# Conceptual Question- Hydrostatic Pressure

• bcjochim07
In summary, the question being discussed is whether the pressure at point A in a figure is larger, smaller, or equal to the pressure at point B. Initially, it is thought that the pressures are equal due to the equal heights of the points, but the presence of a ship above point A raises the question of whether this changes the pressure. It is then explained that the ship exerts pressure on the water surrounding it and displaces a certain volume of water. The comparison is made between the weight of the ship and the weight of the displaced water, and it is suggested to consider what instinct and physics say about the situation.
bcjochim07
b]1. Homework Statement [/b]
In the figure, is pressure at A larger than, smaller than, or equal to the pressure at B?
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## The Attempt at a Solution

My first instinct is that they are equal because they are at equal heights, but then again, isn't the pressure at the surface above A greater than the surface above B because of the force, mg, of the boat exerted over the surface area in addition to the pressure exerted by the atmosphere? Could someone please explain this to me? Thanks.

You have mentioned equal heights -- height above what? I hope you meant depth from the surface of the water. Then the pressures must be equal, since the depths are equal.

But there's a ship above A. Your concern is will that change the pressure at A? (You can safely neglect atmospheric pressure, since that is acting everywhere.)

The ship exerts some pressure on the water surrounding it due to its weight. It also displaces a certain volume of water, which is the volume of the submerged portion of the ship.

Suppose you take out the ship and replace the volume of the submerged portion of the ship by water, so that the water level becomes same everywhere. How much does this volume of water weigh? If it weighs, say, more than the ship, then the pressure on A will definitely be more than that at B.

What does your instinct say? And Physics?

The pressure at A and B will be equal if they are at the same height and have the same fluid density. However, the pressure at A will be greater if there is a force, such as the weight of a boat, acting on the surface above it. This is because the weight of the boat will add an additional force to the pressure exerted by the atmosphere, resulting in a higher overall pressure at A compared to B. This is known as hydrostatic pressure, which is the pressure exerted by a fluid at rest due to the weight of the fluid above it. In this case, the pressure at A will be larger than the pressure at B.

## 1. What is hydrostatic pressure?

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of the fluid above it.

## 2. How is hydrostatic pressure calculated?

Hydrostatic pressure can be calculated using the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the fluid.

## 3. How does hydrostatic pressure change with depth?

Hydrostatic pressure increases with depth due to the weight of the fluid above it. As depth increases, the weight of the fluid above also increases, resulting in an increase in pressure.

## 4. What is the relationship between hydrostatic pressure and density?

Hydrostatic pressure is directly proportional to the density of the fluid. This means that as the density of the fluid increases, the hydrostatic pressure also increases.

## 5. How does hydrostatic pressure affect buoyancy?

Hydrostatic pressure plays a crucial role in determining whether an object will float or sink in a fluid. If the hydrostatic pressure pushing up on the object is greater than the weight of the object, it will float. If the weight of the object is greater than the hydrostatic pressure, it will sink.

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