Suppose a constant height chart for the 3000 meter level and consider two locati

Question

Suppose a constant height chart for the 3000 meter level and consider two locations at a latitude of 30N that are 300 km apart. Suppose the isobars run north and south with the 700 mb isobar running through the western location and the 692 mb isobar passing through the eastern one. Assume the temperature is 268 K at 3000 meters.

i) What is the direction and magnitude of the horizontal pressure gradient between these two locations?

ii) What is the direction and magnitude of the horizontal pressure gradient force Pn?

iii) What is the altitude of the 700 mb pressure surface at the eastern location?

iv) What is the magnitude and direction of the vertical pressure gradient force Pz?

v) What assumptions did you make to obtain Pz?

Explanation / Answer

a) pressure gradient force Pn = difference in pressure/ distance

= (700 - 692) * 10^2 / 300 (here 1mb =100N/m2)

= 2.66 N/km

The pressure is force/area. The horizontal pressure gradient then gives us an expression for the magnitude of the force causing the molecules of air to move horizontally from the region of high pressure toward the region of lower pressure.

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