What is the hydrostatic force on one end of an aquarium filled with water?

In summary, we are asked to find the hydrostatic force on one end of an aquarium that is 8 m long, 4 m wide, and 4 m deep, filled with water. After finding the pressure and force on the bottom of the aquarium, the main issue is understanding what is meant by "end" - whether it refers to one of the side walls or one half of the aquarium. The attempt at a solution was to use the formula Density * gravity * L/2 * W, but that was incorrect. The correct approach is to calculate the force at each point on a wall, which varies with depth, and then sum them together using a Riemann sum or integral. This problem is likely in a section on
  • #1
the7joker7
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Homework Statement



An aquarium `8` m long, `4` m wide, and `4` m deep is full of water. Find the following: the hydrostatic force on one end of the aquarium.

Homework Equations





The Attempt at a Solution



I already found the pressure and force on the bottom of the aquarium...now, my main issue understanding what the question means when it says 'end.' Do they mean one of the side walls? One half of the aquarium? If anyone happens to know what that likely means, that'd be awesome.

What I've tried so far is Density*gravity*L/2*W, which was wrong.

1000*9.8*4*4 = 156800.

Is it just the force on the bottom of the aquarium divided by 2? That almost seems too easy...
 
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  • #2
IF the force is a constant, then the pressure on a surface is just that force times the area of the surface. That, I presume, was how you found the force on the bottom. However, the force, at each point on a wall, is not a constant. It varies with depth. Imagine a thin horizontal line, of width "dx", at depth "x". What is the force at depth x meters below the surface of the water? What is the pressure on that line? (For a very thin horizontal line you may assume the force is (approximately) a constant.) The total pressure on the wall is the sum of the pressure on all those lines. Doesn't that look like a "Riemann sum" to you? You can make it exact by converting the sum into an integral. (I have this suspicion that this problem is in a section on "applications of integrals".)
 

FAQ: What is the hydrostatic force on one end of an aquarium filled with water?

What is a hydrostatic force problem?

A hydrostatic force problem involves calculating the force exerted by a fluid on a submerged object or surface. This force is caused by the pressure of the fluid acting on the object or surface.

How do you calculate the hydrostatic force?

The hydrostatic force can be calculated using the equation F = ρghA, where ρ is the density of the fluid, g is the acceleration due to gravity, h is the depth of the fluid, and A is the area of the submerged object or surface.

What is the significance of hydrostatic force?

Hydrostatic force is important in various fields such as civil engineering, naval architecture, and fluid mechanics. It helps in the design and analysis of structures and objects that are in contact with or submerged in fluids.

How does the shape of an object affect hydrostatic force?

The shape of an object can affect the hydrostatic force as it determines the area (A) in the hydrostatic force equation. The larger the area, the greater the force. Objects with curved or irregular shapes may experience varying hydrostatic forces at different points on their surface.

What factors can affect hydrostatic force?

Aside from the density, depth, and shape of the object, other factors that can affect hydrostatic force include the type of fluid, the pressure of the fluid, and the orientation or position of the object in the fluid. These factors can influence the magnitude and direction of the hydrostatic force.

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