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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

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Answer:

15300 N

Explanation:

[tex]\rho_i[/tex] = Density of air at inlet

[tex]\dfrac{m}{t}[/tex] = Mass flow rate = 60 kg/s

[tex]v_i[/tex] = Inlet velocity = 225 m/s

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

[tex]A_i[/tex] = Inlet area

[tex]A_o[/tex] = Outlet area = [tex]0.5\ \text{m}^2[/tex]

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

[tex]\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}[/tex]

Thrust is given by

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

The thrust generated is 15300 N.

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