Consider a burette (like the one in a chemistry lab) with uniform cross-section and open at both ends so that they are exposed to the atmosphere. Once we open the stopcock/plug (P in the diagram) the water filled inside it will begin to flow down. The speed of the water throughout should be the same as the cross sectional area(A in diagram)is same throughout.But if an analysis using Bernoulli's equation is done involving the top portion(T) and the bottom portion(T) of the water column ( calculation in diagram ), the result is absurd.
What is the mistake in my reasoning? Isn't Bernoulli's equation supposed to be based on conservation of energy ? I believe that Bernoulli's equation is used for a specific instance of time only where the energy remains constant but here the energy changes once the stopcock is opened.