Fluids Mechanics, finding height in the piezometric tube

AI Thread Summary
In fluid mechanics, the discussion focuses on determining the height h in a piezometric tube and the velocity V at a nozzle for a large open tank with water flowing through a pipe. The scenarios analyzed include a blocked nozzle (a = 0), a nozzle area equal to half the pipe area (a = A/2), and a nozzle area equal to the pipe area (a = A). The application of Bernoulli's principle is suggested to solve for the height and velocity in each case. The discussion emphasizes the relationship between flow area and resulting fluid dynamics.
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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