Water upthrust, also known as buoyant force, is calculated by multiplying the volume of water displaced by the density of the water and the acceleration due to gravity.
Understanding Upthrust Calculation
Upthrust is the upward force exerted by a fluid (like water) that opposes the weight of an immersed object. The key to calculating it lies in understanding Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid displaced by the object.
Here's a breakdown of the formula and concepts:
The Formula
The upthrust force can be calculated using the following formula:
Upthrust = (Volume of liquid displaced) * (Density of liquid) * (Acceleration due to gravity)
Where:
- Volume of liquid displaced: This is the volume of the liquid that is pushed away by the object when it's submerged. Importantly, this volume is equal to the volume of the object that is immersed in the liquid.
- Density of liquid: This refers to how much mass of the liquid is packed into a given volume, typically measured in kilograms per cubic meter (kg/m³). For water, this is approximately 1000 kg/m³.
- Acceleration due to gravity (g): This is the acceleration at which objects fall towards the Earth, roughly 9.81 m/s².
Key Components Explained
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Volume of Liquid Displaced: The volume of liquid displaced directly correlates with how much of the object is submerged. If an object floats, only a portion of its volume displaces water. If it's fully submerged, its entire volume is what displaces the water.
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Density: Different liquids have different densities, meaning that the upthrust on the same object will vary if it's submerged in different liquids.
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For instance, an object will experience more upthrust in salt water than freshwater, as saltwater is denser than freshwater.
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Gravity: The earth's gravitational pull influences the weight of the water displaced. This, in turn, affects how strongly the displaced water 'pushes back', creating the upthrust force.
Practical Example
Let’s imagine a wooden block with a volume of 0.01 m³ is fully submerged in water. The density of water is 1000 kg/m³ and gravity is approximately 9.81 m/s². Using the upthrust formula:
- Volume of liquid displaced: 0.01 m³ (since it's fully submerged)
- Density of water: 1000 kg/m³
- Acceleration due to gravity: 9.81 m/s²
Upthrust = 0.01 m³ 1000 kg/m³ 9.81 m/s² = 98.1 N (Newtons)
Therefore, the upthrust force on the wooden block is 98.1 Newtons.
Table Summary
| Parameter | Symbol | Unit | Description |
|---|---|---|---|
| Volume of Liquid Displaced | V | m³ | The volume of the liquid pushed away by the object. |
| Density of Liquid | ρ (rho) | kg/m³ | The mass of the liquid per unit volume. |
| Acceleration due to gravity | g | m/s² | The acceleration caused by gravity, approximately 9.81 m/s² on Earth. |
| Upthrust | Fup | N (Newtons) | The upward force exerted by the fluid on the object. |
Formula: Fup= V ρ g
Tips
- Always ensure the units of volume, density and gravity are consistent. (e.g. Volume in cubic meters, density in kg per cubic meter, gravity in meters per second squared).
- If an object is floating, the upthrust force is equal to the weight of the object. In this case, only a portion of the object's volume is used to calculate the upthrust (the part that is submerged.)
