By G. Hauke
This ebook provides the rules of fluid mechanics and shipping phenomena in a concise manner. it really is appropriate as an creation to the topic because it comprises many examples, proposed difficulties and a bankruptcy for self-evaluation.
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Extra resources for An Introduction to Fluid Mechanics and Transport Phenomena (Fluid Mechanics and Its Applications)
12 , τ13 , τ21 , τ23 , τ31 and τ32 . 3. In Cartesian coordinates, the components of the stress tensor are also denoted by τxx , τyy , τzz , τxy , τxz , and τyz . 3 D fs τ 12 n τ 21 τ 22 τ 23 τ 11 τ 13 P τ 31 C 2 τ 32 τ 33 B 1 Fig. 3. Inﬁnitesimal tetrahedron employed to obtain the stress tensor at the point P. Derivation of the Stress Tensor In order to determine the general expression of the stress at a point P from the stresses on three perpendicular planes, let us select the inﬁnitesimal ﬂuid volume of Fig.
Y dy τ 12 (x,y) τ 21 (x,y+dy) O (x,y) τ 21 (x,y) τ 12 (x+dx,y) x dx Fig. 4. Stresses on a cube acting on the torque balance around the z axis. e. 8) Proof. Let us take an inﬁnitesimal cube of sides dx, dy, dz (see Fig. 4). The angular momentum equation with respect to an axis parallel to z that passes through the point O implies 40 3 Fluid Forces MO = I Ω˙ with MO the external moments around the z axis acting on the cube, I the moment of inertia and Ω˙ the angular acceleration around the z axis.
6), ∇p = ρf m Next we will cover examples on hydrostatics, manometry and forces on submerged structures. 2 Applications 49 P atm z g x Fig. 1. Hydrostatics. Axes. 1 Hydrostatics Hydrostatics is the part of ﬂuid statics dedicated to incompressible ﬂuids. Let us calculate the pressure distribution in a liquid at rest. Take the coordinate axes of Fig. 1, where z is the upward vertical axis. 10) ⎩ ⎭ −ρg where the density ρ is constant. 11) = 0 ⎪ ∂y ⎪ ⎪ ⎪ ⎪ ⎩ ∂p = −ρg ∂z from where the pressure distribution p(x, y, z) can be calculated.