008 Under Pressure

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CUNY Hunter College *

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Mechanical Engineering

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Jan 9, 2024

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docx

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Introductory Physics Hunter College Under Pressure by: Dr. Islam Hoxha with edits from A.Padilla Revised by R. Marx “We must not wait for things to come, believing that they are decided by irrescindable destiny. If we want it, we must do something about it.” Erwin Schrodinger Objective: To learn about the pressure in fluids and the factors that influence it, such as density of the fluid, depth and strength of gravity Background The term fluid is used both for liquids and gases. A fluid in equilibrium exerts forces in the walls of the container it is in. Layers of the fluid exert forces on one another. Pressure is defined as the amount of perpendicular force on an area divided by that area, in other words it is force per unit area. P=F/A Pressure is a scalar quantity; the units of pressure in the SI system are pascals: 1 Pa = 1 N/m 2 For a fluid at rest, pressure is the same in every direction in a fluid at a given depth; At a depth of h below the surface of a liquid, the pressure depends on the weight of the liquid above h . Density of a liquid, or gas ( using the letter rho ⍴) or for that matter any object, is defined as the mass over volume , where V=Ah Since ⍴= mass/volume = m/ Ah

m= ⍴Ah. Now force F=weight W= mg = ⍴Ahg. So substituting terms: Change of Air Pressure With Altitude In discussion of pressure, both gases and fluids operate by the same mathematical considerations. Let us explore Pressure in our atmosphere. Use this link to obtain the app that provides air pressure at different altitudes. https://www.mide.com/air-pressure-at-altitude-calculator Fill in the middle column with the values that the calculator provides. In the column on the right calculate the change in air pressure for each of this 1000 meter changes. Altitude: meters Air pressure Pascals Δ Pressure over 1000 meters Sea level XXXXXXXXXXXXXXXX 1000 2000 3000 4000 5000

Explain why the numbers in the right column exhibit the pattern that they do? The same logic about pressure in air ( a gas) applied to fluids ( water). It is assumed that density is constant and does not change with depth. Atmospheric pressure must also be accounted for in dealing with the pressure inside a fluid. So the the pressure p, at a depth h.in a fluid is p=p 0 + ρgh This means p-p 0 = Δp = ρgh P is absolute pressure. The difference ∆p=p-p 0 is called gauge pressure It is the pressure of the fluid, independent of the atmospheric pressure , p 0 . Note that pressure is measured in N/m 2 or pascal ( Pa) with 1 Pa=1 N/m 2 1 Pa = 1 N/m 2 Experiment : Click here for the “Under Pressure “ simulation. https://phet.colorado.edu/sims/html/under-pressure/latest/under-pressure_en.html Get familiar with the icons and buttons. Notice there are 4 different configurations of the fluid confinement in the left Part 1 - Choose the top configuration. There are two valves: The top left fills the container with liquid and the bottom right one discharges fluid from the container. Choose “Atmosphere On” on the top right -Choose : Units-metric and keep them this way for the entire experiment. -Choose fluid density ; 1000 kg/m 3 and gravity : Earth ( 9.8 m/s 2 ) -Click the “ruler” icon and also check “grid” In this first step empty the basin by pulling on the bottom valve to release the water.

Now place the round pressure gauge at the level of zero Note and record the value of pressure. Next place the gauge at the 1 meter mark. Note and record the pressure. Repeat this for 2 and 3 meters. Level: meters Air Pressure: Pascals Change in Pressure: Pascals 0 1 2 3 Examine the values in the column on the right. For the purposes of this lab in which we are looking at pressure in a liquid, how can we treat the changes in air pressure? Now fill the basin with water to the top. Then, click and drag a pressure gauge to the surface of the liquid. Turn the atmosphere Off. Find the location where the gauge indicates exactly 0 Pa. Then turn the atmosphere back On and read the pressure. This is p 0 . Record it! Place the pressure gauge at different horizontal locations along the level 1 meter below the surface. ( you can use one gauge per location as you can use up to four of them). Does the pressure change along a horizontal level? Find the gauge pressure at this 1 meter level. where p = p o + p g. Prove this.. Show your calculation.

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