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

15300 N

Step-by-step explanation:

`\rho_i` = Density of air at inlet

`(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=((m)/(t))/(\rho_oA_o)\\\Rightarrow v_o=(60)/(0.25* 0.5)\\\Rightarrow v_o=480\ \text{m/s}`

Thrust is given by

`F=(m)/(t)(v_o-v_i)\\\Rightarrow F=60* (480-225)\\\Rightarrow F=15300\ \text{N}`

The thrust generated is 15300 N.