Friction, fluid

As load is increased and relative speed is decreased, the film between the two surfaces becomes thinner, and increasing contact occurs between the surface regions. The coefficient of friction rises from the very low values possible for fluid friction to some value that usually is less than that for unlubricated surfaces. This type of lubrication, that is, where the nature of the surface region is... 

If these assumptions are satisfied then the ideas developed earlier about the mean free path can be used to provide qualitative but useful estimates of the transport properties of a dilute gas. While many varied and complicated processes can take place in fluid systems, such as turbulent flow, pattern fonnation, and so on, the principles on which these flows are analysed are remarkably simple. The description of both simple and complicated flows m fluids is based on five hydrodynamic equations, die Navier-Stokes equations. These equations, in trim, are based upon the mechanical laws of conservation of particles, momentum and energy in a fluid, together with a set of phenomenological equations, such as Fourier s law of themial conduction and Newton s law of fluid friction. When these phenomenological laws are used in combination with the conservation equations, one obtains the Navier-Stokes equations. Our goal here is to derive the phenomenological laws from elementary mean free path considerations, and to obtain estimates of the associated transport coefficients. Flere we will consider themial conduction and viscous flow as examples. 

The dimensionless group hD/k is called the Nusselt number, Nn , and the group Cp i./k is the Prandtl number, Np. . The group DVp/ i is the familiar Reynolds number, encountered in fluid-friction problems. These three... 

The dimensionless relations are usually indicated in either of two forms, each yielding identical resiilts. The preferred form is that suggested by Colburn ran.s. Am. In.st. Chem. Eng., 29, 174—210 (1933)]. It relates, primarily, three dimensionless groups the Stanton number h/cQ, the Prandtl number c Jk, and the Reynolds number DG/[L. For more accurate correlation of data (at Reynolds number <10,000), two additional dimensionless groups are used ratio of length to diameter L/D and ratio of viscosity at wall (or surface) temperature to viscosity at bulk temperature. Colburn showed that the product of the Stanton number and the two-thirds power of the Prandtl number (and, in addition, power functions of L/D and for Reynolds number <10,000) is approximately equal to half of the Fanning friction fac tor//2. This produc t is called the Colburn j factor. Since the Colburn type of equation relates heat transfer and fluid friction, it has greater utility than other expressions for the heat-transfer coefficient. 

Successive reflections of the pressure wave between the pipe inlet and the closed valve result in alternating pressure increases and decreases, which are gradually attenuated by fluid friction and imperfect elasticity of the pipe. Periods of reduced pressure occur while the reflected pressure wave is travehng from inlet to valve. Degassing of the liquid may occur, as may vaporization if the pressure drops below the vapor pressure of the liquid. Gas and vapor bubbles decrease the wave velocity. Vaporization may lead to what is often called liquid column separation subsequent collapse of the vapor pocket can result in pipe rupture. 

Fluid friction in conduits Darcy friction factor = 4/... 

The actual horsepower input to the compressor shaft is the sum of the gas compression horsepower plus losses from the compressor wheel friction, fluid friction, gas turbulence, gas hy-passing internally, and seal and hearing friction. 

When two bodies are in contact and there is a tendency for them to slide with respect to each other, a tangential friction force is developed that opposes the motion. For dry surfaces this is called dry friction or coulomb friction. For lubricated surfaces the friction force is called fluid friction, and it is treated in the study of fluid mechanics. Consider a block of weight W resting on a flat surface as shown in Figure 2-5. The weight of the block is balanced by a normal force N that is equal and opposite to the body force. Now, if some sufficiently small sidewise force P is applied (Figure 2-5b) it will be opposed by a friction force F that is equal and opposite to P and the block will remain fixed. If P is increased, F will simultaneously increase at the same rate until... 

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. 

Klinkenberg, A. and Mqqy, H. H. Chem. Eng. Prog. 44 (1948) 17. Dimensionless groups in fluid friction, heat and material transfer. 

It is now convenient to relate the pressure drop due to fluid friction —APf to the shear stress R0, at the walls of a pipe. If Ry is the shear stress at a distance y from the wall of the pipe, the corresponding value at the wall is given by ... 

The energy required for conveying can conveniently be considered in two parts that required for the flow of the air alone, and the additional energy necessitated by the presence of the particles. It should be noted, however, that the fluid friction will itself be somewhat modified for the following reasons die total cross-sectional area will not be available for the flow of fluid the pattern of turbulence will be affected by the solids and the pressure distribution through the pipeline will be different, and hence the gas density at a given point will be affected by the solids. 

Colburn, A.P. Trans. Am. Inst. Chem. Eng. 29 (1933) 174. A method of correlating forced convection heat transfer data and a comparison with fluid friction. 

Chilton, T.H. and Colburn, A.P. Ind. Eng. Chem. 26 (1934) 1183. Mass transfer (absorption) coefficients — production from data on heat transfer and fluid friction. 

Sherwood, T.K.. Ind. Eng. Chem. 42 (1950) 2077. Heat transfer, mass transfer, and fluid friction. 

Air at 330 K, flowing at 10 m/s, enters a pipe of inner diameter 25 mm, maintained at 415 K. The drop of static pressure along the pipe is 80 N/m2 per metre length. Using the Reynolds analogy between heat transfer and fluid friction, estimate the air temperature 0.6 m along the pipe. 

For planar flow in a viscous fluid, frictional forces between the flow planes give rise to shear stress across the planes of the flow. For flow along x, the shear stress across an area A is... 

J. C., Irreversibility phenomena associated with heat transfer and fluid friction in laminar flows through singly connected ducts, Int. J. Heat Mass Transfer 40 (1997) 905-914. 

Sabersky, R. H., and H. E. Mulligan, 1955, On the Relationship between Fluid Friction and Heat Transfer in Nucleate Boiling, Jet Propulsion 25(9) 12. (5)... 

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Polyacrylamide (Partially Hydrolyzed) 3 34 2 IC S S RF Fluid loss additive in cementing, drilling fluids, friction reduction in fracturing, enhanced oil recovery, scale inhibitor... 

For the conditions specified in Example 1.7, the pressure drop is caused entirely by fluid friction. In general, there will also be static head and accelerative components and in these cases equation 1.37 should be written in the more general form... 

White, C.M., Fluid friction and its relation to heat transfer, Transactions Institution of Chemical Engineers, 10, pp. 66-80(1932). 

Equation 7.10 shows that the total pressure gradient comprises three components that are due to fluid friction, the rate of change of momentum and the static head. The momentum term is usually called the accelerative component. Thus... 

Most studies of hydrocyclone performance for particle classification have been carried out at particle concentrations of about 1 per cent by volume. The simplest theory for the classification of particles is based on the concept that particles will tend to orbit at the radius at which the centrifugal force is exactly balanced by the fluid friction force on the particles. Thus, the orbits will be of increasing radius as the particle size increases. Unfortunately, there is scant information on how the radial velocity component varies with location. In general, a particle will be conveyed in the secondary vortex to the overflow, if its orbital radius is less than the radius of that vortex. Alternatively, if the orbital radius would have been greater than the diameter of the shell at a particular height, the particle will be deposited on the walls and will be drawn downwards to the bottom outlet. 

The general characteristics of vortices have been considered in Volume 1, Chapter 2, where it has been shown that, in the absence of fluid friction, the relation between tangential fluid velocity ut and r is as follows ... 

For a free vortex, it is shown in Volume 1, Chapter 2, that the product of the tangential velocity and the radius of rotation is a constant. Because of fluid friction effects, this relation does not hold exactly in a cyclone separator where it is found experimentally that the tangential velocity is more nearly inversely proportional to the square root of radius,... 

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