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Pressure

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  1. Pressure • Pressure changes provide the push that drive ocean currents • Key is the hydrostatic pressure • Hydrostatic pressure is simply the weight of water acting on a unit area at depth • Total pressure at depth will be sum of the hydrostatic & atmospheric, or pt = ph + pa

  2. Hydrostatic Pressure • Hydrostatic pressure is simply the weight of water acting on a unit area at depth • Mass seawater in column = r A D = [kg] • A = cross-sectional area of column [m2] • D = depth of water column [m] • Weight column = (r A D) * g • Mass * acceleration gravity (g = 9.8 m s-2)

  3. Hydrostatic Pressure • Hydrostatic pressure is the weight per unit area • ph = r g A D / A ph= r g D Holds for r = constant Often ph= - r g z (z+ up) D ph = r g D

  4. Hydrostatic Pressure Example • Let, D = 100 m & r = 1025 kg m-3 • Hydrostatic Pressure, ph= r g D = (1025 kg m-3) (9.8 m s-2) (100 m) = 1,004,500 kg m-1 s-2 [=N/m2] • Pressure is a stress (like tw) but normal to the surface not along it

  5. Example Cont. (or unit hell) • ph = 1,004,500 N m-2 • 1 N m-2 = 1 Pascal pressure • 105 Pa = 1 bar = 10 db • ph = 1,004,500 Pa (10 db/105 Pa) = 100.45 db

  6. 1 db ~ 1m • First, 100 m depth gave a ph = 100.45 db • Rule of thumb: 1 db pressure ~ 1 m depth

  7. Total Pressure • Total pressure = hydrostatic + atmospheric pt = ph + pa • pa varies from 950 to 1050 mb (9.5-10.5 db) • pa = ph(@~10 m) • Mass atmosphere = mass top 10 m ocean

  8. Dealing with Stratification • Density is a f(depth) • Taking a layer approach dp = r(z) g dz dz = layer thickness [m] • Summing over D ph= S r(z) g dz (where S over depth, D) D

  9. Example with Stratification r1 = 1025 kg m-3 r2 = increases from 1025 to 1026 kg m-3 What is ph(100m)??

  10. Example with Stratification • Sum over the top 2 layers ph(100 m) = ph(layer 1) + ph(layer 2) • Layer 1: ph(1) = (1025 kg m-3) (9.8 m s-2) (50 m) = 502,250 N m-2 (or Pa) 105 Pa = 10 db ph(1) = 50.22 db

  11. Example with Stratification • Layer 2: Trick: Use average density!! ph(2) = (1025.5 kg m-3) (9.8 m s-2) (50 m) = 502,500 Pa = 50.25 db • Sum over top 2 layers ph(100 m) = ph(1) + ph(2) = 50.22 + 50.25 = 100.47 db

  12. Hydrostatic Pressure • Hydrostatic relationship: ph = r g D • Links water properties (r) to pressure • Given r(z), we can calculate ph • Proved that 1 db ~ 1 m depth • Showed the atmospheric pressure is small part of the total seen at depth