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It ignores density differences except where they appear in terms multiplied by g, the acceleration due to gravity. The essence of the Boussinesq approximation is that the difference in inertia is negligible but gravity is sufficiently strong to make the specific weight appreciably different between the two fluids.
Below are few ultrarelativistic approximations when .The rapidity is denoted : Motion with constant proper acceleration: d ≈ e aτ /(2a), where d is the distance traveled, a = dφ/dτ is proper acceleration (with aτ ≫ 1), τ is proper time, and travel starts at rest and without changing direction of acceleration (see proper acceleration for more details).
where ħ is the reduced Planck constant, a is the proper uniform acceleration, c is the speed of light, and k B is the Boltzmann constant. Thus, for example, a proper acceleration of 2.47 × 10 20 m⋅s −2 corresponds approximately to a temperature of 1 K. Conversely, an acceleration of 1 m⋅s −2 corresponds to a temperature of 4.06 × 10 ...
The acceleration of a falling body in the absence of resistances to motion is dependent only on the gravitational field strength g (also called acceleration due to gravity). By Newton's Second Law the force F g {\displaystyle \mathbf {F_{g}} } acting on a body is given by: F g = m g . {\displaystyle \mathbf {F_{g}} =m\mathbf {g} .}
Chemical reactions involving thermal runaway are also called thermal explosions in chemical engineering, or runaway reactions in organic chemistry.It is a process by which an exothermic reaction goes out of control: the reaction rate increases due to an increase in temperature, causing a further increase in temperature and hence a further rapid increase in the reaction rate.
For example, two crystal wine glasses may shatter when impacted against each other. A shear pin in an engine is designed to fracture with a specific magnitude of shock. Note that a soft ductile material may sometimes exhibit brittle failure during shock due to time-temperature superposition. A malleable item can be bent by a shock. For example ...
This results in a difference between the directions of absorption and re-emission of radiation, which yields a net force along the direction of motion of the orbit. If the object is a prograde rotator, the force is in the direction of motion of the orbit, and causes the semi-major axis of the orbit to increase steadily; the object spirals away ...
Some energy may be transferred between the surroundings and the reactants in the form of heat or light; thus the products of a reaction have sometimes more but usually less energy than the reactants. A reaction is said to be exothermic or exergonic if the final state is lower on the energy scale than the initial state; in the less common case ...