Pile equations

Abstract. The transition region between two parts of a pile which have different compositions is investigated. In the case where the moderator is the same in both parts of the pile, it is found, that the diffusion constant times fast neutron density satisfies the usual pile equations everywhere, right to the boundary. More complicated formulae apply in a more general case. 

The advantage of the above way of writing the ordinary pile equations is that it does not assume that the fission neutrons are monochromatic. 

As in CP-1461 rif is the sum of the velocities of all the thermal neutrons which are present in a cubic centimeter and n/ is the sum of the velocities of the fast neutrons present in a cubic centimeter. The pile equations then are... 

The pile equations will be used here in the form given in CP-3048, except that the effect of the delayed neutrons will also be taken into accoimt. We have... 

For the stationary case, in a simple bare pile, equations (1) have been solved before (CP-3048), except that the existence of delayed neutrons was not taken into account there. As pointed out there, this does not introduce any difficulties. In order to save some space, the stationary problem will not be treated separately but we go over at once to periodic solutions, i.e., assume that all quantities c,-, n depend on time by means of a factor This means that... 

Actually, this is not altogether justified since the slowing down power does change at low energies because of the effects of chemical binding and lattice structure. These effects are not properly within the scope of the pile equations which we use, just as the whole notion of thermal neutrons is inaccmrate. Since, however, there is no better theory available at present, this difiiculty will be disregarded. 

All pile equations considered heretofore have the form... 

Abstract. Simplified pile equations are derived under the assumption that the fast neutrons have at every collision with the moderator the same probability of reaching thermal energy. The approximation involved is much less accurate than Fermi s whose pile equations assume that the slowing down occurs in a definite number of collisions. However, the resulting equations are much more easily solved than Fermi s since they are ordinary instead of partial differential equations. 

The pile equations become, if one uses the above simplified picture in which a fast neutron has, at every collision, an equal chance [Pg.554]

The Zi, Z2, a, 6 are only partially determined by the equations (8a) and (9) and are more carefully determined by the boimdary conditions which are imposed on rtf or n/. If these boundary conditions are the same for rtf and n/, as is the case e.g. for an ordinary pile without control rods, one can set 5 = 0 and one obtains the usual pile equation. In the following the above equations will be applied to the case of a single rod in the center of a cylindrical pile to calculate the reduction in the effective multiplication constant. It will also be applied for the same purpose in case of a regular array of control rods as is the case for instance in the central region of the W pile. 

Viking Lander, 355 vinyl chloride, 764 virial coefficient, 168 virial equation, 168 viscosity, 186 visible light, 4, 6 vision, 113 vitamin, 74 vitamin C, F48 volatile, 310 volt, 492, A4 Volta, A., 483 voltage, 490 voltaic cell, 490 voltaic pile, 483... 

The proportionality constant g includes such parameters as the number of thermoelectric couples in the pile, their thermoelectric power, and the gain of the amplification device. It is supposed, moreover, that the response of the recording line is considerably faster than the thermal lag in the calorimeter. The Tian equation may also be written therefore ... 

For pipe networks the pressure will increase in front of the flame front as the flame travels through the network. The downstream pressure may be 8 to 16 times greater than the original upstream pressure. This concept is called pressure piling. With pressure piling, therefore, p2 = Pi X 8 X 8 and p2 = P X 16 X 16 for Equations 12-1 and 12-2, respectively. 

To estimate pressures resulting from a detonation and pressure piling, we estimate the original deflagration test pressure px using Equation 12-2 ... 

A detonation with pressure piling is now computed using Equation 12-3 ... 

Applying Equations (5.21) to the adiabatic time corresponding to the critical Damkohler number, and realizing for a three-dimensional pile of effective radius, r,. A 3 (e.g. Sc = 3.32 for a sphere for Bi —> oo), then we estimate a typical ignition time at 6 = Sc 3 of... 

Toxic material was placed many years ago in the sediments of a lake. Sedimentation since that time has continued their burial. Now, a harbor authority would like to put in ship piers with pilings that may disturb the toxic compounds in the sediments. You would like to know if the concentrations of the toxic compound have reached a sufficient level that the pilings will create an environmental threat. Which equation would you use for a quick, first estimate (See Figure E2.3.1.)... 

EPA requires that deck drainage be disposed of with no free oil." If the drainage is merely contaminated rainwater, disposal-pile diameter can be estimated from the following equation which assumes the need to separate 150-micron droplets ... 

The determination of skim pile length is the same as for other disposal piles. Because of the complex flow regime, a suitable equation has yet to be developed to size skim piles for Hrrk drainage However, field exjv-rienee ha indicated that acceptable effluent is obtained with a 20-min retention time in the baffled section. 

---