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Pressure PowerPoint PPT Presentation


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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 p t = p h + p a.

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Pressure

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Pressure l.jpg

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


Hydrostatic pressure l.jpg

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)


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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


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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


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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


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1 db ~ 1m

  • First, 100 m depth gave a ph = 100.45 db

  • Rule of thumb:

    1 db pressure ~ 1 m depth


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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


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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


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Example with Stratification

r1 = 1025 kg m-3

r2 = increases from 1025 to 1026 kg m-3

What is ph(100m)??


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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


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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


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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


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