Frictional resistance: calculation

Power. The power requited to drive a belt conveyor is derived from the tensile forces requited to propel or restrain the belt at the design speed. These include the tensile forces produced by the frictional resistance of the drive, conveyor components, and material the acceleration of the material and the gravitational forces requited to lift or lower the material. Detailed information and methods of calculation can be found in belt conveyor design handbooks and in Reference 9. 

Note that for preliminary calculations, the frictional resistances in piping can be neglected but should be included in final calculations, particularly at high recirculation ratios. 

Start the mud pump, running as slowly as possible, to pump fluid at a rate of 1.5 to 2.0 bbl/min. This reduces fluid friction resistance pressures to a minimum and pumps at minimum standpipe pressure for circulation. The standpipe pressure (for 1.5 to 2.0 bbl/min) can be found from standard fluid hydraulic calculations. 

The velocity distribution and frictional resistance have been calculated from purely theoretical considerations for the streamline flow of a fluid in a pipe. The boundary layer theory can now be applied in order to calculate, approximately, the conditions when the fluid is turbulent. For this purpose it is assumed that the boundary layer expressions may be applied to flow over a cylindrical surface and that the flow conditions in the region of fully developed flow are the same as those when the boundary layers first join. The thickness of the boundary layer is thus taken to be equal to the radius of the pipe and the velocity at the outer edge of the boundary layer is assumed to be the velocity at the axis. Such assumptions are valid very close to the walls, although significant errors will arise near the centre of the pipe. 

Molecular size greatly affects transport across cellular membranes. As molecular size increases, transport across membranes decreases, because increases in molecular size will increase "frictional resistance" and decrease the diffusivity through the cell membrane. Since molecular size is generally directly proportional to molecular mass, and molecular mass is easily calculated molecular mass is often used as a descriptor of molecular size. Hence, as a general rule, the lower the molecular mass, the smaller are the molecules composing the substance, and the more easily the substance can cross membranes and be absorbed from the gastrointestinal tract, lung, and skin. 

Petukhov, B.J. Popov, N.V. Theoretical calculation of heat exchange and frictional resistance in turbulent flow in tubes of an incompressible fluid with variable physical properties. High Temperature 1 (1963) 69-83... 

In this chapter, we address in considerable depth empirical methods and models found in the literature, as well as variables that affect compressibility such as moisture, temperature, and particle size and shape. Compressibility can be used in feeder designs to calculate loads that act on a feeder or gate and angle of wall friction to calculate the pressures acting perpendicular to the hopper wall. Furthermore, it can be used for quality control to determine the resistance of materials to breakage, from the production process to the consumer. 

We will now develop an expression for the sonic speed experienced in the throat/outlet of a convergent-only nozzle and at the throat of a convergent-divergent nozzle when the expansion is frictionally resisted. Sonic conditions will exist in the throat when the velocity calculated by applying equation (14.45) to the convergent section of the nozzle has reached the local speed of sound, i.e. ... 

Figure 6.2 shows the back-calculated values of a for drilled shafts obtained from instrumented load tests. Skin friction resistance in the upper 1.5 m of the shaft, and at the base of the shaft (at height equal to the diameter of the shaft from the base), is usually ignored. 

A drop rises or falls through a liquid as the result of buoyancy or gravity forces opposed by frictional resistance to motion. The latter is characterized by a drag coefficient, the knowledge of which makes it possible to calculate drop velocity and hence the residence time of the drop in the column. Although the variation of drag coefficients with Reynolds number is well known for solid spheres, this is not the case for liquid drops, as shown by the bottom line of Fig. 2. 

According to the geological survey data, F was suggested to be calculate by the ratio of end resistance to the estimated bearing capacity, and F was the ratio of friction resistance to the estimated bearing capacity, seen equation 8 and 9. Defined SRE of the pile-soil system as F, and the relation of F, Fj and Fj was given by equation 10. 

The flow in the gas channels and in the porous gas diffusion electrodes is described by the equations for the conservation of momentum and conservation of mass in the gas phase. The solution of these equations results in the velocity and pressure fields in the cell. The Navier-Stokes equations are mostly used for the gas channels while Darcy s law may be used for the gas flow in the GDL, the microporous layer (MPL), and the catalyst layer [147]. Darcy s law describes the flow where the pressure gradient is the major driving force and where it is mostly influenced by the frictional resistance within the pores [145]. Alternatively, the Brinkman equations can be used to compute the fluid velocity and pressure field in porous media. It extends the Darcy law to describe the momentum transport by viscous shear, similar to the Navier-Stokes equations. The velocity and pressure fields are continuous across the interface of the channels and the porous domains. In the presence of a liquid phase in the pore electrolyte, two-phase flow models may be used to account for the interaction between the gas phase and the liquid phase in the pores. When calculating the fluid flow through the inlet and outlet feeders of a large fuel cell stack, the Reynolds-averaged Navier-Stokes (RANS), k-o), or k-e turbulence model equations should be used due to the presence of turbulence. 

These are noteworthy relations. They express neatly the way in which the diffusion coefficient (to which diffusion rates are proportional) depends on a balance between thermal energy, represented by kT, and frictional resistance to motion, represented by /. They allow the calculation of diffusion coefficients by classical hydrodynamic methods. Such values of D are important when, as often, experimental values are not available and when they are available, comparison with experiment permits tests of the assumptions of the theoretical models. 

Calculation of the extrusion force, i. e. of the necessary ram force, at close approximation is only possible in few, particularly simple cases, because it depends on a variety of factors that can only be evaluated in an imperfect manner. These factors include the resistance to deformation of the alloy to be extruded, in dependence of the temperature and speed at which the work is performed, the resistances caused by the varying flow phenomena in the billet, the frictional resistance on the tools, the extrusion ratio, the shape of the section, etc. The latter factor alone may essentially increase the required force, if the section is of intrical shape as compared with round rods of identical cross-sectional area (see Fig. 107). 

The frictional resistances and k are empirical values. They are dependent on the shape of the tools, their surface finish, lubrication etc. and represent a very uncertain factor in the calculation which may greatly affect the final result. 

On the other hand, the cooperative effects which minimize the frictional resistence to the chain rotations in the barrier crossings, enter automatically into the treatment as a consequence of the geometry dependence of the friction, and they mainly affect the calculated values of the kinetic rates. 

When fluid phase flowing through the catalyst, the frictional resistance is created. The coefficient of the frictional force can be calculated by the modified Ergun equation [6] ... 

Slip resistance expressed as the coefficient of fiiction of footwear is determined with glycerine used as a lubricant of footwear on a test surface. Testing is done under a load of 500 N. Dynamic coefficient of friction is calculated. If footwear has a coefficient of friction of less than 0.15, it is unclassified. If footwear has a coefficient of friction between 0.15 and 0.25, it belongs to Class I if the coefficient of friction is above 0.25, the footwear belongs to the Class II of slip-resistant footwear. ... 

Note Beyond 122.8 inches (10.2 ft.) the soil friction will overcome the tensile stress force developed by thermal contraction of the pipeline. This is calculated by dividing the tensile force in the pipe by the frictional resistance of the soil (i.e. 827.3 lbs. ( 6.363 lbs./in. = 130 inches). 

Anchors need not be designed for shear if it can be shown that the factored shear loads are transmitted through frictional resistance developed between the bottom of the base plate and grout at the top of the concrete foundation. If there is moment on a base plate, the moment may produce a downward load that will develop frictional resistance even if the eolumn or vertical vessel is in uplift, and this downward load ean be eonsideied in calculating frictional resistance. Care should be taken to assure that the downward load that produces frictional resistance occurs simultaneously with the shear load. 

The following equations may be used to calculate the frictional resistance (Figure 3.28). 

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