fluid dynamics - A book sits on a table. What is the net force of air pressure?

An elementary problem asks,

A book is at rest on a table top. In what direction is the net force of air pressure on the book?

Is this a meaningful question, and if so, what's the answer?

If we imagine that the book and table are completely smooth, there's no air between the book and table. Then the air pressure from above the book creates a large net downward force of hundreds of pounds. (This will be countered by an upward force from the table.)

On the other hand, if we imagine that due to the rough nature of the book and table, there is some air between the book and the table at most places, maybe there is enough air underneath the book to provide a net pressure force that is upwards. The scale height of the atmosphere is about 10^4m, so a 1cm book needs to have less than 1 part in 10^6 in contact with the table to have net upward force from air pressure.

How realistic are these approaches? Do we need a molecular view of the book, table, and air to understand the situation? For a typical, everyday book and table, is it meaningful to ask what direction the net force of air pressure pushes?

Answer

How realistic are these approaches? Do we need a molecular view of the book, table, and air to understand the situation?

It is realistic. There are no need to consider the molecular nature of air.

See http://www.nanovea.com/Application%20Notes/paperroughness.pdf. According to their data, the typical length in paper's surface variation is in order of $10^{-5}$ meters, while air's mean free path is $6.8\times 10^{-8}$ m (at room temperature, ambient pressure.) That means the room below the book cannot be thin enough to prevent significant amount of air sitting there (Babou actually reasoned his/her answer from wrong assumptions)

Considering the deformation of 'peaks' of surface of cover of a (heavy) book, it is likely that the book is in contact with the table more than 1 part in $10^6$. Therefore I'd guess that the net force is downward.

However, our static approach cannot be used if someone is picking up the book. S/he may experience the 'suction cup' effect (described in Babou's answer) when the book s/he lifted feels like "glued" to the table at one instant. When the book is lifted, air trapped below the book experiences a rapid, adiabatic expansion. Viscosity prevents surrounding air from entering the expanding room (below the book's surface) so rapidly. Hence the pressure below the book drops, and pressure from air above the book wins.