By G. Hauke
This ebook offers the principles of fluid mechanics and delivery phenomena in a concise approach. it's appropriate as an creation to the topic because it includes many examples, proposed difficulties and a bankruptcy for self-evaluation.
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Additional resources for An Introduction to Fluid Mechanics and Transport Phenomena (Fluid Mechanics and Its Applications)
The pressure diﬀerence between two points inside a liquid depends only on the height diﬀerence between the points. P atm z h x Fig. 2. The depth h as a coordinate axis. The Hydrostatic Pressure as a Function of Depth Frequently, instead of the vertical axis z, the depth with respect to the free surface h is employed (see Fig. 2). 19) Consequences. (a) The pressure at a point in a liquid depends on the depth of that point with respect to the free surface. (b) The pressure increases linearly with depth.
The opposite convention for i and j is equally found. This has no practical implication since, as shown below, the stress tensor is symmetric. 3 (Normal stress). e. τ11 , τ22 and τ33 . 4 (Shear or tangential stress). e. τ12 , 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.
4 with a decreasing cross sectional area between x = 0 and x = L be given by the one-dimensional velocity ﬁeld ⎫ ⎧ ⎫ ⎧ 1x ⎪ ⎨ V0 (1 + ⎨ vx ⎬ ⎪ )⎬ 2L v = vy = 0 ⎪ ⎩ ⎭ ⎪ ⎭ ⎩ vz 0 Calculate the acceleration of the ﬂuid particle. Solution. Since the ﬂuid ﬂow is in the x direction, ay = az = 0. Even though there is no temporal dependency of the ﬂow (∂vx /∂t = 0) the ﬂuid particle is still experiencing acceleration. Indeed, because the section of the nozzle is decreasing in the direction of the ﬂow, the velocity will increase.