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
• 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)
Hydrostatic
Pressure
• Hydrostatic pressure is the
weight per unit area D
• ph = r g A D / A
ph = r g D
Holds for r = constant
Often ph = - r g z (z+ up) ph = r g D
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
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
1 db ~ 1m
• First, 100 m depth gave a ph = 100.45 db
• Rule of thumb:
1 db pressure ~ 1 m depth
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
Dealing with
Stratification
• Density is a f(depth)
• Taking a layer approach D
dp = r(z) g dz
dz = layer thickness [m]
• Summing over D
ph = S r(z) g dz (where S over depth, D)
Example with Stratification
Sigma - t
0
-10
-20 r1 = 1025 kg m-3
-30
-40
depth (m)
-50 r2 = increases from
-60 1025 to 1026 kg m-3
-70
-80
-90
What is ph(100m)??
-100
24.5 25 25.5 26 26.5
(kg m-3)
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
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
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