How Do You Calculate Hydrostatic Pressure and Force in an Aquarium?

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SUMMARY

The calculation of hydrostatic pressure and force in an aquarium involves using the equations P = g * ρ * h and F = m * g = g * ρ * A * h. In this case, for an aquarium measuring 5ft long, 2ft wide, and 3ft deep, the correct hydrostatic pressure is 187.5 lbs/ft² and the hydrostatic force on the bottom of the tank is 1875 lbs. The initial miscalculations stemmed from incorrectly applying the force of gravity twice in the equations.

PREREQUISITES
  • Understanding of hydrostatic pressure concepts
  • Familiarity with the equations P = g * ρ * h and F = g * ρ * A * h
  • Knowledge of units such as lbs/ft³ and lbs/ft²
  • Basic principles of fluid mechanics
NEXT STEPS
  • Study the derivation and application of hydrostatic pressure equations
  • Learn about fluid statics and dynamics in engineering contexts
  • Explore the concept of buoyancy and its relation to hydrostatic pressure
  • Investigate real-world applications of hydrostatic pressure in various engineering fields
USEFUL FOR

Students in physics or engineering courses, educators teaching fluid mechanics, and professionals involved in aquarium design or hydraulic systems will benefit from this discussion.

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Homework Statement



An aquarium 5ft long, 2 ft wide, and 3 ft deep is full of water. Find the hydrostatic pressure and the hydrostatic force on the bottom of the tank.

Homework Equations



P=g*\rho*h

F=m*g=g*\rho*A*h

\rho=62.5 \frac{lbs}{ft^3}

g=32 \frac{ft}{s^2}

The Attempt at a Solution



P=(32)(62.5)(3)=6000 \frac{lbs}{s^2}

F=(32)(62.5)(10)(3) = 60000 \frac{ft*lbs}{s^2}

I know the answers should be 187.5 \frac{lbs}{ft^2} and 1875 lbs, respectively, so I've done these problems wrong. They seem so simple though that I'm thrown for a loop. Are my equations wrong?
 
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Nevermind, I realized that since I was dealing with lbs, I was including the force of gravity a second time!
 

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