Flow rate relation with height

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The flow rate of water through the tube is influenced by the height of the water bag due to gravitational potential energy, described by the equation mgh, which indicates that as height increases, flow rate should also increase. The Hagen–Poiseuille equation is relevant for understanding how the diameter and length of the tube affect flow rate, emphasizing that these factors are significant. The relationship between height and flow rate is not strictly linear; instead, it may exhibit a concave down trend or plateau at higher heights due to factors like increased resistance in the tube. The total energy conservation principle, combining potential and kinetic energy, confirms that as water flows down, its velocity must increase. Ultimately, there may be a point where the flow rate stabilizes, indicating a plateau effect at certain heights.
Byron CTL
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The scenario:

I have a bag containing 3L of water, attached to a tube with the end placed on the floor (or a fixed height from the floor e.g. a bucket placed on top of a chair at 60 cm). I plan to hang this bag at heights of 100 cm, 120 cm, 140 cm, etc... until say about 200 cm from the floor (or a bucket placed at a fixed height). Now, my aim is to find out whether the flow rate of the water through the tube increases when I place the bag of water at ever increasing height (100 cm until 200 cm). Logically it should, right? So I would like to know which equation/formula/physics law should I use to explain this (can be more than one law/formula/equation). Now, the second thing I want to know is the trend of increment in the water flow rate as I increase the height in a linear manner (fixed increment in height of 20 cm each time); will the flow rate of the water increase linearly (as in a straight line on the graph) or in other manners (e.g. a graph that is concave down in an increasing trend, or with a plateau at the end). This can be explained by the equation(s), isn't it? That's why I need you to tell me which are the ideal equation(s) to use. Also, aside from those two issues above, I want to confirm whether the length and diameter of the tube is important as well. So far I am just using the Hagen–Poiseuille equation, but I am not sure whether the gravitational potential energy principle can also be used it this situation. Most importantly, I want to know whether there will be a plateau in the flow rate of water through the tube when the water bag is at a particular height.

Thank you for your time and answer.
 
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Any idea please?

Thank you.
 
Use potential energy, mgh, and kinetic energy, (1/2)mv^2. Since the total energy is constant, as the water flows down, it velocity must increase so that (1/2)mv^2+ mgh= constant.
 
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