Fluid Statics/depth in a cylinder

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.
  • #1
tennisgirl92
43
1

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
multiply.gif
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?
 
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  • #2
Perhaps you should be more systematic, Starting with your equation
Ptotal=Patmosphere+Pwater+Pmercury
substitute
Pwaterwaterg hwater
Pmercurymercuryg hmercury
and solve for hmercury.
 
  • #3
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?
 
  • #4
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?
 
  • #5
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?
 
  • #6
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
 
  • #7
kuruman said:
Since the cylinder is filled to the top,
Height of water = height of cylinder - height of mercury

thank you! Got it!
 

Related to Fluid Statics/depth in a cylinder

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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