Accurately calculate the weight of water displaced by the metal cylinders
Cylinder Displacement Calculator
Enter the outer diameter of the metal cylinder in centimeters.
Please enter a valid positive diameter.
Enter the height or length of the cylinder in centimeters.
Please enter a valid positive height.
Total number of identical cylinders being submerged.
Please enter at least 1 cylinder.
Fresh Water (1000 kg/m³)
Salt Water (1025 kg/m³)
Ice/Glacial Water (917 kg/m³)
Mercury (13500 kg/m³) – Hypothetical
Select the density of the fluid displaced.
Total Weight of Water Displaced (Buoyant Force)
0 N
0 cm³Total Volume
0 kgDisplaced Mass
0 lbsWeight (Imperial)
Physics Applied: Archimedes' Principle states that Buoyant Force = Weight of Fluid Displaced = Fluid Density × Volume × Gravity.
Figure 1: Weight Displaced vs. Submersion Percentage
Submersion %
Volume Displaced (Liters)
Buoyant Force (Newtons)
Table 1: Step-by-step displacement based on submersion depth.
What is the Calculation for the Weight of Water Displaced by Metal Cylinders?
In maritime engineering, physics, and fluid mechanics, the need to calculate the weight of water displaced by the metal cylinders is paramount for determining buoyancy. This calculation is derived directly from Archimedes' Principle, which posits that any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.
This concept is not just theoretical; it is the foundation for designing pontoons, floating docks, sensors, and even offshore oil rig supports. When engineers calculate the weight of water displaced by the metal cylinders, they are effectively determining the maximum load the cylinders can support before sinking. This value represents the "Buoyant Force."
Common misconceptions include thinking that the weight of the cylinder itself determines displacement. In reality, only the volume of the submerged part and the density of the fluid matter. A hollow steel cylinder and a solid gold cylinder of identical dimensions will displace the exact same weight of water if fully submerged, despite their massive difference in actual weight.
Formula and Mathematical Explanation
To accurately calculate the weight of water displaced by the metal cylinders, we must follow a two-step process: first determining the volume, and then converting that volume to weight based on fluid density and gravity.
Step 1: Calculate Cylinder Volume
The volume \( V \) of a single cylinder is calculated using the geometric formula for a cylinder:
\( V_{cyl} = \pi \times r^2 \times h \)
Where \( r \) is the radius (half the diameter) and \( h \) is the height.
Step 2: Calculate Total Volume
If you have multiple cylinders, multiply by the count \( n \):
\( V_{total} = n \times V_{cyl} \)
Step 3: Calculate Weight of Displaced Fluid
Finally, to find the weight (force), we use the density of water (\( \rho \)) and the acceleration due to gravity (\( g \approx 9.81 \, m/s^2 \)):
\( W_{displaced} = V_{total} \times \rho \times g \)
Variable
Meaning
Unit (Metric)
Typical Range
\( r \)
Radius of Cylinder
Meters (m)
0.1m – 5.0m
\( h \)
Height/Length
Meters (m)
1m – 20m
\( \rho \)
Fluid Density
kg/m³
1000 (Fresh) – 1025 (Salt)
\( W \)
Weight/Buoyancy
Newtons (N)
Varies
Practical Examples (Real-World Use Cases)
Example 1: Floating Dock Pontoons
A marina is installing a new dock supported by 6 hollow metal cylinders. Each cylinder has a diameter of 0.6 meters and a length of 4 meters. They need to calculate the weight of water displaced by the metal cylinders to ensure the dock can support a 5,000 kg walkway.
Displacement: Using fresh water density (1000 kg/m³), the mass displaced is 6,780 kg.
Result: The upward buoyant force is approx 66,511 Newtons. Since 6,780 kg > 5,000 kg, the dock floats easily.
Example 2: Industrial Sensor Buoy
An engineer designs a small sensor encased in a single steel cylinder (Diameter 10cm, Height 30cm) to float in seawater. They must calculate the weight of water displaced by the metal cylinders to calibrate the sensor's depth.
Input: 1 cylinder, 10cm diameter, 30cm height. Fluid: Salt Water.
Result: The buoy generates ~23.6 Newtons of lift. If the sensor weighs less than 2.41 kg, it will float.
How to Use This Displacement Calculator
Follow these steps to effectively use the tool above:
Measure Geometry: Input the Diameter and Height of your cylinders in centimeters. Ensure accuracy, as volume scales with the square of the radius.
Count Cylinders: Enter the total number of identical cylinders in your system.
Select Fluid: Choose between Fresh Water (lakes/rivers) or Salt Water (oceans). Salt water is denser and provides more buoyancy.
Analyze Results:
Total Weight (N): The upward force exerted on the object.
Displaced Mass (kg): The maximum mass the cylinders can support before becoming neutrally buoyant.
Key Factors That Affect Displacement Results
When you set out to calculate the weight of water displaced by the metal cylinders, several external factors can influence the final financial or engineering decision:
Fluid Density (Salinity): Seawater (1025 kg/m³) provides roughly 2.5% more lift than fresh water. This is crucial for ocean-bound vessels.
Temperature: Water density changes with temperature. Warm water is less dense, providing slightly less buoyancy than cold water.
Manufacturing Tolerances: If metal cylinders are manufactured with a -5% tolerance on diameter, the volume (and thus buoyancy) decreases by roughly 10%.
Submersion Depth: The calculator assumes full submersion for maximum capacity. Partial submersion results in linearly less displacement.
Gravitational Variance: While we use standard gravity ($9.81 m/s^2$), this varies slightly by latitude, affecting precise weight calculations in high-precision scientific instruments.
Additional Equipment Weight: The "Net Buoyancy" is the displaced weight minus the weight of the metal cylinders themselves. Don't forget to subtract the steel's weight!
Frequently Asked Questions (FAQ)
Does the weight of the cylinder itself affect the water displaced?
No. Archimedes' principle depends only on the volume of the object submerged. However, if the cylinder is heavier than the water it displaces, it will sink.
How do I calculate for a hollow cylinder vs. a solid one?
For displacement, it does not matter if the cylinder is hollow or solid, as long as the outer shape displaces the water. The internal structure only affects the cylinder's own weight, not the buoyant force.
Why is the result in Newtons and Kilograms?
Newtons (N) measure Force (Weight), which is the scientifically correct unit for buoyancy. Kilograms (kg) measure Mass, which is often easier to visualize as "lifting capacity."
Can I use this for other fluids like oil?
Yes. Although designed to calculate the weight of water displaced by the metal cylinders, you can assume a different density (e.g., Oil ~800 kg/m³) and the volume math remains the same.
What if my cylinder is only half submerged?
If the cylinder is 50% submerged, simply multiply the final Weight of Water Displaced by 0.5. The relationship is linear for vertical cylinders.
Does the shape of the end caps matter?
This calculator assumes flat ends. If your cylinder has hemispherical caps, the volume calculation would need to include the volume of spheres, slightly increasing displacement.
How does this relate to boat hull design?
Pontoons are essentially metal cylinders. Engineers use this exact logic to determine how many pontoons are needed to keep a dock or boat afloat.
Is the density of water constant?
No, it varies with temperature and pressure. Standard Engineering usually assumes 1000 kg/m³, but precision tasks require temperature correction.