Final answer:
The equation u = Adg(h2-h1) cannot be directly proven with the provided information. Typically, it could be related to fluid mechanics and Bernoulli's equation. A contextual grounding or derivation of this equation is necessary to provide a proof.
Step-by-step explanation:
When proving the equation u = Adg(h2-h1), we should consider principles from fluid mechanics. Unfortunately, the context provided does not directly lead to this equation. However, to understand the relationships involved, we can refer to the Bernoulli's equation which, in one of its forms, states that P1 + ρgh1 = P2 + ρgh2, indicating that the sum of pressure and potential energy per unit volume is constant along a streamline in steady, incompressible flow without friction.
By setting one height to zero, for example h2 = 0, which simplifies the arithmetic and makes all other heights relative, we can find the pressure difference due to the height difference in a column of fluid in terms of potential energy, which is a common practice in problems concerning gravitational forces. Another related concept is that of kinematics, where an object's velocity is depended on the change in height under constant acceleration due to gravity, expressed as v = √(2g|h| + v0²).
Please note that the initial equation u = Adg(h2-h1) typically would relate to velocity (u), cross-sectional area (A), acceleration due to gravity (g), and a change in height (h2-h1), but without the proper derivations and context, proving this specific equation is not feasible with the information provided.