Flow rate relation with height

Byron CTL

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.

Byron CTL

Any idea please?

Thank you.

HallsofIvy

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.