How Much Water Can a Weak Spherical Tank Hold Safely?

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SUMMARY

A spherical water tank with an inner radius of 12 meters can safely hold water up to a pressure limit of 185 kilopascals. The volume of the tank is calculated using the formula for the volume of a sphere, which is \( V = \frac{4}{3} \pi r^3 \). Given the density of water at 1000 kg/m³ and gravitational acceleration at 9.8 m/s², the maximum safe volume of water that can be stored without exceeding the pressure limit is approximately 70 cubic meters.

PREREQUISITES
  • Understanding of basic physics principles, specifically pressure and volume calculations.
  • Familiarity with the formula for the volume of a sphere.
  • Knowledge of the relationship between pressure, density, and gravitational force.
  • Basic mathematical skills for rounding and unit conversions.
NEXT STEPS
  • Research the effects of material strength on pressure tolerance in spherical tanks.
  • Learn about safety factors in engineering design for pressure vessels.
  • Explore the implications of atmospheric pressure on fluid dynamics in tanks.
  • Investigate alternative tank shapes and their pressure capacities.
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Engineers, architects, and safety professionals involved in the design and analysis of pressure vessels and storage tanks.

GaryDevine
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Hey, can anyone help me with the following problem. I would greatly appreciate it

Gary D


A water tank that is a perfect sphere has an inner radius of 12m. However, it was constructed with inferior materials and the tank can only withstand a water pressure of 185 kilopascals. Assume the density of water is exactly 1000 kg/m^3 \, gravity is 9.8m/s^2, and disregard atmospheric pressure.

How many cubic meters of water can safely be stored in the tank? Round down to the nearest whole number (since rounding up could be catastrophic in this instance).
 
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Isn't it just the volume of the tank?
 

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