Define pressure - Leaving Cert Physics - Question a - 2009

To demonstrate that pressure in a liquid increases with depth, the following experiment can be conducted:

Apparatus

• Tall container filled with liquid (e.g., water)
• Funnel
• Pressure sensor or manometer
• Holes at different depths in the side of the container

Procedure

1. Connect the tubing from the funnel to the pressure sensor.
2. Immerse the funnel into the liquid so that the open end is at the surface level.
3. Carefully fill the funnel with liquid to minimize air bubbles.
4. Observe the pressure readings at different depths by inserting the pressure sensor into the liquid at various levels (ensuring it is sealed).
5. Record the pressure readings as you measure at increasing depths.

Observation/Conclusion

As the depth increases, it will be observed that the pressure increases. This is due to the weight of the liquid above the measurement point contributing to the total pressure.

To calculate the increase in pressure as the diver goes from a depth of 5 m to 30 m, we need to find the pressure at both depths using the hydrostatic pressure formula:

$$P = \rho g h$$

where:

• $ho = 1000 \text{ kg m}^{-3}$ (density of water)
• $g = 9.8 \text{ m s}^{-2}$ (acceleration due to gravity)
• $h$ is the depth in meters.

1. Calculate pressure at depth 5 m:

   $$P_{5} = 1000 \times 9.8 \times 5 = 49000 \text{ Pa}$$

2. Calculate pressure at depth 30 m:

   $$P_{30} = 1000 \times 9.8 \times 30 = 294000 \text{ Pa}$$

3. Calculate the increase in pressure:

   $$\Delta P = P_{30} - P_{5} = 294000 - 49000 = 245000 \text{ Pa}$$

Thus, the increase in pressure on the diver at the new depth of 30 m is 245000 Pa.