Show that a tilted free liquid surface undergoes shear stress

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SUMMARY

The discussion centers on the concept of shear stress in fluid mechanics, specifically regarding a tilted free liquid surface as presented in question 1.3 of "Fluid Mechanics" by Frank M. White. Participants clarify that while the shear stress on the free surface is zero, shear stress exists on a plane of constant y in the x direction, influenced by the surface's orientation. The confusion arises from the relationship between pressure and area, particularly why the solution does not include area in the shear stress formula despite the equation F = P * A being applicable.

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i really can't understand the answer of this question, is the question 1.3 in fluid mechanics by Frank ,M White

For the triangular element in Fig P1.3, show that a tilted free liquid surface, in contact with an atmosphere at pressure pa, must undergo shear stress and hence begin to flow.

i repeat i know the answer ,there is a solutionary of this book but i CANT understand why does the pressures at the bottom of the triangle are higher ,and why did the solutionary did n0t put Area in the formula since F=P*A ,
someone please explain this
 

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The shear stress on the free surface is obviously zero. But, the shear stress on a plane of constant y in the x direction is not zero. So, it depends on the orientation of a surface whether there is shear stress on it or not.
 

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