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5 February, 11:17

Air flows into a jet engine at 70 lbm/s, and fuel also enters the engine at a steady rate. The exhaust gases, having a density of 0.1 lbm/ft3, exit through a circular cross section with a radius of 1 ft at 1450 ft/s relative to the engine. Find the mass of fuel which is supplied to the engine each minute.

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  1. 5 February, 11:40
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    1387908 lbm/h

    Explanation:

    Air flowing into jet engine = 70 lbm/s

    ρ = Exhaust gas density = 0.1 lbm/ft³

    r = Radius of exit with a circular cross section = 1 ft

    v = Exhaust gas velocity = 1450 ft/s

    Exhaust gas mass (flow rate) = Air flowing into jet engine + Fuel

    Q = (70+x) lbm/s

    Area of exit with a circular cross section = π*r² = π*1² = π m²

    Now from energy balance

    Q = ρ*A*v

    ⇒70+x = 0.1*π*1450

    ⇒70+x = 455.53

    ⇒ x = 455.53-70

    ⇒ x = 385.53 lbm/s

    ∴ Mass of fuel which is supplied to the engine each minute is 1387908 lbm/h
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