# Flow rate relation with height

• Byron CTL
In summary: As the height decreases, the velocity increases.In summary, the speaker has a bag of water attached to a tube and plans to hang it at different heights to measure the flow rate. They are looking for equations or laws to explain the increase in flow rate with increasing height and the trend of increment in a linear manner. They also question the importance of tube length and diameter and mention the Hagen-Poiseuille equation and potential energy principle. The suggested equations to use are potential energy and kinetic energy, with the understanding that as height decreases, velocity increases due to the constant total energy.
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.

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.

## What is flow rate?

Flow rate is the volume of a fluid that passes through a particular point in a given amount of time. It is usually measured in units such as liters per second or cubic meters per hour.

## How does flow rate relate to height?

Flow rate is directly proportional to the height of the fluid. This means that as the height of the fluid increases, the flow rate also increases. This relationship is known as the Bernoulli's principle.

## What is the formula for calculating flow rate?

The formula for calculating flow rate is Q = A * V, where Q is the flow rate, A is the cross-sectional area of the fluid, and V is the velocity of the fluid.

## How does the diameter of the pipe affect flow rate?

The diameter of the pipe has a significant effect on flow rate. A larger diameter pipe allows for a higher flow rate as it has a larger cross-sectional area, which means there is more space for the fluid to flow through.

## What factors can affect the flow rate-height relationship?

Some factors that can affect the flow rate-height relationship include the viscosity of the fluid, the shape and size of the container, and the presence of obstacles or bends in the pipe. Changes in these factors can result in changes to the flow rate-height relationship.

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