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Unformatted text preview: Fluids Intro and Pressure RHJansen Fluids
Defining Property Fluids Flow Which States of Matter flow? Liquids, an obvious choice Gases, which are always overlooked RHJansen Density Mass, m
Amount of matter: measured in kilograms, kg Volume, V
Amount of space: measured in liters, m3 Density, (this is not a " p". It is the Greek letter ro)
Amount of matter occupying an amount of space Measured in kg/m3 (note: Chemistry uses g/mL) = RHJansen Fresh Water Density is a means of comparing different substances. To make this easier it makes sense to take the most common substance and make it the reference standard. Water is very abundant, and fresh water without dissolved salts makes a great standard. A number had to be chosen for the standard, so and easy number was chosen. The density of fresh water was chosen to be = 1.00 RHJansen Density of Fresh Water However, the density was chosen to be 1 for chemistry, using the chemistry units g/mL . Physics using the kms units kg/m3 . 1 = 1.00 1000 1,000,000 = 1000 3 3 1 The density of water is worth memorizing. Since it is the reference standard, they may not give it to you. Other densities can be found in a table in the text, or on line. Also remember the conversion (mulitply by 1000) to switch from Chemistry units to Physics units RHJansen Pressure Force is a good problem strategy when you have a large object acted upon by a few easily identifiable and quantifiable forces. However fluids involve countless invisible atoms that are moving in random directions at random speeds. Solving for the force of each atom of a liquid or a gas and then adding them all up is impossible. Instead we will look Pressure The total force of many atoms delivered to an area. P= measured in N 2 m known as a Pascal Pa RHJansen Pascals The kms unit of pressure is the Pascal, Pa . Pressures are often given in atmospheres and will need to be converted into Pascals. 1atm = 101,325 For the exam they allow this number to be rounded off. 1atm = 100,000 1atm = 1 10 5 RHJansen Conversions
mass length area volume volume volume density pressure g to kg cm to m cm2 to m2 cm3 to m3 mL to m3 L to m3 g/cm3 to kg/m3 atm to Pa 10-3 10-2 (10-2)2 (10-2)3 10-6 10-3 103 105
Note the relationship between the conversions involving centimeters to meters. When the unit is squared (area), so is the conversion. When the unit is cubed (volume), so is the conversion RHJansen Conversions
mass g to kg The conversions shown in red are a must to know. They will be used the most often. In addition, don't forget to memorize the density of fresh water. 1000 kg/m RHJansen Example 1 Determine the density of a 250 g mass occupying a volume of 0.50 L. 250 10-3 = = = 500 3 -3 0.50 10 Determine the density of a 50 g mass occupying a volume of 2.0 cm3. Example 2 50 10-3 = = = 25000 3 -6 2.0 10 RHJansen Pressure of a Fluid When you scuba dive, the weight of the water above you creates the pressure on you. A h P= The water above your head forms a column that extends from your head all the way to the surface. The column has an area A that matches the area of you head and shoulders. It also has a height h that represents the depth that you are diving at. The area and height together describe the volume of the column. RHJansen Pressure of a Fluid
As you go deeper the area of the column does not change. The height increases, which increases the weight and pressure. P= Height is critical and needs to be worked into the equation. A h A P= Area and height describe the volume of the column h P = Mass divided by volume is density P = RHJansen Gauge Pressure
A P = This version of the pressure equation only solves the pressure of the fluid you are examining. It is called gauge pressure as this would give you the reading of a pressure gauge submerged in this fluid. However, this is not the entire pressure on you when you are at the bottom of a lake. There is another fluid above the water, and this fluid's pressure is not recorded by the gauge. RHJansen h Absolute Pressure
A The fluid above the water is the air (don't forget: gases are fluids) There is a column of air extending from the lake to space The pressure of the air on earth at seas level is known P0 = 1 = 1 105 h The absolute (total) pressure is the sum of the air pressure and any other fluids, such as the water P = + 0 RHJansen Gauges Absolute pressure Gauge pressure P = + 0 P = The air we live in has enough pressure to bend steel, and yet we don't feel it or think about it. We pretty much consider the normal atmospheric pressure as zero. What concerns us most is pressures that are different from normal. The gauges that we design typically measure pressures greater than normal, and these gauges will say zero when they are in air. Thus, gauge pressure does not include the atmospheric pressure. RHJansen Height P = + 0 Whether you work with gauge pressure or absolute pressure the key variable is height of the fluid column. The greater the height the greater the pressure. Rate the pressure at the points below from highest to lowest. A B C E D F E B, C, F A, D Does horizontal motion change pressure? NO, only depth matters. RHJansen Example 3
P = A scuba diver is 15 m below the ocean's surface. a. Determine the gauge pressure acting on the diver
You will need to know the density of fresh water by heart, but not the density of sea water. Densities other than fresh water are found in the text. P = (1.03 103 ) ( 9.8) (15) = 1.514 105 b. Determine the absolute pressure acting on the diver P = + 0
P = (1 105 ) + (1.03 103 ) ( 9.8) (15) = 1.514 105 RHJansen ...
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