the tank to fall from 10.00 to 9.90 m is 30,0 min, how much time will it take to half-empty the tank (from a height of 10.0 m down to a height of 5.0 m) (6) If the tank has a diameter of 2.0 m and the pipe has a diameter of 0.050 m with a length of 200 m, what is the flow consistency index of the solution The solution has a density of 1200 kg/m, ... 

There are molecular theories relating the viscosity of a linear polymer melt to chain length, but the most useful viscosity equations are empirical. Data are often represented by a power law (sometimes called the Ostwald-de Waele model) ... 

In many situations, t]o rioc Ky l,and 77,is small. Then the Cross equation (with a simple change of the variables K and m) reduces to the well-known power-law (or Ostwald-de Waele) model, which is given by... 

On the other hand, measurements of shear stress versus shear rate, when plotted on logarithmic scales, may often be represented by a linear expression over a limited range of shear rate (in this case, from 7 to 158 s ). The equation which represents this behavior is usually called the power-law or the Ostwald-De Waele model ... 

Otherwise, bear in mind that very often the range of shear rates to which a process fluid is exposed in pip>e flow is often cjuite limited, and because of this it is often possible to adecjuately represent the flow behavior of a process fluid over a limited range of shear rates by the power law or Ostwald de Waele model, and the Metzner-Reed Reynolds number, which we shall shortly discuss. Meanwhile, in the absence of any lab equipment to provide you with shear-stress versus shear-rate data, we suggest that you vary the flow rate to provide several flow rates, and run pressure drop surveys over the pipeline in question. Tabulate the data and use this to develop a "power law" relationship (see following sections) as a first approximation for your pijjeUne and process fluid. Most likely you will not need to perform any more elaborate study than that... 

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