Pressure Problem: Finding Length of Air Column in Pipe

[Petrulis]

Homework Statement

First here's the drawing which shows the situation:

http://img81.imageshack.us/my.php?image=phyxt3.jpg

So there is 1 metre length and 2 millimetres diameter glass pipe which is bent. The angle ABC is equal to 90 degrees. The part of the pipe ADB is horizontal and the part BC is vertical. The end A is closed and the end C is open. 75 % of pipe is filled with water (black color). In the part AD there is an air. The pipe during one minute is rotated clockwise 90 degrees so the part BC becomes horizontal and the part ADB becomes vertical. After that the system during one minute is rotated counterclockwise 90 degrees to the previous position.

What is the length of the air column in the pipe dependence on the time (I need, for example, to find the function which argument is the time and the result is the length of air column)?

Homework Equations

The Attempt at a Solution

Please just give an idea what I have to do and with what I have to start. I absolutelly don't have any ideas.

 

[anathema]

Hello, I am a scientist and I will help you with your problem. To find the length of the air column in the pipe, we will need to use some basic principles of fluid mechanics and rotational motion.

First, we need to understand that the water in the pipe is in a state of equilibrium due to gravity and surface tension. This means that the pressure at any point in the water column is equal to the pressure at any other point at the same height. This is known as Pascal's law.

Next, we need to consider the rotational motion of the pipe. When the pipe is rotated clockwise, the water will move towards the outside of the bend due to centrifugal force. This will cause the water level on the inside of the bend to decrease and the level on the outside to increase. The opposite will happen when the pipe is rotated counterclockwise.

Now, let's focus on the air column in the pipe. As the water level changes, the air column will also change in length. When the pipe is rotated clockwise, the air column will decrease in length due to the increase in water level. When the pipe is rotated counterclockwise, the air column will increase in length as the water level decreases.

To find the length of the air column at any given time, we can use the following equation:

L(t) = L0 - (Vw/Va)*(t/T)

Where L(t) is the length of the air column at time t, L0 is the initial length of the air column, Vw is the volume of water in the pipe, Va is the volume of air in the pipe, and T is the total time for one complete rotation (2 minutes in this case).

We can calculate the volumes of water and air using the following equations:

Vw = (pi/4)*(D^2)*Lw

Va = (pi/4)*(D^2)*La

Where D is the diameter of the pipe, Lw is the length of the water column, and La is the length of the air column.

Now, we can plug these equations into our first equation and solve for L(t). This will give us the length of the air column at any given time. I hope this helps you get started on solving your problem. Good luck!

 

[ogb p]

I would approach this problem by first identifying the relevant physical principles involved. In this case, we are dealing with fluid dynamics and pressure. The pressure of a fluid is determined by the height of the fluid column above it, as well as the density of the fluid. In this situation, the pressure at point A will be determined by the height of the water column above it, while the pressure at point B will be determined by the height of the air column above it.

Next, I would consider the changes that occur during the rotation of the pipe. When the pipe is rotated clockwise, the water column will shift from point A to point B, and the air column will shift from point B to point A. This will result in a change in the pressure at both points A and B.

To determine the length of the air column, we can use the ideal gas law, which states that the pressure of a gas is inversely proportional to its volume. We can set up an equation where the initial pressure of the air column at point B is equal to the final pressure of the air column at point A, and solve for the length of the air column.

However, in this problem, we also have to take into account the movement of the water column. As the water column shifts, it will also change the pressure at point A, which will in turn affect the pressure at point B. This means that the length of the air column will not remain constant during the rotation of the pipe.

To find the function that describes the length of the air column as a function of time, we will need to use a combination of equations for fluid dynamics and the ideal gas law, and take into account the changes in pressure and height of the water column during the rotation of the pipe. This may require some experimentation and data collection to determine the exact relationship between the length of the air column and time.