# Vertical distance of water inside an downward vessel

• Tulatalu
In summary, In this problem, we have a vessel with a volume of 9 m^3 being lowered into a fresh water lake until the volume of air inside becomes 5 m^3. We are given the atmosphere pressure of 760 mmHg and the density of water and mercury. Using the equations for pressure and the relationship between pressure and volume, we can solve for the vertical distance of the water level inside the vessel from the surface of the lake. We can also use a drawing to visualize the problem and fill in the known variables to find the solution.
Tulatalu

## Homework Statement

A vessel of internal volume 9 m^3 is lowered with its mouth downward into fresh water lake until the volume of the air in the vessel becomes 5 m^3. Given that the atmosphere pressure is 760 mmHg, what is the verrtical distance of the water level inside the vessel from the surface of the lake? Temperature remains unchanged. Density of water = 1000 kg/ m^3 of mercury = 13600 kg / m^3

## The Attempt at a Solution

I don't know how to approach this problem. Is it right that the pressure inside the vessel is the same as the atmosphere pressure? What formula should i base on to calculate the height of water ?[/B]

Hi Tulu,

If you find a relevant equation, you find your answer. Is there a context to this problem, or was it in a chapter about optics ?

Hi BvU,
It's in an examination paper which consists of many problems from random topics so I'm afraid we will have to figure out the solution.

Last edited:
I see. Still, we need two relevant equations. Anything you have to couple p and V ? And what about pressure under water as a function of depth ?

Pressure=height x density x g and pV = constant ?

Pressure=height x density x g and pV = constant ?

Bingo.

Make a little drawing (actually, two: one for when the vessel touches the surface (*) and one for when the volume inside is 5 m3).
Fill in the known variables and you're done !

(*) because, as you say "the pressure inside the vessel is the same as the atmosphere pressure" at that point

## 1. What is the vertical distance of water inside a downward vessel?

The vertical distance of water inside a downward vessel refers to the measurement of the height of the water level inside the vessel, from the bottom of the vessel to the top of the water surface.

## 2. How is the vertical distance of water affected by the shape of the vessel?

The vertical distance of water inside a downward vessel is affected by the shape of the vessel. A wider vessel will have a shorter vertical distance of water, while a taller and narrower vessel will have a longer vertical distance of water.

## 3. Does the density of the water affect the vertical distance inside the vessel?

Yes, the density of the water can affect the vertical distance inside the vessel. If the water is more dense, the vertical distance will be shorter, and if the water is less dense, the vertical distance will be longer.

## 4. How can the vertical distance of water be measured accurately?

The vertical distance of water inside a downward vessel can be measured accurately by using a ruler or measuring tape. The measurement should be taken from the bottom of the vessel to the highest point of the water surface.

## 5. What is the significance of knowing the vertical distance of water in a downward vessel?

Knowing the vertical distance of water in a downward vessel is important in various applications, such as in the design of plumbing systems, determining water pressure, and calculating the volume of water in a container. It can also help in understanding the principles of fluid mechanics and hydrostatics.

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