Total surface torque

Total Pressure Loss. Since bit life is not an issue in a short deviation control motor run operation, it is desirable to operate the positive displacement motor at as high a power level as possible during the run. The motor has a maximum pressure loss with which it can operate. This is 580 psi (see Table 4-114). It will be assumed that the motor will be operated at the 580 psi pressure loss in order to maximize the torque output of the motor. To obtain the highest horsepower for the motor, the highest circulation flowrate possible while operating within the constraints of the surface mud pump should be obtained. To obtain this highest possible, or optimal, circulation flowrate, the total pressure losses for the circulation system must be obtained for various circulation flowrates. These total pressure losses tabulated in the lower row of Table 4-117 represent the surface standpipe pressure when operating at the various circulation flowrates. 

KOH pellets (112 g, 2 mol) were heated to 110 C, under a slow stream of 02-free N2, in a 750-mL Pyrex flanged flask equipped with a Nichrome high-torque stirrer and a double-surface water-cooled reflux condenser topped with a cold finger (— 23 "C) condenser. 3-Bromo-l,l,3,3-tetrafluoroprop-l-ene (10 131.0 g. 0.68 mol) was added dropwise to the KOH, and fresh KOH pellets were added (total, 224 g) as discoloration occurred. Distillation of the product, collected in traps at — 72 and — 196 C, gave 11 yield 25.1 g (33%) bp — 37.6 C. 

Until fairly recently, the theories described in Secs. II and III for particle-surface interactions could not be verified by direct measurement, although plate-plate interactions could be studied by using the surface forces apparatus (SFA) [61,62]. However, in the past decade two techniques have been developed that specifically allow one to examine particles near surfaces, those being total internal reflection microscopy (TIRM) and an adapted version of atomic force microscopy (AFM). These two methods are, in a sense, complementary. In TIRM, one measures the position of a force-and torque-free, colloidal particle approximately 7-15 fim in dimension as it interacts with a nearby surface. In the AFM method, a small (3.5-10 jam) sphere is attached to the cantilever tip of an atomic force microscope, and when the tip is placed near a surface, the force measured is exactly the particle-surface interaction force. Hence, in TIRM one measures the position of a force-free particle, while in AFM one measures the force on a particle held at a fixed position. 

Figure 3-4). Ignoring the discontinuity where the conical and cylindrical surfaces meet, the total torque is given in terms of the arithmetic mean stress, Oxa ... 

With the annular cone there is no comparable error since the whole of the torque is developed over the conical surface bounded by radii at and a-2- Consequently there is no limitation to the value of a2, and the gap width can be comparatively large. As ai/a2 approaches unity the system approximates to a ring and plate configuration. The condition of uniform shear rate is maintained and the total torque t developed over the conical surface is given by... 

Although the derivation of the continuity equation by use of a fixed control volume is perfectly satisfactory, it is less obvious how to apply Newton s laws of mechanics in this framework. The familiar use of these principles from coursework in classical mechanics is that they are applied to describe the motion of a specific body subject to various forces or torques. To apply these same laws to a fluid (i.e., a liquid or a gas), we introduce the concepts of material points and a material volume (or material control volume) that we denote as Vm(t). Now a material point is a continuum point that moves with the local continuum velocity of the fluid. A material volume Vm (t), is a macroscopic control volume whose shape at some initial instant, / = 0, is arbitrary, that contains a fixed set of material points. Because the material volume contains a fixed set of such points, it must move with the local continuum velocity of the fluid at every point. Hence, as illustrated in Fig. 2-3, it must deform and change volume in such a way that the local flux of mass through all points on its surface is identically zero for all time (though, of course, there may still be exchange of molecules due to random molecular motion). Because mass is neither created nor destroyed according to the principle of mass conservation, the total mass contained... 

Total torque = torque from the vane cylindrical shearing surface -t- torque from both vane end shearing surfaces... 

However, the skin friction coefficient cannot be determined directly from the experimental data, as the total torque measured (Cy), includes a component due to end effects (Gp) as well as the cylinder surface component (Cc). 

The variation of the total torque for the 121mm rotor with rotor Reynolds number could then be predicted by integrating the local skin friction coefficient over the complete rotor surface. The end effects were included as an extra axial length of cylinder. The predicted total torque and the experimental data are plotted in Figure 7 and show good agreement. 

The proportion of the total torque due to the radial surfaces is small, typically around 15%, but the estimate of the total torque is still sensitive to large errors in the estimate of the radial surface torque. Figure 7 shows a recalculated prediction assuming that the local skin friction coefficient for the radial surfaces was double the value for the cylindrical surfaces. It can be seen that the prediction differs significantly from the experimental data. 

It can be concluded that, for this type of geometry where the proportion of total torque due to the radial surfaces is small, taking the local radial surface skin friction coefficient to be equal to the cylinder surface skin friction coefficient is a valid approach to predicting the total torque. 

However, this level of agreement between prediction and experimental data is not conclusive as the long plain cylinder component swamped any influence of the end effects on the total torque. There remains, therefore, some end effects which are a function of unknown effects in the flow over the rotating surface, and it is still not clear if they are unique to the test rig or are generally applicable. 

In evaluating the total torque and power loss associated with the cam care must be taken. The total load acting due to normal mean pressure may be equated to a force system acting at the Instantaneous centre of curvature (Figure (1)). This will assist in determining cam torque for the case of rigid surfaces. 

The principal scheme of the torque pendulum is shown in Figure 5.21. A disk of radius R is placed at the surface of the liquid or at the interface between the two liquids (a polar aqueous surfactant solution phase and a nonpolar phase, that is, hydrocarbon or fluorocarbon). The disk is suspended on a thin wire that serves as a dynamometer. Turning this wire by an angle f produces a torque M, while the turn of a cuvette by an angle ( ) with respect to the disk leads to the total shear deformation of the adsorption film. The principle of operation of this instrument is similar to that of a rotation viscometer, with one principal difference in the torque pendulum it is not possible to utilize a thin gap between a disk and a cuvette. Because of this the stresses and the deformations in the film are not uniform. 

Consider the liquid in the element of the space between the cone and plate surfaces and between distances r and r + dr from the axis of rotation. Using the notation of Fig. 6.4, if the rate of rotation of the plate is cj rad s", the rate of shear of the liquid in the element is cor/y. Now yjr equals tan 0, so that the rate of shear at a distance r from the axis is co/tan B which is independent of r. When 6 is small, which is the usual condition, yjr B and the rate of shear is cj/B. Let the shear stress on this element be r. The torque exerted through the element of liquid lying between radii r and r + dr is then Inrdrrr and the total torque T is given by ... 

The amplitude of oscillation in torque-time curve or that of the ram movement decreases as the contents becomes more homogeneous. In order to use these or total energy for deciding the endpoint, the dispersion must be examined ahead of time to assure a satisfactory result. The reproducibility in the same type mixer but different machines may be a problem. There may be a difference in the extent of wear of the rotor blades. The cooling surface may have scale build-up such that the cooling efficiency may be different. 

Total internal reflection microscopy enables the measurement of colloidal forces down to weak forces of 10 fNf under conditions of free Brownian motion that may better resemble true colloidal systems compared to other methods where force distance curves are recorded via enforced movement of surfaces. However, its application is limited to transparent surfaces and repulsive interaction potentials. Magnetic tweezers allow the measurement of forces down to 10 pN. Therefore, magnetic tweezers have mainly been applied to the measurement of molecular interactions. One advantage is the possibility to apply a defined torque, which has made them the most prominent tool to study twisting of molecules such as DNA. 

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