Derive the Bernoulli equation. Show all intermediate steps and state the assumpt

Question

Derive the Bernoulli equation. Show all intermediate steps and state the assumptions at the point they are used as part of the derivation. What is the physical meaning of the Bernoulli equation? A large tank, with its top open to the atmosphere, is filled with liquid to a height h (see figure). Then a hole is opened near the bottom of the tank that allows the fluid to exit to the atmosphere. Apply Bernoulli's equation (neglect friction) to a fluid streamline that extends from the surface of the liquid at the top to a point in the exit stream, just outside the vessel, to determine the exit velocity. Why can you neglect the velocity of the receding fluid at the top surface?

Explanation / Answer

http://en.wikipedia.org/wiki/Bernoulli's_principle#Derivations_of_Bernoulli_equation use this webpage to answer your doubt the velocity of the receding fluid at the top is neglected as it is small and already absorbed in the mass change ie. the pressure change term in the equation If we assume a steady, incompressible, inviscid flow along a single streamline, we can apply Bernoulli

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