Division 8*. Section B-1*. National defense research committee
(NDRC) of the office of scientific research and development by H.
A. Bethe Coell University Consultant to Subsection B-1-B OSRD
N
545. Serial N
237. Date: May 4, 1942. 86 p.
Бете Г. Теория ударных волн для произвольного уравнения состояния. Полностью распознано. Данная работа Ганса Бете по атомному проекту (Теоретические разработки).
Аннотация:
This report deals with the general conditions for the existence of shock waves in any medium. It includes theorems conceing the relations between the velocities of infinitesimal waves and shock waves, between the entropy, pressure, and volume changes, and so forth. It should be of interest in the theoretical treatment of shock waves in air, water, metals, or other materials.
Contents:
Introduction
Equation of state, notation, assumptions
The shock equations
General theory for ordinary substances
Small Shockwaves
General proof of the increase of entropy for compression waves
Existence of solutions
The shock curve
Proof of the monotonic behavior1 of the entropy
Behavior of volume, energy, and pressure on the shock curve
Relation between velocity and entropy
Stability of shock waves against splitting into waves moving in the same direction
Stability against any splitting
Investigation of the three conditions
The condition (d^2p/d V^2)s more than 0 for single-phase systems
The condition (d^2p/dV^2)s more than 0 for phase transitions
Consequences of the breakdown of condition at phase boundaries
Condition (II): V(dp/dE)v more than -2
Condition (III): (dp/dV)E less than 0
Discussion of a hypothetical case: A material which satisfies conditions (I) and (II) but not
(III)
Conclusion
Relation to the theory of Duhem
Summary
545. Serial N
237. Date: May 4, 1942. 86 p.
Бете Г. Теория ударных волн для произвольного уравнения состояния. Полностью распознано. Данная работа Ганса Бете по атомному проекту (Теоретические разработки).
Аннотация:
This report deals with the general conditions for the existence of shock waves in any medium. It includes theorems conceing the relations between the velocities of infinitesimal waves and shock waves, between the entropy, pressure, and volume changes, and so forth. It should be of interest in the theoretical treatment of shock waves in air, water, metals, or other materials.
Contents:
Introduction
Equation of state, notation, assumptions
The shock equations
General theory for ordinary substances
Small Shockwaves
General proof of the increase of entropy for compression waves
Existence of solutions
The shock curve
Proof of the monotonic behavior1 of the entropy
Behavior of volume, energy, and pressure on the shock curve
Relation between velocity and entropy
Stability of shock waves against splitting into waves moving in the same direction
Stability against any splitting
Investigation of the three conditions
The condition (d^2p/d V^2)s more than 0 for single-phase systems
The condition (d^2p/dV^2)s more than 0 for phase transitions
Consequences of the breakdown of condition at phase boundaries
Condition (II): V(dp/dE)v more than -2
Condition (III): (dp/dV)E less than 0
Discussion of a hypothetical case: A material which satisfies conditions (I) and (II) but not
(III)
Conclusion
Relation to the theory of Duhem
Summary