# Fluid Statics/depth in a cylinder

• tennisgirl92
In summary, the mercury would be at a depth of 0.8 m below the surface of the water in a cylindrical container with a pressure of 1.3 atm and a height of 0.8 m.
tennisgirl92

## Homework Statement

Mercury is added to a cylindrical container to a depth d and then the rest of the cylinder is filled with water. If the cylinder is 0.8 m tall and the pressure at the bottom is 1.3 atmospheres, determine the depth of the mercury. (Assume the density of mercury to be 1.36
104 kg/m3.)

## Homework Equations

Ptotal=Patmosphere+Pwater+Pmercury
P=density x g x height
1 atmosphere=1.013e5 Pa
density of water=1 x 103 kg/m3
pressure of atmosphere=1 atm

## The Attempt at a Solution

I first subtracted out the pressure of the atmosphere, so
.3 atm=Pwater + Pmercury
.8m=Hwater + Hmercury
Pmercury=1.36 x 104 x 9.8 x Hmercury
Pwater=1 x 103 x 9.8 x Hwater

I am having difficulty putting all 4 of these equations together. I feel like there is substitution needed, but which equations should I use?

Perhaps you should be more systematic, Starting with your equation
Ptotal=Patmosphere+Pwater+Pmercury
substitute
Pwaterwaterg hwater
Pmercurymercuryg hmercury
and solve for hmercury.

tennisgirl92 said:

## Homework Statement

Mercury is added to a cylindrical container to a depth d and then the rest of the cylinder is filled with water. If the cylinder is 0.8 m tall and the pressure at the bottom is 1.3 atmospheres, determine the depth of the mercury. (Assume the density of mercury to be 1.36 View attachment 195815 104 kg/m3.)

## Homework Equations

Ptotal=Patmosphere+Pwater+Pmercury
P=density x g x height
1 atmosphere=1.013e5 Pa
density of water=1 x 103 kg/m3
pressure of atmosphere=1 atm

## The Attempt at a Solution

I first subtracted out the pressure of the atmosphere, so
.3 atm=Pwater + Pmercury
.8m=Hwater + Hmercury
Pmercury=1.36 x 104 x 9.8 x Hmercury
Pwater=1 x 103 x 9.8 x Hwater

I am having difficulty putting all 4 of these equations together. I feel like there is substitution needed, but which equations should I use?
You have 4 linear algebraic equations in 4 unknowns. Are you familiar with Gaussian elimination?

kuruman said:
Perhaps you should be more systematic, Starting with your equation
Ptotal=Patmosphere+Pwater+Pmercury
substitute
Pwaterwaterg hwater
Pmercurymercuryg hmercury
and solve for hmercury.

Ok, if I do that
.3atm=(1000 x 9.8 x Hwater) + (1.36 x 104 x 9.8 x Hmercury)
I still need to find the height of water, right? Where would that come from?

Chestermiller said:
You have 4 linear algebraic equations in 4 unknowns. Are you familiar with Gaussian elimination?
No, never heard of that. What is Gaussian elimination?

tennisgirl92 said:
I still need to find the height of water, right? Where would that come from?
Since the cylinder is filled to the top,
Height of water = height of cylinder - height of mercury

kuruman said:
Since the cylinder is filled to the top,
Height of water = height of cylinder - height of mercury

thank you! Got it!

## 1. What is fluid statics?

Fluid statics is the study of fluids at rest, or in a state of equilibrium. This branch of fluid mechanics focuses on the behavior of fluids when they are not in motion, and the forces acting on them.

## 2. Why is depth important in a cylinder?

The depth of a fluid in a cylinder is important because it determines the pressure at a certain point. The deeper the fluid, the greater the pressure at that point. This is due to the weight of the fluid above pushing down.

## 3. How do you calculate pressure in a fluid cylinder?

The pressure in a fluid cylinder can be calculated using the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the gravitational acceleration, and h is the depth of the fluid.

## 4. Can the pressure at the bottom of a cylinder be higher than the pressure at the top?

Yes, the pressure at the bottom of a cylinder can be higher than the pressure at the top. This is because the pressure in a fluid increases with depth, as the weight of the fluid above increases. Therefore, the pressure at the bottom of a cylinder is greater than the pressure at the top.

## 5. What is the relationship between depth and pressure in a fluid cylinder?

The relationship between depth and pressure in a fluid cylinder is directly proportional. This means that as the depth of the fluid increases, the pressure also increases. Similarly, as the depth decreases, the pressure decreases.

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