Bernoulli filling

The results of the studies.discussed in Section II,C permit calculations to be made of the time required for the flame to spread to the entire propellant surface. Once this phase of the motor-ignition process has been completed, the time required to fill the combustion chamber and establish the steady-state operating conditions must be computed. This can be done by the formal solution of Eq. (7). Because this equation is a Bernoulli type of nonlinear equation, the formal solution becomes... 

Consider the condition, which determines the velocity of the curved flame front propagation in the channel. Inside the stagnation zone filled by combustion products the pressure is constant and is equal to the value at infinity (when x = oo). Because of Bernoulli s integral along the streamline restricting the stagnation zone, the gas motion velocity remains unchanged. Since at x = oo the flow is plane-parallel (ptJO = const, v — 0), distributions of velocity u and of the stream function are associated with the vorticity distribution ... 

The velocity of a fluid approaching an orifice or nozzle or similar device is called the velocity of approach. For example, consider a large tank, filled with liquid, with a small orifice on its wall, near the bottom. It is assumed that the area of the tank is so large relative to that of the orifice that the velocity at the surface of the liquid (point 1) is negligible. Let the Bernoulli theorem be written between point 1 at the surface and point 2 at the orifice jet discharge, assuming the pressure is the same at both points. Let h equal the height of the liquid, measured from the surface level to the center of the orifice. Then 0 + /i + 0 = 0 + 0 + Vj2/2g, from which... 

We model the binder by a so-called BemouUifilUng, where in each layer Bernoulli experiments with probability p > 0 are performed for each cell of the PLT independently. If the Bernoulli experiment is successful, the cell is filled with binder, either completely or partially. An example can be seen in Figure 24.5, where in (a) the fiber system without binder is shown, (b) depicts the fiber system with a cell completely filled with binder, and in (c) the fiber system with a partially filled cell can be seen. A 3D realization of the stochastic multi-layer model including binder is shown in Figure 24.6. 

Even the great names of Becher and Stahl were hardly known although Jean Bernoulli s work on fermentation and Boerhaave s on fire were praised, the far greater views of Stahl on the same subjects existed only for a few chemists. The revolution which would raise chemistry to the rank it merits, and place it on a level with mathematical physics, can be accomplished only by a clever, enthusiastic, and bold chemist, who finds himself in a favourable position and profits by happy circumstances. Venel awaited the appearance of this new Paracelsus . He could hardly have hoped that, in so short a time, this role would be filled by his countryman, Lavoisier. ... 

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