ME3560 – Equation-sheet. Test I.
Relation between Shear Stress and Rate of Shearing Strain:
߬=ߤ
߲‫ݑ‬
߲‫ݕ‬
Manometers: ܲ = ߩ݃ℎ
Hydrostatic Forces on Submerged Surfaces:
‫ܨ‬ோ = ߩ݃ℎ௖ ‫ܣ‬
‫ܫ‬௫ᇱ
‫ݕ‬ோ = ‫ݕ‬௖ +
‫ݕ‬௖ ‫ܣ‬
For Curved Surfaces:
•The vertical force, FV, is the weight of the fluid above the
curved surface up to the free surface.
•The line of action of FV passes through the centroid of the
volume of fluid above the curved surface.
•The horizontal force, FH, is determined by projecting the
curved surface onto the vertical plane (y–z) and calculating
the force that the fluid would exert on this imaginary vertical
surface.
•The point of application of FH corresponds to the location where the force would act on the imaginary
(projection) vertical surface.
Additional Relevant Relations:
ܲ=
ߤ = ߩߥ
݀‫ܨ‬
݀‫ܣ‬
ܸ = ܴ߱
ܶ = ‫ܴܨ‬
Moment of inertia of a Rectangle:
ܾℎଷ
‫ܫ‬௫ᇱ =
12
Moment of Inertia of a Circle:
‫ܫ‬௫ᇱ =
ߨܴ ସ
4
ߛ = ߩ݃