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When density and gravity are approximately constant (that is, for relatively small changes in height), simply multiplying height difference, gravity, and density will yield a good approximation of pressure difference. If the pressure at one point in a liquid with uniform density ρ is known to be P 0, then the pressure at another point is P 1:
Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting on it. Suppose that, when the rock is lowered into the water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyant force: 10 − 3 = 7 newtons.
Gravity decreases with altitude as one rises above the Earth's surface because greater altitude means greater distance from the Earth's centre. All other things being equal, an increase in altitude from sea level to 9,000 metres (30,000 ft) causes a weight decrease of about 0.29%.
However, the group velocity first increases by 20% with respect to its deep-water value (of c g = 1 / 2 c 0 = gT/(4π)) before decreasing in shallower depths. [1] In fluid dynamics, wave shoaling is the effect by which surface waves, entering shallower water, change in wave height.
Tidal range is the difference in height between high tide and low tide. Tides are the rise and fall of sea levels caused by gravitational forces exerted by the Moon and Sun, by Earth's rotation and by centrifugal force caused by Earth's progression around the Earth-Moon barycenter. Tidal range depends on time and location.
The change in potential energy moving from the surface (a distance from the center) to a height above the surface is = + = (+ /) If / is small, as it must be close to the surface where is constant, then this expression can be simplified using the binomial approximation + / to [()] As the gravitational field is = /, this reduces to Taking = at ...
Stokes drift – Average velocity of a fluid parcel in a gravity wave; Undertow (water waves) – Return flow below nearshore water waves. Ursell number – Dimensionless number indicating the nonlinearity of long surface gravity waves on a fluid layer. Wave shoaling – Effect by which surface waves entering shallower water change in wave height
Geopotential height differs from geometric height (as given by a tape measure) because Earth's gravity is not constant, varying markedly with altitude and latitude; thus, a 1-m geopotential height difference implies a different vertical distance in physical space: "the unit-mass must be lifted higher at the equator than at the pole, if the same ...