Show that a tilted free liquid surface undergoes shear stress

In summary, the conversation discusses the concept of shear stress on a tilted free liquid surface in contact with an atmosphere at pressure pa. The question is about the pressures at the bottom of a triangular element and why the solutionary did not include area in the formula for shear stress. The answer is that the orientation of the surface determines whether there is shear stress on it or not.
  • #1
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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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  • #2
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.
 

1. What is a tilted free liquid surface?

A tilted free liquid surface refers to the surface of a liquid that is not level or flat, but rather has a slope or tilt to it.

2. What is shear stress?

Shear stress is a type of stress that occurs when two layers of a substance slide past each other in opposite directions, causing deformation or strain.

3. How does a tilted free liquid surface undergo shear stress?

A tilted free liquid surface undergoes shear stress when the upper layer of liquid slides past the lower layer due to the tilt or slope of the surface, causing deformation and strain in the liquid.

4. What factors affect the amount of shear stress on a tilted free liquid surface?

The amount of shear stress on a tilted free liquid surface can be affected by the angle of the tilt, the viscosity of the liquid, and the velocity at which the upper layer of liquid is moving.

5. What applications does the study of shear stress on tilted free liquid surfaces have?

The study of shear stress on tilted free liquid surfaces has applications in various fields such as fluid mechanics, chemical engineering, and geology. It can also help in understanding the behavior of liquids in containers or tanks with sloped bottoms.

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