2-3 Stress field Surface and body forces body force: gravitational body force pge Stress force(nine quantities )to specify the state of stress in a fluid Imagine any surface within a flowing fluid, and consider the contact force applied to the fluid on one side by that on the other, surrounding point C, the surface 84
2-3 Stress Field • Surface and body forces: • body force:gravitational body force • Stress force (nine quantities)to specify the state of stress in a fluid • Imagine any surface within a flowing fluid, and consider the contact force applied to the fluid on one side by that on the other,surrounding point C, the surface gdV A
the unit normal vector outwardly the force, n acting on SF nay be resolved in two components, one normal to and the other tangent to the area. The s4 normal stress g and a shear stress tn are then defined as F Im n84n084 (26) L lim oF (2.7) in→04
the unit normal vector outwardly , the force, , acting on nay be resolved in two components, one normal to and the other tangent to the area. The normal stress and a shear stress are then defined as: n ˆ F A n n lim (2.7) 0 n t A n A F n → = lim (2.6) 0 n n A n A F n → =
the rectangular coordinates the stress acting on the which the stress acts. The second one indicates the p'Or planes whose outwardly drawn normals are in thex y, z directions, The first subscript indicate the plane direction in which the stress acts SF lin 4→0A SF SF T =Im (28) &Ax>0 SA 4→>04
the rectangular coordinates the stress acting on the planes whose outwardly drawn normals are in the x,y, or z directions, The first subscript indicate the plane on which the stress acts. The second one indicates the direction in which the stress acts lim lim (2.8) lim 0 0 0 x z A xz x y A xy x x A xx A F A F A F x x x → → → = = =
The stress at a point is specified by the nine components denote the normal stress and shear stress
The stress at a point is specified by the nine components z x z y z z yx yy yz xx xy xz denote the normal stress and shear stress
2-4 viscosity We have defined a fluid as a substance that continues to deform under the action of a shear stress. Consider the behavior of a fluid element between the two infinite plates SH dF a4→>0C4
2-4 viscosity • We have defined a fluid as a substance that continues to deform under the action of a shear stress. Consider the behavior of a fluid element between the two infinite plates y x y x A yx dA dF A F y = = → 0 lim