What is the relationship between the cross-sectional area of a container and the height of the water inside? To find a relationship between cross-sectional area and the height of water, we must have a fixed volume of water in order to see the difference in height as the cross-sectional area changes. We will use containers with a wide range of cross-sectional areas in order to see the outcome of the height of water with a fixed volume. We will measure the height of the water in different containers in order to achieve sufficient data.
Variables:
Independent Variable: Cross-sectional Area of container (cm^2) Dependent Variable: Height of water (cm) Controlling Variable(s): Volume of water (mL)
Procedure:
Step 1: Measure the length and width of the square-based containers in centimeters. Measure the radius of the circle-based containers in centimeters as well. Calculate the cross-sectional area using the measurements taken (independent variable). Step 2: Measure 20mL of water in a measuring cylinder to get a set volume of water (controlling variable). Step 3: Pour the 20mL of water into the smallest container and measure the height that the water reaches within the container in centimeters using a ruler. Then, pour the 20mL of water into the biggest container to establish a range for the data (dependent variable). Step 4: Pour the 20mL of water into another container and record the height of the water. Once the height of the water has been recorded, pour it into another container. Repeat this step till you have measured the height of water in every container.
Labeled Diagram:
Recorded Raw Data:
Big Carton: - Length: 9.5cm - Width: 9.5cm Small Carton: - Length: 5.7cm - Width: 5.7cm Wide Circle Container: -Radius: 4.2cm Tall Cylinder: -Radius: 2.4cm Medium Cylinder: -Radius: 1.5cm Small Cylinder: - Radius: 1.15cm Volume of Water: - 20mL
Processed Raw Data:
Graphical Analysis:
Cross-Sectional Area Vs. Height of Water
The slope is an inverse function because the height of the water can physically never be 0, the water will always have a height no matter the cross-sectional area. The y-intercept represents how much water we had to begin with.
Formula for graph: h=21.69/A^0.9589
Conclusion:
As the cross-sectional area increases, the height of the water decreases. It is an inverse function that never approaches zero because with the set volume of water, the height of the water can physically never be zero. The relationship between the cross-sectional area and the height of water are inversely related. This can be seen in the graphical evidence where as the height decreases, the cross-sectional area is increasing. Therefore, the bigger the area needed to fill, the more water is needed.
Evaluation of Procedure:
Throughout this experiment, my partners and I encountered some weaknesses and sources of uncertainty. We reused the water from the containers which caused the volume of water used to decrease every time we changed container. The decreased volume of water affected the overall height of it. An improvement to solve this source of uncertainty, is to measure out 20mL for each of the containers so that every container gets exactly 20mL. This ensures that we will not get a lower volume of water over time and that the data collection is accurate and precise.