 water at 4° C = 1.000 x 103 kg/m3 SI unit = kg/m3  varies with temperature and pressure Significantly for gases Not much for liquids or solids  water at 4° C = 1.000 x 103 kg/m3 (We can use this value for water at any temperature.) © Laura Fellman, PCC Rock Creek Campus

Pressure Box of air Total Force  to surface Notes on Pressure SI unit = N/m2 = 1 Pascal (Pa) 1 Pa is a very small amount of pressure: Normal air pressure  105 Pa = 1 bar 1 atmosphere (1 atm) = 1.01x105 Pa = atmospheric pressure at sea level 1 mmHg = 133 Pa = 1 Torr mm of mercury © Laura Fellman, PCC Rock Creek Campus

One atmosphere (atm) is the average pressure exerted by the earth’s atmosphere at sea level 1.00 atm = 1.01 x105 N/m2 = 101.3 kPa What is the approximate mass of air above you in Mussoorie?

NZ Weather Maps

© Laura Fellman, PCC Rock Creek Campus Fluids exert pressure on all surfaces they contact: *Pressure is not a vector: Total magnitude (without direction) © Laura Fellman, PCC Rock Creek Campus

Why doesn’t the box collapse?? .20m [1]Find the total force on the outside of the box due to 1 atm of air pressure. Why doesn’t the box collapse?? [2] Estimate the pressure exerted on a floor by a 50 kg model standing momentarily on a single spiked heel (area = 0.05 cm2) and compare it to the pressure exerted by a 1500 kg elephant standing on one foot (area = 800 cm2). Ans: 9.8 x 107 Pa; 1.8375 x 105 Pa © Laura Fellman, PCC Rock Creek Campus

More pressure examples Snowshoes: Bed of nails: © Laura Fellman, PCC Rock Creek Campus

Why does pressure increase with depth in a fluid, and by how much? Pressure and Depth Why does pressure increase with depth in a fluid, and by how much? P2 P1 h Imagine a tank of water at rest. We’ll focus on a column of this water. Draw a free body diagram of the vertical forces on the column of water. Since it is in equilibrium, the forces must sum to zero. Solve for the pressure at the bottom of the column. P2 = P1 + gh Does pressure vary horizontally?? © Laura Fellman, PCC Rock Creek Campus

P2 P1 h

Static fluid Pressure does not depends on shape, mass or surface area of the liquid

Static fluid Pressure does depends on depth Hydrostatic Pressure Water Pressure Applet

Find the pressure at 100 m below sea level. Ex: Find the pressure at 100 m below sea level. A newspaper article reports the pressure at the depth of the Titanic wreck as 6,600 pounds per square inch. Calculate its depth in km.

= 3.7x104 Pa PGAUGE = P PISTON Pabs = PPISTON + Patm = 1.38x105 Pa A 30.0-kg piston holds compressed gas in a tank of volume 100 m3. The radius of the piston is 0.050 m. a. Determine the gauge pressure of the gas in the tank. m = 30 kg V = 100 m3 r = 0.05 m = 3.7x104 Pa PGAUGE = P PISTON b. Determine the absolute pressure Pabs = PPISTON + Patm = 3.7x104 + 1.01x105 = 1.38x105 Pa

© Laura Fellman, PCC Rock Creek Campus Pressure Gauges 1) Mercury Barometer (measures atmospheric pressure) density of mercury P1 = 0 h P2 = P1 + gh Patm = mgh P2 = Patm © Laura Fellman, PCC Rock Creek Campus

Hydrostatic Pressure in Liquids (U-tube) 2) Open-Tube Manometer Fluid in a manometer Hydrostatic Pressure in Liquids (U-tube) 2) Open-Tube Manometer (measures the pressure of this substance) P2 = P1 + gh Psubst = Patm + mgh P1 = Patm Psubst - Patm = mgh h = Gauge Pressure = the amount that pressure differs from the atmosphere P2 = Psubst. mercury © Laura Fellman, PCC Rock Creek Campus

Gauge Pressure – pressure relative to atmospheric pressure Positive – above atmospheric pressure Negative – below atmospheric pressure Absolute Pressure – the true value of pressure applied to an object = atmospheric pressure + gauge pressure

[3] A novice scuba diver has an extra 12 kilopascals of air pressure on her while underwater. What is her depth? P = Po + ρ g h Po = 101 000 pascals so P = 113 000 pascals 113 000 = 101 000 + (1000)(9.8) h 12 000 = 9800 h ANSWER: h = 1.22 meter [4] A tire gauge reads 220 kPa. What is the absolute pressure within the tire? Ans: 321 kPa