Question

A ramjet operates by taking in air at the inlet, providing fuel for combustion, and exhausting the hot air through the exit. Th e mass fl ow at the inlet and outlet of the ramjet is 60 kg/s (the mass fl ow rate of fuel is negligible). Th e inlet velocity is 225 m/s. Th e density of the gases at the exit is 0.25 kg/m3 , and the exit area is 0.5 m2 . Calculate the thr

Answer 1

Answer:

15300 N

Explanation:

$\rho_i$ = Density of air at inlet

$\dfrac{m}{t}$ = Mass flow rate = 60 kg/s

$v_i$ = Inlet velocity = 225 m/s

$\rho_o$ = Density of gas at outlet = $0.25\ \text{kg/m}^3$

$A_i$ = Inlet area

$A_o$ = Outlet area = $0.5\ \text{m}^2$

Since mass flow rate is the same in the inlet and outlet we have

$\rho_iv_iA_i=\rho_ov_oA_o\\\Rightarrow v_o=\dfrac{\dfrac{m}{t}}{\rho_oA_o}\\\Rightarrow v_o=\dfrac{60}{0.25\times 0.5}\\\Rightarrow v_o=480\ \text{m/s}$

Thrust is given by

$F=\dfrac{m}{t}(v_o-v_i)\\\Rightarrow F=60\times (480-225)\\\Rightarrow F=15300\ \text{N}$

The thrust generated is 15300 N.