Fluids Mechanics, finding height in the piezometric tube

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bermet
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A large open tank, shown below, contains water at a height H. The water is allowed to flow out through a pipe whose cross-sectional area is A. The pipe has a nozzle at the end, whose area is a. Assuming frictionless flow, determine (i) the height h to which the water rises in the piezometer tube, and (ii) the velocity V at the nozzle, for the following three cases:
a = 0, i.e., the nozzle is blocked and no flow is allowed.

a = A/2

a = A

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I tried to solve the problem using Bernoulli's at the points shown below:
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