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P3slides - PRODUCTION OF THRUST Newtons 2nd Law (e.g. S F =...

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PRODUCTION OF THRUST Newton’s 2 nd Law ( e.g . S F = d/dt (mv)) for a control volume of fixed mass with steady flow in and out and no acceleration of the frame of reference relative to inertial coordinates: Û Â F = Ù u ( r u )⋅ nds ı s Sum of external forces on control volume, e.g. Net flux of momentum through Pressure forces surface of control volume Shear forces Body forces Reaction forces For x-component of vectors: Û Â F = Ù u r u nds x ı x s Waitz, 2002 1
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PRODUCTION OF THRUST Û T - D + Â Pr essure Forces = Ù r u ( u n ) dA ı x s ˘ Û È Û T - D + Í - P A + P A - Ù ( P R - P ) dA R = Ù r u ( u n ) dA Î e e o e ı A R o ˙ ˚ ı x s Û Û Ù r u u ndA = r u A u - r u A u + Ù r u u x e e e e o o o o x ı s ı C - A - A s o e Û ˙ ˙ = m u - m u + Ù r u u e e o o ı C x - A - A s o e Û Û ˙ ˙ T - D - ( P - P ) A - Ù ( P R - P ) dA R = m u - m u + Ù r u u e o e e e o o ı A R o ı C s - A e - A o x Waitz, 2002 2
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PRODUCTION OF THRUST Everything that relates to flow through the engine is conventionally called thrust. Everything that relates to the flow on the outside of the engine is conventionally call drag. Therefore, gathering only those terms that relate to the fluid that passes through the engine, we have: ˙ ˙ T = m e u e - m o u o + ( P e - P o ) A e The thrust is largely composed of the net change in momentum of the air entering and leaving the engine , with a typically small adjustment for the differences in pressure between the inlet and the exit.
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P3slides - PRODUCTION OF THRUST Newtons 2nd Law (e.g. S F =...

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