Consider a rocket that burns steadily. The higher pressure inthe combustion chamber, the faster the propellant burns. Why isthis? The relationship is such that the higher the pressure, thecloser the gaseous flame is to the surface and the more effectivelyit can transfer heat back to the surface thereby gasifying thepropellant quicker. The rate of gas generation, ?_? , can bedescribed by the equation: ?_?=?_1 ?^?, where P is the pressure,and C1 and n are the constants for a given propellant with givenexposed surface area.
The hot gas leaving the rocket must pass through the throat of theexhaust nozzle at sonic velocity.
â–ªThe higher the pressure, the greater the density of this gasand the greater the rate of mass flow at sonic velocity. (The speedof sound in a gas is independent of pressure.) Accordingly, therate of gas escape, ??r_e , is described by theequation:??=?2?r_e=C_2P where C2 is a constant, dependent on cross section area of thenozzle throat and on the velocity of sound in the combustionproducts.
â–ªWhat is the steady operating pressure of asolid-propellant rocket for the given values of the constants C1 ,C2, and n? What values of n keep it stable?
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