How Much Fresh Water Is Needed to Submerge a Submarine in Salt Water?

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SUMMARY

The discussion focuses on calculating the mass of fresh water required to keep a submarine submerged when transitioning from freshwater to saltwater. The submarine, modeled as a cylinder with a volume of 1.5 cubic meters, experiences a buoyant force of 15,082.88 N in saltwater, which has a density of 1025 kg/m³. The key takeaway is that the difference in buoyant forces between freshwater and saltwater necessitates the addition of mass to the submarine's ballast to maintain submersion. The calculations reveal that the mass of fresh water needed is derived from the difference in buoyancy due to the varying densities of the two water types.

PREREQUISITES
  • Understanding of buoyancy principles and Archimedes' principle
  • Familiarity with density calculations (e.g., density of fresh water vs. sea water)
  • Knowledge of basic physics equations related to volume and buoyant force
  • Ability to perform unit conversions and mass calculations
NEXT STEPS
  • Calculate the mass of fresh water needed using the formula: Mass = Buoyant force / Acceleration due to gravity
  • Explore the differences in buoyancy between various fluids, including other densities
  • Investigate the implications of buoyancy on submarine design and operation
  • Learn about the effects of salinity on buoyancy in marine engineering
USEFUL FOR

This discussion is beneficial for physics students, marine engineers, and anyone involved in submarine design or fluid dynamics, particularly those interested in buoyancy and density effects in different water types.

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Homework Statement



William Smith built a small submarine capable of diving as deep as 30.0 m. The submarine's volume can be approximated by that of a cylinder with a length of 3.00 m and a cross-sectional area of 0.500 square meters. Suppose this submarine dives in a freshmwater river and then moves out to sea, which naturally consists of salt water. What mass of fresh water must be added to the ballast to keep the submarine submerged? The density of fresh water is 1000 kg/m3, and the density of sea water is 1025 kg/m3.

Homework Equations



Cylinder volume = Base area x height
Buoyant force = Fluid density x Volume x Acceleration due to gravity (9.81 m/s2)

The Attempt at a Solution



I found the volume, which is 1.5 cubic meters.
I then found the buoyant force, which is 15,082.88 N.
Then I tried to divide the weight of the fluid displaced, which is the buoyant force, by the acceleration due to gravity to try to find the mass...but that didn't seem right.
I got 1,537.5 kg, but if I try to find the weight, I'll just be back to the buoyant force...and if the buoyant force equals the weight of the object...the object is still floating.
 
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There are two different boyant forces - one for sea water and one for fresh.
The difference between them is the extra mass you need.
 

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Yes, that makes sense. Thank you for pointing that out.
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