24. Liquid Pressure & Upthrust

1. Factors Affecting Liquid Pressure

Pressure in a liquid is primarily caused by the collisions of water molecules, but it is also influenced by the weight of the liquid above an object.

• Depth: As an object moves deeper, the column of liquid above it increases. This added weight results in higher pressure.

• Density: Denser liquids have a larger mass per unit of volume, meaning the weight of the liquid column is greater, leading to higher pressure.

• Gravitational Field Strength ($g$): This determines the weight for a given mass. On Earth, $g$ is approximately $9.8 N/kg

2. Calculating Liquid Pressure

The equation for pressure at a certain depth in a liquid is:

$\text{Pressure} = \text{height of column} \times \text{density} \times \text{gravitational field strength}$

$P = h \times \rho \times g$

• Pressure (P): Measured in Pascals (Pa).

• Height ($h$): The depth of the object in meters (m).

• Density ($\rho$): The density of the liquid in kg/m³.

• $g$: Gravitational field strength (N/kg).

3. Upthrust

Upthrust is the resultant upwards force exerted by a fluid on a submerged object.

• How it works: Because pressure increases with depth, the bottom of a submerged object experiences a larger upwards force than the downwards force acting on the top.

• Resultant Force: This difference in force creates an overall upwards force called upthrust.

4. Floating and Sinking

Whether an object floats or sinks depends on the balance between its weight (acting downwards) and the upthrust (acting upwards).

• Sinking: Occurs if the object's weight is greater than the upthrust.

• Floating: Occurs if the upthrust is equal to or greater than the object's weight.

The Density Rule:

A simpler way to predict if an object will float is by comparing densities:

• Sink: If the object is more dense than the liquid (e.g., a rock in water).

• Float: If the object is less dense than the liquid (e.g., an apple in water).

5. Summary Table