Calculating pressure within a system at a specific location?

[russiansplash]

Homework Statement

Solution:

Homework Equations

dp/dz = -ρh

Pressure varies linearly with the depth.

The Attempt at a Solution

Firstly, I have calculated the pressure at point B.
P_B = P_A - (0.3m)*(1000kg/m^3)*(9.81m/s^2)
P_B = 88057 Pa

Calculating the pressure at point C. However, my attempt is incorrect and I do not understand why I cannot use the pressure at point B to calculate the pressure at point C.

P_C = P_B - (0.6m)*(1.225kg/m^3)*(9.81m/s^2)
P_C = 88049 Pa[/B]

I would appreciate any sort of assistance! Thank you in advance.

 

[Chandra Prayaga]

I see two solutions, one called the "solution", and another called "The attempt at a solution". Is the first one a solution given to you, along with the problem, or is it a first attempt by you to get a solution?
Let us first state the principles: How did you translate the pressure from one column to the other? For example, in your calculation of p_B, which is the same in both solutions, you used a principle, which allowed you to use the extra height of water in the middle column. What is that principle?

 

[Chestermiller]

Calculating the pressure at point C. However, my attempt is incorrect and I do not understand why I cannot use the pressure at point B to calculate the pressure at point C.

P_C = P_B - (0.6m)*(1.225kg/m^3)*(9.81m/s^2)
P_C = 88049 Pa

I would appreciate any sort of assistance! Thank you in advance.

You can indeed calculate the pressure at point C, given the pressure at point B. But you need to do it correctly. What was your rationale for writing the equation the way you did? From the diagram, do you expect the pressure at C to be higher than at B or lower than at B?

 

[russiansplash]

You can indeed calculate the pressure at point C, given the pressure at point B. But you need to do it correctly. What was your rationale for writing the equation the way you did? From the diagram, do you expect the pressure at C to be higher than at B or lower than at B?

Thank you for the speedy response. The pressure at C should be lower as it is at a higher elevation. However, in the provided solution it quotes a value of pressure higher than that of point B. I am probably missing a point but I do not seem to understand how the pressure is higher at C.

 

[russiansplash]

I see two solutions, one called the "solution", and another called "The attempt at a solution". Is the first one a solution given to you, along with the problem, or is it a first attempt by you to get a solution?
Let us first state the principles: How did you translate the pressure from one column to the other? For example, in your calculation of p_B, which is the same in both solutions, you used a principle, which allowed you to use the extra height of water in the middle column. What is that principle?

Sorry for not making it clear, the attached image is the solution to the problem and my attempt was a first attempt. Also, I translated the pressure from one column to the other because at the same elevations the pressure remains constant?

 

[Chestermiller]

Thank you for the speedy response. The pressure at C should be lower as it is at a higher elevation. However, in the provided solution it quotes a value of pressure higher than that of point B. I am probably missing a point but I do not seem to understand how the pressure is higher at C.

The pressure at C is higher than at B because the column above the water surface is filled with (very low density) air. So the pressure at C is essentially the pressure at the water surface below C. Is that water surface above B or below B?

 

[Chestermiller]

Sorry for not making it clear, the attached image is the solution to the problem and my attempt was a first attempt. Also, I translated the pressure from one column to the other because at the same elevations the pressure remains constant?

The pressure remains constant at a given elevation only if it is the same fluid.

 

[russiansplash]

The pressure at C is higher than at B because the column above the water surface is filled with (very low density) air. So the pressure at C is essentially the pressure at the water surface below C. Is that water surface above B or below B?

Sorry, I do not understand what you mean by whether the water surface is above or below point B? I cannot get my head around this, could you perhaps provide more guidance? I'd really appreciate it.

 

[Chestermiller]

Sorry, I do not understand what you mean by whether the water surface is above or below point B? I cannot get my head around this, could you perhaps provide more guidance? I'd really appreciate it.

Look in the right hand section where C is located. How far above the bottom of the tank is the water surface? How far above the bottom of the tank is the water surface located in the middle section, where point B is located? Is the water surface in the right hand section higher of lower than the water surface in the center section?