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I. Pressure as a function of depth As we saw in the Pressure in a Liquid tutorial, the pressure in a liquid varies as a function of depth in that liquid. As long as two points are in the same body of the same liquid, we can relate their pressures using the equation presented in lecture and the tutorial: p2 = p1 + ?gdz,1 Which is to say: p2, the pressure at point 2, is equal to p1 plus a term that is the density of the liquid both points are in multiplied by the strength of gravity multiplied by the depth of point 2 below point 1. (If point 2 is above point one, then this depth would be negative.) This formula can only be used to relate the pressures of two points in the same body of the same type of liquid. So it can't be used to directly relate the pressures of two points in two different containers, or to directly relate the pressures of two points in two different kinds of liquid. But with some additional refinements, we can use this to indirectly relate the pressures between two points in a wider variety of circumstances. A. Pressure in a gas – On human scales, the pressure in a gas is for the most part uniform, independent of height. In theory, the pressure in a gas should vary according to height in a similar way to the pressure in a liquid, but the density of gasses is so small that the rate at which it changes means you have to change height a great distance before seeing an appreciable change in pressure. For example, you will have calculated that changing your depth in water by about 10 meters causes a change in pressure of about 1 atmosphere, on the other hand, changing your height in the atmosphere by about 1 mile, traveling from Seattle to Denver for example, only decreases the pressure by about 0.2 atmospheres. So when you have a volume of gas, the pressure in that gas will be uniform. If that gas is open to the atmosphere, then that gas will be at atmospheric pressure. 1. Pockets of gas are trapped in the containers at right, the surface of the water in each container is as shown, and the surface of the larger tray is exposed to the atmosphere. Compare the pressures of the gasses at point A, B, and C. Explain 2. Are each of these points above, below, or equal to atmospheric pressure? Explain. Do your answers agree with what you may think would happen if a small hole were put in the containers with regards to air being pushed out or sucked in?

I. Pressure as a function of depth

As we saw in the Pressure in a Liquid tutorial, the pressure in a liquid varies as a function of depth in that liquid. As long as two points are in the same body of the same liquid, we can relate their pressures using the equation presented in lecture and the tutorial:

p2 = p1 + ?gdz,1

Which is to say: p2, the pressure at point 2, is equal to p1 plus a term that is the density of the liquid both points are in multiplied by the strength of gravity multiplied by the depth of point 2 below point 1. (If point 2 is above point one, then this depth would be negative.) This formula can only be used to relate the pressures of two points in the same body of the same type of liquid. So it can't be used to directly relate the pressures of two points in two different containers, or to directly relate the pressures of two points in two different kinds of liquid. But with some additional refinements, we can use this to indirectly relate the pressures between two points in a wider variety of circumstances.

A. Pressure in a gas – On human scales, the pressure in a gas is for the most part uniform, independent of height. In theory, the pressure in a gas should vary according to height in a similar way to the pressure in a liquid, but the density of gasses is so small that the rate at which it changes means you have to change height a great distance before seeing an appreciable change in pressure. For example, you will have calculated that changing your depth in water by about 10 meters causes a change in pressure of about 1 atmosphere, on the other hand, changing your height in the atmosphere by about 1 mile, traveling from Seattle to Denver for example, only decreases the pressure by about 0.2 atmospheres. So when you have a volume of gas, the pressure in that gas will be uniform. If that gas is open to the atmosphere, then that gas will be at atmospheric pressure.

1. Pockets of gas are trapped in the containers at right, the surface of the water in each container is as shown, and the surface of the larger tray is exposed to the atmosphere. Compare the pressures of the gasses at point A, B, and C. Explain

2. Are each of these points above, below, or equal to atmospheric pressure? Explain. Do your answers agree with what you may think would happen if a small hole were put in the containers with regards to air being pushed out or sucked in?

I. Pressure as a function of depth

As we saw in the Pressure in a Liquid tutorial, the pressure in a liquid varies as a function of depth in that liquid. As long as two points are in the same body of the same liquid, we can relate their pressures using the equation presented in lecture and the tutorial:

p2 = p1 + ?gdz,1

Which is to say: p2, the pressure at point 2, is equal to p1 plus a term that is the density of the liquid both points are in multiplied by the strength of gravity multiplied by the depth of point 2 below point 1. (If point 2 is above point one, then this depth would be negative.) This formula can only be used to relate the pressures of two points in the same body of the same type of liquid. So it can't be used to directly relate the pressures of two points in two different containers, or to directly relate the pressures of two points in two different kinds of liquid. But with some additional refinements, we can use this to indirectly relate the pressures between two points in a wider variety of circumstances.

A. Pressure in a gas – On human scales, the pressure in a gas is for the most part uniform, independent of height. In theory, the pressure in a gas should vary according to height in a similar way to the pressure in a liquid, but the density of gasses is so small that the rate at which it changes means you have to change height a great distance before seeing an appreciable change in pressure. For example, you will have calculated that changing your depth in water by about 10 meters causes a change in pressure of about 1 atmosphere, on the other hand, changing your height in the atmosphere by about 1 mile, traveling from Seattle to Denver for example, only decreases the pressure by about 0.2 atmospheres. So when you have a volume of gas, the pressure in that gas will be uniform. If that gas is open to the atmosphere, then that gas will be at atmospheric pressure.

1. Pockets of gas are trapped in the containers at right, the surface of the water in each container is as shown, and the surface of the larger tray is exposed to the atmosphere. Compare the pressures of the gasses at point A, B, and C. Explain

2. Are each of these points above, below, or equal to atmospheric pressure? Explain. Do your answers agree with what you may think would happen if a small hole were put in the containers with regards to air being pushed out or sucked in?

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