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Key Concept: In fluid statics there is no flow of the fluid and no relative motion. So there

are no shear stresses in the fluid. Consequently pressure is the only important variable.

In a Nutshell: To investigate pressure at a point start with a free body diagram of an arbitrary piece

of fluid as shown in the figure below and sum forces in the y and z directions.

Σ Fy = P_y δy δz – P_s δs δx sin θ = 0 and δs sin θ = δz So P_y = P_s

Σ Fz = P_z δy δx – P_s δs δx cos θ = 0 and δs cos θ = δy So P_z = P_s

Result: P_s = P_y = P_z Pressure at a point is independent of direction.

Another important question is, “How does the fluid pressure vary from point to point? “

In a Nutshell: To investigate how pressure varies from point to point construct a free body diagram

of an arbitrary volume of fluid and sum forces in the x, y, and z directions. Note that gravity results

in a pressure gradient (change in pressure) from point to point.