# Can pressure gradient force be balanced by Coriolis force?

I was learning about wind from my class textbook. In that there is first a description of forces affecting the velocity and direction of wind followed by that is geostrophic wind.

My question is:

At one instance it is written that Coriolis force acts perpendicular to the pressure gradient force and in the next paragraph it is written that ...the pressure gradient force is balanced by the Coriolis force....

If two vectors are perpendicular to each other then they are independent and so do not affect each other.

Following are the images of my text book:

In the figure, horizontal pressure gradient force and Coriolis force are opposite to each other, but since pressure gradient force and Coriolis force are perpendicular so the component of pressure gradient force in direction of Coriolis force must be zero.

Please help me understand which of the two highlighted(red) text is true. Or if both are true and I am making some mistake then kindly clarify.

Let me first get this out of the way: clearly you shouldn't try to learn from that book at all. It seems likely that it contains many more fatal errors.

In the case of a high pressure area or a low pressure area over time there is a tendency for air mass to start flowing around that area. That is, there is a tendency to develop air flow roughly perpendicular to the pressure gradient, hence roughly parallel to the isobars.

The coriolis effect acts perpendicular to the direction of the air flow.

Therefore in the case where the wind is perpendicular to the pressure gradient the pressure gradient and coriolis effect will act in opposite directions.

Now, of course there will also be circumstances where the air flow does occur right down the pressure gradient. In that specific circumstance the coriolis effect comes out perpendicular to the pressure gradient since the coriolis effect is always perpendicular to the direction of air flow

• But sir, air flow is decided by the combined affect of pressure gradient, friction and Coriolis force(reference, from my text book). From this point of view it is hard for me to understand that Coriolis force is perpendicular to the air flow. Kindly elaborate a little more. Commented Jun 7, 2020 at 16:34

I wouldn't say the book is wrong, but it certainly isn't very clear.

Both of the descriptions - the Coriolis force is perpendicular to the horizontal pressure gradient force (hpgf), and the Coriolis force balances the hpgf - are correct at different times, as the wind changes direction under the influence of the Coriolis force.

When the wind is not blowing there is no Coriolis force, because it acts only on moving bodies. When the wind first starts, it moves perpendicular to the isobars, blowing from high pressure to low. The Coriolis force appears, acting perpendicular to the wind (to the right in the northern hemisphere, to the left in the southern hemisphere). This deflects the wind accordingly, and so the Coriolis force changes its direction to maintain the perpendicularity, causing further deflection. This continues until the hpgf and the Coriolis force are equal and opposite. At this point, in the absence of friction, the wind will be blowing parallel to the isobars.

A video of this is available here: http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/geos.rxml

I hope that's helpful.