Why does a 64 mm-Hg low pressure zone raise water level by only 0.85 m?

[qspartan570]

Homework Statement

Suppose that a zone of low atmospheric pressure (a "low") is at some place on the surface of the sea. The pressure at the center of the "low" is 64 mm-Hg less than the pressure at a large distance from the center. By how much will this cause the water level to rise at the center?

Homework Equations

p-p0= -p(density)gy

The Attempt at a Solution

First I converted 64 mm-Hg to Pa using 1.01X10^5 Pa/760 mm-Hg and I got 8505.27 Pa

p-p0=-p(density)gy
101325 Pa-8505.27 Pa=1000X9.8Xh
h=92819.73/9800=9.47 m

According to the book, the answer is 0.85 m

 

[gneill]

Homework Statement

Suppose that a zone of low atmospheric pressure (a "low") is at some place on the surface of the sea. The pressure at the center of the "low" is 64 mm-Hg less than the pressure at a large distance from the center. By how much will this cause the water level to rise at the center?

Homework Equations

p-p0= -p(density)gy

The Attempt at a Solution

First I converted 64 mm-Hg to Pa using 1.01X10^5 Pa/760 mm-Hg and I got 8505.27 Pa

p-p0=-p(density)gy
101325 Pa-8505.27 Pa=1000X9.8Xh
h=92819.73/9800=9.47 m

According to the book, the answer is 0.85 m

The pressure value that you've been given is already a pressure difference, so there's no need to invoke atmospheric pressure. All you need is the height of a column of water (seawater, which has a slightly different density than pure water!) that will produce that pressure at its base.