# Force to lift a pyramid that is sitting in a water tank

• paulie
In summary: I'm sorry, I may have misunderstood the problem statement. Can you please clarify what is meant by "underneath the floor of the tank and on the water surface there is air at atmospheric pressure"? Is there a gap between the floor of the tank and the water surface where air is present? And is the pyramid sitting on top of this air layer or submerged in the water?In summary, a 4000 lb pyramid with a base of 6ft square and an altitude of 4ft is sitting on the floor of a tank with a 4ft depth of water. The base of the pyramid covers an opening in the floor, with air at atmospheric pressure present underneath the floor and on the water surface. To determine the vertical force required

## Homework Statement

A pyramid weighing 4000 lb has a base 6ft square and an altitude of 4ft. The base covers an opening in the floor of a tank in which there is water 4 ft deep. Underneath the floor of the tank and on the water surface there is air at atmospheric pressure. What vertical force is required to lift the pyramid off the floor?

## Homework Equations

F=δV

Where F is the force; δ=specific weight of the liquid; V is volume

## The Attempt at a Solution

I'm not really sure if I analyze what it should look like, but here is my attempt.

Fv is the force by the fluid against the pyramid

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Use the UPLOAD button on the post editor.

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paulie
How big is the opening in the floor of the tank below the pyramid?

Chestermiller said:
How big is the opening in the floor of the tank below the pyramid?
It was not stated, there's no figure too provided by the book. :( The answer is provided around 10000

I think that you have to assume that the hole covers essentially the entire bottom of the pyramid except for the very edge, with a gasket at the very edge of the pyramid to provide the seal to the bottom. So this is not the usual buoyancy situation because the pressure at the very bottom of the pyramid is atmospheric, rather than hydrostatic. What would the buoyancy force of the pyramid be if, rather than having atmospheric air on the bottom, it were totally surrounded by water?

Yeah, I don't think "hole size" matters at all. You are assuming the water isn't free to flow under and lift the pyramid (it's an idealized situation, i.e., there's nowhere for the water to go, at least not until after the pyramid has been lifted off).

Given that this is a hydrostatics problem — there's an easy way to solve this problem without worrying about things such as hole size or even some of the details of the pyramid's shape.

I confirm the 10,000 lb.

olivermsun
I think, I'm just missing another 6' in the computation of volume in the liquid.

That "6ft square" means (6)^2 and not 6ft^2. (I assumed that 6ft^2 is the area).

I got around 9990 lbs at the end. Although still not sure how can I use the atmospheric pressure on the problem...

paulie said:
I think, I'm just missing another 6' in the computation of volume in the liquid.

That "6ft square" means (6)^2 and not 6ft^2. (I assumed that 6ft^2 is the area).

I got around 9990 lbs at the end. Although still not sure how can I use the atmospheric pressure on the problem...
In order for us to help you, we need to see detail on exactly what you did, and your reasoning.

olivermsun
paulie said:
Although still not sure how can I use the atmospheric pressure on the problem...
Hydrostatic balance applies for the atmosphere, too. You may be forgetting a pair of forces on the pyramid ...

## 1. How is the force required to lift a pyramid in a water tank calculated?

The force required to lift a pyramid in a water tank is calculated by using the formula F = ρVg, where F is the force, ρ is the density of water (1000 kg/m^3), V is the volume of the pyramid, and g is the acceleration due to gravity (9.8 m/s^2). This formula takes into account the weight of the pyramid and the buoyant force exerted by the water.

## 2. Does the shape of the pyramid affect the force required to lift it?

Yes, the shape of the pyramid does affect the force required to lift it. The greater the surface area of the pyramid, the more water it will displace and the greater the buoyant force will be. This means that a pyramid with a larger base will require more force to lift compared to a pyramid with a smaller base.

## 3. How does the depth of the water tank affect the force required to lift the pyramid?

The depth of the water tank does not affect the force required to lift the pyramid. As long as the entire pyramid is submerged in water, the force required will be the same regardless of the depth of the tank. However, if the water level in the tank changes, the force required to lift the pyramid will also change.

## 4. Is the force required to lift a pyramid in a water tank the same as the force required to lift it in air?

No, the force required to lift a pyramid in a water tank is not the same as the force required to lift it in air. This is because the buoyant force exerted by the water will reduce the overall force needed to lift the pyramid. In air, the force required will be equal to the weight of the pyramid.

## 5. How does the weight of the pyramid affect the force required to lift it in a water tank?

The weight of the pyramid directly affects the force required to lift it in a water tank. The greater the weight of the pyramid, the more force will be needed to lift it. This is because the weight of the pyramid must be overcome by the buoyant force exerted by the water in order to lift it.