15.4.1: Hydrostatics
Objectives
- Determine the relationship between pressure and depth.
- Determine the relationship between pressure and density.
- Determine the density of an unknown fluid.
Directions for depth dependence
- Start with the default settings (water density and Earth's gravity).
- Fill the tank with water by pulling the valve on the spigot.
- Select “Ruler”, and move the ruler so that zero is the surface.
- Move the pressure gauge toward the water. Measure the pressure in the water at every 0.50 m from the surface to the bottom. Record your results in a table like the one below. Note that the simulation will give you kPa. Convert to Pa before entering the values on the table.
-
Use Excel or Python, to make a graph of pressure vs depth. We saw in this chapter that pressure can be described \(P_1 = P_0 + \rho gh\).
- What is the physical meaning of the slope of your graph?
- What is the physical meaning of the y-intercept of your graph?
- Add a theoretical model to your graph using the equation above.
| Depth (m) | Pressure (Pa = N/m 2 ) |
| 0.5 | |
| 1.0 | |
| 1.5 | |
| 2.0 |
Directions for density dependence
- Now, pick a depth and vary the fluid density from 700 to 1,400 kg/m3. Record your results in a table like the one below. Note that the simulation will give you kPa. Convert to Pa before entering the values on the table.
- Record your chosen depth.
-
Use Excel or Python, to make a graph of pressure vs density. We saw in this chapter that pressure can be described \(P_1 = P_0 + \rho gh\).
- What is the physical meaning of the slope of your graph?
- What is the physical meaning of the y-intercept of your graph?
- Add a theoretical model to your graph using the equation above.
| Density (kg/m 3 ) | Pressure (Pa = N/m 2 ) |
| 700 | |
| 900 | |
| 1100 | |
| 1300 |
Further questions to test
- How would your two graphs differ if you gathered data from Mars? Jupiter? Explain why. Write a hypothesis and then test it.
- Click on the icon with the question mark on the sink to access the mystery fluid portion. Determine the density of a mystery fluid. Describe your method and results.
- Based on your results in this activity, how does the model work for determining the pressure in a fluid?