Friction viscous

Gearbox, lead-screw and machine-table. With reference to Figure 2.9 (free-body diagram of a gearbox), the motor-shaft will have zero viscous friction Cm, hence equation (2.22), using Laplace notation, becomes... 

The output shaft in this case is the lead screw, which is assumed to have zero moment of inertia /q and viscous friction Cq. The free-body diagrams of the machine-table and lead-screw are shown in Figure 4.30. 

Therefore, the inertia forces have an insignificant influence on the sedimentation process in this regime. Theoretically, their influence is equal to zero. In contrast, the forces of viscous friction are at a maximum. Evaluating the coefficient B in equation 55 for a = 1 results in a value of 24. Hence, we have derived the expression for the drag coefficient of a sphere, = 24/Re. 

Another velocity finally appears in a system where a liquid is in contact with an interface. The interface energy 7 then works as a static driving force. This can trigger a current which is damped by a dynamic force, the viscous friction, in the case of density difference between crystal and liquid. Taking the ratio... 

It is well known, that under industrial conditions a method of introducing filler into the polymer mixture is used. In this case, the filler is introduced in the form of paste containing up to 60 per cent water in order to reduce viscosity, As heating is affected by viscous friction, the temperature conditions are not stable on mixing and, therefore, conductivity of the conducting polymer composite becomes unreproducible. Up to now this factor has not been taken into consideration. 

Fig. 23—A schematic force curve plotted as a function of sliding velocity. A viscous friction forms the background of the force curve upon which the frictions from superharmonic and parametric resonance are superposed.

The velocity v of liquid motion can be found from the condition that the electric force should be compensated by the viscous friction force /f. The latter is proportional to the velocity gradient in the layer of slipping charges ... 

A flowing fluid is required to do work to overcome viscous frictional forces so that in practice the quantity W0 is always positive. It is zero only for the theoretical case of an inviscid fluid or ideal fluid having zero viscosity. The work W, may be done on the fluid by a pump situated between points 1 and 2. 

The coefficient C in equation 30 is a function of two phenomena. First, the presence of viscous friction accounts for a small loss of energy. Nozzle orifice contraction results in discharge coefficients which range from 0.5 to 0.85. The coefficient falls in the upper portion of this range when the length of the nozzle is two or three times its diameter, and in the lower end of the range where the nozzle diameter is more than five times its length. 

For systems which spread spontaneously it is well-known that a spreading drop forms a thin (< 0.1 pm) primary or precursor film [279-282], Its thickness and extension are determined by surface forces. In the precursor film, energy is dissipated by viscous friction. The liquid transport in the precursor film is driven by the disjoining pressure in the precursor film which sucks liquid from the wedge of the drop. 

Since in hydrodynamic lubrication the friction force is completely determined by the viscous friction of the lubricant, the coefficient of friction can be calculated from hydrodynamics using the Navier-Stokes equations. This had already been done in 1886 when Reynolds published his classical theory of hydrodynamic lubrication [494], The friction force Fp between two parallel plates of area A separated by the distance d is given by ... 

In practical applications, the increase of viscous friction with speed is often lower than expected from Eq. (11.9). The explanation is that friction leads to an increased temperature of the lubricant which reduces the viscosity. For most lubricants the temperature dependence of the viscosity is given by... 

A cylindrical axis of 1 cm diameter and 10 cm length is rotating in a precision bearing with an inner diameter, which is only 6 /xm larger. We use octadecane as the lubricant. Due to friction it heats up to 50°C, where its viscosity is 2.49 mPa s. The axis rotates with 80 rotations per second. What is the torque we have to apply to overcome the viscous friction ... 

For natural convection, a correlation was established between the Nusselt criterion, which compares convective and conductive resistances to heat transfer and the Rayleigh criterion, which compares buoyancy forces with viscous friction ... 

If two systems, such as a model and its prototype or two pipelines with different fluids, are to be dynamically equivalent so far as inertia and viscous friction are concerned, they must both have the same value of Nr. For the same fluid in both cases, the equation shows that a high velocity must be used with a model of small linear dimensions. It is also possible to compare the action of fluids of very different viscosities, provided only that L and V are so chosen as to give the same value of Nr. 

In addition to the entropy creation due to heat transfer, there are entropy creations A and B due to viscous friction in the fluid in the tubing and on the shell side of the exchanger respectively. For example (32,33),... 

This is generally a so-called conservative force and depends only on the position of the body. Second is the frictional force, which always opposes the motion of the body through its medium. This includes sliding friction if the body is slipping across a solid surface. Most relevant is viscous friction due to the drag forces of air, water, or other fluids that retard the motion of any body passing through them. For low velocities, this force is directly... 

Calculate the drag (viscous-friction) force on the plate in Prob. 5-21 under the conditions of no heat transfer. Do not use the analogy between fluid friction and heat transfer for this calculation i.e., calculate the drag directly by evaluating the viscous-shear stress at the wall. 

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