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InterviewSolution
| 1. |
State and prove bernaullies theorem |
| Answer» Statement: For the streamline flow of non-viscous and incompressible liquid, the sum of potential energy, kinetic energy and pressure energy is constant.\xa0Proof:\xa0\xa0Let us consider the ideal liquid of density ρ flowing through the pipe LM of varying cross-section.Let P1\xa0and P2\xa0be the pressures at ends L and M and A1\xa0and A2\xa0be the areas of cross-sections at ends L and M respectively.Let the liquid enter with velocity V1\xa0and leave with velocity v2.\xa0Let A1\xa0> A2.\xa0Now, by equation of continuity,\xa0Since, A1\xa0> A2Therefore,\xa0v2\xa0> v1\xa0and P1\xa0> P2\xa0Let, m be the mass of liquid enetring at end L in time t.\xa0The liquid will cover a distance = v1t\xa0Therefore, the work done by pressure on the liquid at end L in time t is,\xa0W1\xa0= Force\xa0\xa0 = P1A1v1t ... (1)\xa0Since same mass m leaves the pipe at end M in same time t, in which liquid will cover the distance given by\xa0v2t.Therefore, work done by liquid against the force due to pressure P1\xa0is given by,\xa0\xa0 W2\xa0= P2A2v2t ... (2)\xa0Net ork done by pressure on the liquid in time t is,\xa0W = W1\xa0- W2\xa0 =P1A1v1t -\xa0P2A2v2t ... (3)\xa0This work done on liquid by pressure increases it\'s kinetic energy and potential energy.\xa0Increase in K.E of liquid is,\xa0That is,\xa0\xa0 | |