k A large ballistic rocket vehicle has the following charact

k A large ballistic rocket vehicle has the following characteristics: propellant mass flow -rate: 12 slugs/sec (1 slug = 32.2 Ibm 14.6 kg); nozzle exit velocity: 7100 ft/sec;

Solution

a) The thrust equation for a rocket is given by

Thrust (N) = mV_e + (p_e p_o) A_e

m\' - mass flow rate of propellent, Ve - exit velocity (sea level), Pe- exit pressure at nozzle, Po- atmospheric pressure, Ae - exit area of the nozzle

replacing with the values,

Thrust (N) = 14.6 x 12 x 7100 x 0.3048 + ( 5 x 6894.76 - 14.7 x 6894.76 ) x 0.00064516 x 400

Thrust (N) = 379146.816 + (-16719.793) = 362427.023 N or 36.24 kN

b) effective velocity is the ratio of thrust over the mass rate,

F / m\' = v_eff where v_eff - effective exhaust velocity, F - thrust , m\' - mass flow rate of propellent

replacing with values,

(36.24 x 10³ ) / (14.6 x 12) = 207.03 m/s

c) Initial thrust (F) = 36.24 kN or 36.24 x 10³ (sea level) and Weight (take off) = 12 tons = 12 x 10³ N

F / W = (36.24 x 10³) / (12 x 10³) = 3.02 (unitless)

d) Initial acceration (a_i) = (v- u) / t, where v - final velocity (nozzle exit velocity) u - intial velocity, t - time (burning time)

a_i = ( (7100 x 0.3048) - 0 ) / 50 = 43.28 m / s²

d) inverse mass flow ratio = m_o / m_f where m_o - take off mass, m_f = fuel mass (mass flow of propellent x burning time)

(12 x 10³) / (7100 x 0.3048 x 50) = 0.1109 (dimensionless)