Problem 1 Consider a 2-dimensional rocket shown in the following figure. The roc

Question

Problem 1 Consider a 2-dimensional rocket shown in the following figure. The rocket is in an atmosphere with a pressure Pa. The nozzle exit pressure is Pe. The exhaust velocity is Ue. The exhaust jet flow rate is m. (In the 2-dimensional space, take the surface area to be dA=1"dl, where 1 is the length) fure aoth sure Pa lhe d D 1 surface) due to the atmospheric pressure Pa (both in x and y direction) b) Apply the momentum equation to the gas inside the chamber to calculate the force on rocket internal surface from the propellant (both in x and y direction). Internal Suvfpce c) Show that the net force on rocket along x is

Explanation / Answer

Given that, P1 = Pa    and    P2 = Pe

                  Exhaust jet flow rate = mI

     a) The force on rocket , F = ?

   We know that, F = ma from the newtons second law

From that many equations has been derived.

     For this rocket ,

    In X direction,

    F = ( Pa - Pe ) A + Mg dU

       = ( Pa - Pe ) d + mI Ue   [ Hence , Mg also can be written after further assumptions and derivations as mI Ue ]

In Y - direction :

F = ( Pa - Pe ) A - Mg dU

      = ( Pa - Pe ) d - m1 Ue

[ since, A is directly proportional to d (diameter) ]

b)

Momentum of the rocket :

    Change in momentum = Impulse = Force

     MdUe - dmV = [ ( Pa - Pe ) A - Mg ] dt

         MdUe = [ (Pa - Pe )A + mI Ue ] dt

        

c) The net force in the X direction has been shown in the part-a

           Fx = ( Pa - Pe ) A + Mg dU

       = ( Pa - Pe ) d + mI Ue   [ Hence , Mg also can be written after further assumptions and derivations as mI Ue ]

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