p0634 - 720 CHAPTER 6 CONTROL-VOLUME METHOD 6.34 Chapter 6...

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720 CHAPTER 6. CONTROL-VOLUME METHOD 6.34 Chapter 6, Problem 34 Problem: The mass-flow rate through a nozzle is ˙ m =0 . 65 p c A t / RT c ,where p c and T c are pressure and temperature in the rocket chamber, respectively, and R is the gas constant of the gases in the chamber. The propellant burning rate (surface-regression rate) can be expressed as ˙ r = ap n c ,whe re a and n are constants. As a result, gas of density ρ p that is initially motionless enters the chamber. (a) Denoting the propellant surface burning area and nozzle throat area by A p and A t , respectively, show that p c =( a ρ p / 0 . 65) 1 / (1 n ) ( A p /A t ) 1 / (1 n ) ( RT c ) 1 / [2(1 n )] (b) If the operating chamber pressure of a rocket motor is 5 MPa and the exponent n = 0.25, to what value will chamber pressure increase if a crack develops in the grain, increasing the burning area by 20%? You may assume all variables except p c and A p remain constant. p c , ρ c ,T c Area = A p Area = A t ˙ m u cv r e r u cv r e r . . . . . . . . . . . . .
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