An ocean current circulating counter-clockwise when viewed from directly overhea
ID: 2076262 • Letter: A
Question
An ocean current circulating counter-clockwise when viewed from directly overhead is dis-covered in the ocean with a period of rotation of 14 hours. Assume the current is circular and that the rate of circulation is constant throughout the whole 14 hour period. Also, assume the current occurs at a specic depth below the surface of the ocean, i.e. any forces toward or away from the surface of the ocean are matched by gravitational, pressure, or other forces so the net force lies entirely in the plane parallel to the ocean;s surface. At what latitude and in what hemisphere was the current detected? An ocean current circulating counter-clockwise when viewed from directly overhead is dis-covered in the ocean with a period of rotation of 14 hours. Assume the current is circular and that the rate of circulation is constant throughout the whole 14 hour period. Also, assume the current occurs at a specic depth below the surface of the ocean, i.e. any forces toward or away from the surface of the ocean are matched by gravitational, pressure, or other forces so the net force lies entirely in the plane parallel to the ocean;s surface. At what latitude and in what hemisphere was the current detected?Explanation / Answer
Due to the rotation of earth, the water in southern hemisphere circulates anti clock wise direction due to the deflection of water bodies towards left.
The coriolis force F=2vpw*sin (x)
where 'v' is the velocity of water body
'p' is the air density=1.225 kg / cubic meter
'w' is the angular velocity of earth = 7.29*10^-5 rad / s
'x' is the geometrical latitude
v can be calculated from the formula v= (2 * pi) / r * T
where r is the radius of the circular path of current circulation which can be calculated from the formula
r = T / 2 * pi
T = 14 hrs , which is the period of circulation as given in the problem.
From the data, we can calculate the following quantities as
r=8.01818 km
v=0.9990 m/s
Thus, coriolis force F = - 2 m (w x v) = 20.391588 *10^21
Thus from eq.1, x=65 degree from north. this is the latitude.