Does the density of a fluid affect the rate of exponential decay, shown by the rate of depreciation of height of remaining fluid in a cylindrical structure?


I first noticed that the rate of flow of water out of a bottle is not a linear relationship when a water bottle had a small hole in my sports kit bag. Within five minutes, almost all of the water had leaked into the bag. However, after rotating the bottle, the rate of flow of water was very slow. I soon discovered that this was due to the fact that because the height of the water in the bottle had changed, this had affected the rate at which water flowed out from the hole. I later discovered that the rate at which water flowed out of the bottle could be likened to exponential decay. Exponential decay is defined as decay of a quantity where the rate of decay is directly proportional to the quantity remaining. The best way to measure what volume was ‘being lost’ in a given time period (i.e. diminishing height of the fluid) was to use a burette, as markings are already present. The use of a burette also adds personal significance; these are regularly used in IB chemistry experiments, a subject at which I take at higher level. We often use substances of different concentration and viscosity in chemistry, e.g. in titrations. I therefore wanted to see the rate at which liquid leaves the burette, as this will assist with accuracy of my experiments. This is because a better understanding of the rate of flow of a liquid will mean I will be cautious of leaving the burette completely open and free to flow in important scenarios that require accuracy. A burette was chosen instead of a simple two-litre bottle was as drawing height markings in cm markings would have introduced significant error.


The research question is attempting to ascertain if the viscosity and density of a fluid will affect the rate at which the fluid flows out of a circular aperture of constant diameter.

There are many phenomena in the world in which exponential decay is referred to. The most common example of an area of interest using exponential decay is in radioactivity, where the decay constant is used to determine half-life, and other important figures. The change in decay constant in an element will affect the half-life of the element. This means that the half-life of an element can vary from seconds to millions of years. It is for this reason that studying the change in decay constant is so fascinating; it can indicate how radically differently things can behave with the simple change in decay constant. This may however, be somewhat unsuitable to investigate in a school laboratory, due to the danger of radioactive decay. It is still interesting nevertheless to see that the decay constant is able to change with viscosity and decay, which is a more appropriate school-based experiment, but still very interesting!


The tables below show criteria under explorations. These are the variables and the necessary accompaniments to show how and why that variable is being measured.


A table to show the variables in the experiment and their correspondence with type of variable, measuring tool,and the reason for choosing that piece of kit
Variable Type of Variable Measuring Tool Reason for Kit
Density of fluid Independent Hydrometer The most common method of measuring density is using the formula \(\rho = \frac{m}{V}\). However, there are several inaccuracies when using this method. Not only is more error introduced into precision calculations, but there is also error which is not possible to quantify. This comes in the form of residue of beakers left behind when transporting the fluid to measure from one container to another. This means that the volume of the fluid will be kept constant, which is a control. It is therefore best to minimise transferring fluids, so a hydrometer is used.
Half Life Dependent This will be calculated by timing the period for the initial height of the fluid to fall to half of its original value. A stop-clock will be used to measure this time. By using a burette instead of a cylindrical structure it is easier to be accurate when ascertaining how much the height of the fluid has fallen. This is because the percentage error of the factory markings are smaller than self-imposed markings.
Temperature Control Digital Thermometer By ensuring that all liquids are at the same temperature, there is only one independent variable in the experiment, thus temperature should have no bearings on the results. A digital thermometer is used for ensuring better precision and accuracy.
Starting Volume of Solution Control Burette A constant starting volume is required so that there is only one independent variable in the experiment. If this is kept constant, it is therefore only the kinematic viscosity that determines the variation in results.