Hi! Can anyone give me some tips on how i would determine the shape of a vessel from a graph of volume vs time?
"a set volume of water is poured steadily into a vessel, the height at set volume intervals is recorded." "determine a possible vessel shape based on this data"
Volume Height
1 1
2 5
3 12
4 16
5 21
6 24
7 25
I have made a graph of this, and then used gradients to find a possible shape by using the amount of water increases at each step..
any ideas? thanks
The maximum gradient occurs at the bottom, so this suggests a bowl shape to me.
The surface area of the water times change in height = change in volume approximately
So, we can start finding the cross sectional area as a function of height.
for example assume the area is 0 at 0 height
then at height one the volume is one
so the average area between 0 and one is
A = 1/1 = 1
now between volume of 1 and volume of 2 the average area is
1/(5-1) = 1/4
between volume of 2 and volume of 3 we have
1/(12-5) = 1/7
between volume of 3 and volume of 4 it is
1/(16-12) = 1/4
etc
if that area is square, then the sides are sqrt area
if the areas are circles, the radius = sqrt(area/pi)
To determine the shape of a vessel based on a graph of volume vs time, you can follow these steps:
1. Plot the data points on a graph with volume (x-axis) and height (y-axis).
2. Look for patterns or trends in the data. In this case, observe how the height changes as the volume increases.
3. Calculate the differences in height as the volume increases. This can be done by subtracting the previous height from the current height.
- For example, the difference in height between volume 2 and volume 1 is 5 - 1 = 4.
- Similarly, the difference in height between volume 3 and volume 2 is 12 - 5 = 7.
4. Examine the pattern of differences in height to determine the shape of the vessel.
- If the differences in height increase at a constant rate, such as 4, 7, 4, 5, 3, 1, it suggests a linear shape.
- If the differences in height increase at a decreasing or concave rate, such as 4, 3, 2, 1, 0, it suggests a rounded or curved shape.
- If the differences in height increase at an increasing or convex rate, such as 4, 5, 9, 8, 3, it suggests a more abrupt or angular shape.
5. Use the shape determined from the pattern of differences to estimate the actual vessel shape. In this case, since the differences in height increase at a relatively constant rate, it suggests a linear shape.
- The vessel could be a cylindrical shape, where the height increases linearly with the volume. However, other factors such as the angle of the walls or the base shape could also influence the vessel's shape.
- Note that this is just a possible interpretation based on the given data. Additional data points or context may be needed to confirm the specific vessel shape.
It's important to note that this is a simplified approach and assumes a linear relationship between volume and height. In reality, the relationship could be more complex, and additional information would be needed to accurately determine the vessel shape.