Momentum, rate

Rate of input of momentum Rate of output of momentum + Rate of generation of momentum Rate of accumulation of momentum... 

Rate at which momentum /Rate at which momentum ... 

Includes the effects of skin friction and the change in the momentum rates in the entrance region (developing flows)... 

The strategy for solving fluid dynamics problems begins by putting a control volume within the fluid that matches the symmetry of the macroscopic boundaries, and balancing the forces that act on the system. The system is defined as the fluid that is contained within the control volume V, which is completely surrounded by surface S. Since a force is synonymous with the time rate of change of momentum as prescribed by Newton s laws of motion, the terms in the force balance are best viewed as momentum rate processes. The force balance for an open system is stated without proof as l = 2- -3H-4- -5, where... 

Momentum Rate Processes Due to External Body Forces (i.e., 5)... 

The value of the apparent friction factor can be calculated by means of Eq. 13 if the total pressure drop from z = 0 to z is known. The apparent value of the friction factor takes into account both the skin friction and the change in momentum rate due to change in the shape of the velocity profile in the hydrodynamic entrance region (see Fig. 1). 

Rate input of momentum — Rate output Rate of accumulation = of momentum -I- Rate of forces acting on or momentum the volume element, ... 

The momentum rate expressions would include both a convective (for example,... 

The equation of momentum conservation, along with the linear transport law due to Newton, which relates the dissipative stress tensor to the rate of strain tensor = 1 (y. 4, and which introduces two... 

A specific unimolecular rate constant for the decay of a highly excited molecule at energy E and angular momentum J takes the fomr... 

Regardless of the nature of the intramolecular dynamics of the reactant A, there are two constants of the motion in a nnimolecular reaction, i.e. the energy E and the total angular momentum j. The latter ensures the rotational quantum number J is fixed during the nnimolecular reaction and the quantum RRKM rate constant is specified as k E, J). 

When Che diameter of the Cube is small compared with molecular mean free path lengths in che gas mixture at Che pressure and temperature of interest, molecule-wall collisions are much more frequent Chan molecule-molecule collisions, and the partial pressure gradient of each species is entirely determined by momentum transfer to Che wall by mechanism (i). As shown by Knudsen [3] it is not difficult to estimate the rate of momentum transfer in this case, and hence deduce the flux relations. 

Equations (2.15) or (2.16) are the so-called Stefan-Maxwell relations for multicomponent diffusion, and we have seen that they are an almost obvious generalization of the corresponding result (2.13) for two components, once the right hand side of this has been identified physically as an inter-molecular momentum transfer rate. In the case of two components equation (2.16) degenerates to... 

Equations (2.10), (2.18) and (2.24) provide the flux relations in situations where each of the three separate mechanisms of momentum transfer dominates. However, there remains the problem of finding the flux relations in "intermediate" situations where all three mechanisms may be of comparable importance. This has been discussed by Mason and Evans [7], who assumed first that the rates of momentum transfer due to mechanisms (i) and (ii) should be combined additively. If we write equation (2.10) in the form... 

The right hand side represents the rate of momentum transfer from species r by mechanism (i) and, combining this with the rate of transfer by mechanism (ii) as given by equation (2.IS), we obtain... 

These are the flux relations associated with the dusty gas model. As explained above, they would be expected to predict only the diffusive contributions to the flux vectors, so they should be compared with equations (2.25) obtained from simple momentum transfer arguments. Equations (3,16) are then seen to be just the obvious vector generalization of the scalar equations (2.25), so the dusty gas model provides justification for the simple procedure of adding momentum transfer rates. 

Momentum Flow Meters. Momentum flow meters operate by superimposing on a normal fluid motion a perpendicular velocity vector of known magnitude thus changing the fluid momentum. The force required to balance this change in momentum can be shown to be proportional to the fluid density and velocity, the mass-flow rate. 

The servo voltage is a function of mass-flow rate. Axial-flow angular-momentum meters are sometimes used in measuring jet engine fuel flow as the fuel energy content correlates much mote closely with mass than volume. 

---