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Static Fluids

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Author: Janice VanCleave

Fluids at Rest

Static means no motion, and fluids are liquid or gaseous materials that can flow. Thus static fluids is the study of the characteristics of liquids and gaseous materials that are at rest.

In this project you will experimentally compare air pressure in different directions at a given point. You will experimentally determine the relationship between pressure and depth in a static liquid. You will also experimentally test Pascal's law, which states that pressure applied to an enclosed fluid is transmitted equally in all directions and to all parts of the enclosing vessel.

Getting Started

Purpose: To compare air pressure in different directions at a given point.

Materials

• 1-pint (500-ml) jar
• tap water
• 1 index card
• large bowl

Procedure

1. Fill the jar with water.
2. Cover the mouth of the jar with the card.
3. Hold the jar over the bowl.
4. With one hand over the card, invert the jar.
5. Carefully remove your hand from the card.
6. Keeping the mouth of the jar at relatively the same height, slowly rotate the jar through a complete 360° circle, so that the mouth of the jar faces down, then up, and then down again.
7. Observe the surface of the card over the jar.

Results

The card remains over the mouth of the jar through the entire rotation. The part of the card over the mouth of the jar has no noticeable change in its slight concave (curved inward) shape throughout the rotation.

Why?

The water around the mouth of the jar wets the paper, and cohesion (the force of attraction between like molecules) between the water molecules and adhesion (the force of attraction between unlike molecules) between the water molecules and the paper molecules forms a seal. But this seal alone is not enough to overcome the force of gravity. The concave (inward curve like the surface of a plate) shape of the card over the mouth of the jar indicates that the card is being pushed into the jar by an outside pressure. This is atmospheric pressure (force that gases in the atmosphere exert on a particular area).

At a given point in a fluid, such as air (the name for the mixture of gases in earth's atmosphere), pressure exerted by the fluid acts at right angles at every point on a submerged object. The card stays in place over the mouth of the jar regardless of orientation, showing that an equal air pressure is exerted on the card from all directions. In the same way, at a specific height above Earth, atmospheric pressure is the same on all sides of an object as indicated by no noticeable change in the concave shape of the paper covering.

Try New Approaches

1. Does the size of the jar affect the results? Repeat the investigation using jars of different sizes, but with the same mouth size as the original jar.
2. Does the size of the mouth of the jar affect the results? Repeat the investigation using jars with the same size but with different mouth sizes.

1. The relationship between the pressure of a liquid and the depth (height) of that liquid is expressed by the formula Pliquid = dgh, where d is the density of the liquid, g is the acceleration (an increase in velocity) due to gravity (9.8 m/s2), and h is the height of the fluid column above the point in question. For a specific fluid such as water, if the density of water (1 × 103 kg/m3) remains the same throughout, since gravity is relatively constant, the only variable is depth. Thus the pressure on the liquid is directly related to the depth or height of the liquid in the cup.
2. Design a way to test this. One way is to fill a container with water and make holes of identical size in the container at various depths (see Figure 33.2). The length (L) of the stream of water spurting from each hole can be used to compare pressure. The greater the depth of the liquid, the greater the pressure. Use a tall paper cup and make a hole near the bottom with the point of a pencil. Put a piece of tape over the hole and fill the cup. Measure the height from the hole to the top of the water's surface. Record this as the depth of hole A in a Pressure Data table like Table 51.1. Use this height and the equation Pwater= dgh to determine the pressure of water with a density of 1 × 103 kg/m3 at the depth of hole A measured in meters. Example: The pressure of water at a depth (h) of 0.03 m is:

Pwater = dgh
Pwater = 1 × 103 kg/m3 × 9.8 m/s2 × 0.03 m
= 0.294 kg · m · m/m3 · s2
= 0.294 × 103 N/m2
= 0.294 kPa

Note that the units kg·m·m/m3·s2 can be grouped forming kg·m/s2·m2.

Since 1 kg·m/s2 = 1 N, then 0.294 kg·m·m/m3·s2 = 0.294 × 103 N/m2, and since 1000 N/m2 = 1 kPa, then 0.294 × 103 N/m2 = 0.294 kPa. Kilopascal (kPa) is a practical metric unit for measuring pressure since Pascal (Pa) is generally too small.

Elevate the cup on an inverted rectangular container at one end of a tray so that the hole points toward the tray. Remove the tape, and mark where the water squirting out of the hole first lands. Measure the distance from the hole to this mark and record it as the length of the water stream for hole A. Repeat this procedure for two other holes, B and C, above hole A, making sure you open only one hole at a time and that all the holes are of equal size.

3. Blaise Pascal (1623–1662), a French mathematician and inventor, was the first to discover that fluids at rest exert pressure equally in all directions. Pascal's law states that the pressure applied to an enclosed fluid is transmitted equally in all directions and to all parts of the enclosing vessel, if the fluid is incompressible. Design an experiment to test Pascal's law. One way is to squeeze a 2-liter plastic soda bottle containing both water and a transparent condiment with an air bubble. The bubble of air in the condiment will increase or decrease depending on the pressure applied to it. When the bottle is squeezed, the liquid is not compressed but transmits the pressure in all directions, resulting in the compression of the air bubble inside the packet; thus the average density of the packet increases and the packet is less buoyant. Prepare the bottle by first selecting the best condiment packet. Do this by filling a quart (liter) jar about three-fourths full of water and dropping several condiment packets into the water. Select the packet that just barely sinks below the water's surface. Insert the condiment packet into an empty 2-liter plastic soda bottle. Fill the bottle to overflowing with tap water. Secure the cap on the bottle. Then squeeze the bottle with your hands. The condiment packet will sink when the bottle is squeezed and rise when the bottle is released. Note the size of the air bubble in the condiment as it sinks and rises.
4. Earth's atmosphere is kept around Earth by gravity. Atmospheric pressure, which is created by air molecules hitting and bouncing off surfaces, including one another, keeps gravity from pulling all of the air molecules to Earth's surface. Gravity pulls the atmosphere downward and air pressure pushes the atmosphere upward. The result of the original experiment showed equal air pressure from all directions. Design another experiment to measure atmospheric pressure from different directions. One way is to use a manometer (an instrument used to measure the pressure of fluids). See Appendix 7 for instructions on how to make a manometer. Test atmospheric pressure by holding one end of the manometer tube in different directions: right, left, up, and down. The water level in the tubes will be even if the pressure on both sides is equal.

Get the Facts

1. In physics, pressure is defined as a force measured over an area. In the International System of Units (SI), one unit of pressure is newtons (N) per square meter. In honor of Pascal, the Pascal (Pa) unit is also used to measure pressure. It is equal to one newton per square meter. There are other units of measuring pressure, such as atmosphere, millimeters of mercury, bar, milibar, barye, and torr. Find out more about Pascals and other units of pressure. How do the other units compare to the Pascal unit? For information see a physics text.
2. How does Pascal's law explain the workings of a hydraulic jack? For information see Karl F. Kuhn's Basic Physics (New York: Wiley, 1996), pp. 75–76.