Find Elevation at Point A - Math Homework

[MrMechanic]

Homework Statement

Find the elevation at point A. in the figure shown.

Homework Equations

P = pgh

The Attempt at a Solution

So i Converted 0.21kg/cm^2 to Kn/m^2 and i got 20.6kN/m^2 or 20.6kPa

and -30cm Hg i got 40kN/m^2 or 40kPa

 

[haruspex]

I'm not sure I understand the diagram. It appears to be two tanks side by side, connected by a pipe at the bottom and sealed at the top. Pressures in the airspaces in the tanks are given. Right?
So, now calculate the pressures at 33m in each, then at 30m in each, etc.

 

[MrMechanic]

Yes the pressure in the airspaces in the tanks are given.
I'll start with the left tank
P = Patm + (0.82)(9.81)(38-30)
is it correct?

 

[haruspex]

Yes the pressure in the airspaces in the tanks are given.
I'll start with the left tank
P = Patm + (0.82)(9.81)(38-30)
is it correct?

If by Patm you mean the pressure of the air in that tank, that term is ok. But watch out for the units in the other term. What does "specific gravity" mean exactly?

 

[MrMechanic]

Specific gravity is the ratio of the density of a substance to the density. that's why it has no unit
yes If Patm =14.7 psi = 101.325kPa = 101.325kN/m^2
and
P = 101.325 + (0.82)(9.81(38-30)
P = 36.9714 kPa
What i don't know is how to do I form an equation where i can get the height (h)

 

[haruspex]

Specific gravity is the ratio of the density of a substance to the density. that's why it has no unit

OK, but you need to specify the reference substance. Did you mean

Specific gravity is the ratio of the density of a substance to the density of water.​

?
The density of that substance should therefore figure in the formula. As it stands you have (spec grav) * (acceleration) * ( height), which has dimension L²/T².

What i don't know is how to do I form an equation where i can get the height (h)

If you continue to work out the pressure at each height, working down from the top, and put in an unknown h for the height you need, you eventually get to two expressions for the pressure right at at the bottom. They must be equal, of course.

 

[MrMechanic]

is this correct?
(-40) + (0.82)(9.81)(38-30) + (1.5) (9.81) (h) - (9.81)(h+3) - 20.6 = P1
and i'll perform another on the other side? or should I set P1 = 0?

 

[MrMechanic]

When I perform P1 = 0
I get h = 5.235

 

[haruspex]

is this correct?
(-40) + (0.82)(9.81)(38-30) + (1.5) (9.81) (h) - (9.81)(h+3) - 20.6 = P1
and i'll perform another on the other side? or should I set P1 = 0?

Two problems.
1. I had been ignoring the minus sign in "-30cm Hg". I don't understand how an absolute air pressure can be negative. These are sealed containers, so it shouldn't be relative to ambient pressure. Do you have any explanation for that?
2. You are ignoring my comment about density and units. If the s.g. is 0.82 relative to water, what is the density in kg/m³?

 

[MrMechanic]

The minus sign is not an absolute pressure i think.
The density of oil is not given. And also gasoline. In order to get their density you have to multiply their specific gravity to the density of water which is 9.81kg/m^3

 

[haruspex]

to get their density you have to multiply their specific gravity to the density of water which is 9.81kg/m^3

No, that's where you are going wrong. The 9.81 is gravitational acceleration. That factor converts mass to weight. The density of water is much larger.

 

[MrMechanic]

Oh yeah sorry. It's not kg/m^3 ... It's 9.81 kN/m^3 forgot to change that sorry

 

[haruspex]

Oh yeah sorry. It's not kg/m^3 ... It's 9.81 kN/m^3 forgot to change that sorry

Right, but answer my other question; what is the density of water in these units?