Practice - The Burns Home Page

Pressure vs. DepthIncompressible Fluids (liquids)• Due to gravity, the pressure depends ondepth in a fluid• Consider an imaginary fluid volume (acube, each face having area A)The sum of all the forces on this volumemust be ZERO as it is in equilibrium.» There are three vertical forces:• The weight (mg)• The upward force from the pressureon the bottom surface (F 2 )• The downward force from thepressure on the top surface (F 1 )• Since the sum of these forces isZERO, we have: F 2 -F 1 =mgF 1F 2y 1yp 21ASame fluid)p 2mg1 22 1p0F mg F 0F 0mg F FF F mg2 1Pressure vs. DepthIncompressible Fluids (liquids)F Fmg2 1P A PA mg2 1Now since P2A Force=pressure× PA1VgAreaNow since Mass=Density× VolumeP2A P1A y2 y1 AgP P y y g Volume is area x height21 2 1P ghThe pressure at the bottom of a vertical column is equalto the pressure at the top of the column (P o , Usuallyatmospheric) , plus the pressure due to all the water inthe column of height , h. (density x gravity x height).F 1F 2y 1yp 21ASame fluidp 2mgp0P P0ghGAUGE Pressure• One must be careful when we are talking aboutpressure. Do we want to include atmospheric pressurein our calculations?• If we want the pressure over and above atmosphericpressure, we have P 0 =0. This is called the GaugePressure.• If we need to include atmospheric pressure we use:P 0 =1x10 5 N/m 2 = 100 kPa• Most pressure gauges register the pressure over andabove atmospheric pressure.• For example a tire gauge registers 220 kPa, the actualpressure within the tire is 220 kPa +100 kPa = 320 kPaGauge Pressure in a Tank Filled with Gasoline and WaterWhat is the pressure at point A? At point B?kgAt point A:G 6803mPA P0GghGkg kg m W10000 680 9.83 3 2 10mm m s N 666402mAt point B:10m3 mP P ghB A W WN kg m 66640 1000 9.82 3 2 3mm m s N 960402mPage 5