By G. Hauke

This booklet offers the principles of fluid mechanics and shipping phenomena in a concise manner. it's compatible as an advent to the topic because it comprises many examples, proposed difficulties and a bankruptcy for self-evaluation.

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**Sample text**

26) Integrating dQ over the whole surface, the ﬂow rate Q is calculated. 5. Since n is the outward normal vector to the surface, then outgoing ﬂow rates are positive and inward ﬂow rates, negative. 9 (Mean velocity). 11 (Volumetric ﬂow rate for uniform velocity v parallel to the normal vector of the surface A). In this case, the volumetric ﬂow rate is simply Q = vA The mean velocity is v¯ = Q/A = v r R v(r) z Fig. 13. Fully developed laminar ﬂow in a constant section pipe. 12 (Laminar ﬂow in a circular cross-section pipe).

It can also be deﬁned as the average normal stress of the ﬂuid particle, technically speaking, the trace of the stress tensor. 7. For a gas, the pressure is a thermodynamic variable. In this case, the pressure cannot be deﬁned as the average normal stress of the ﬂuid particle. 1. 1. SI and non-SI common units of pressure. Name Symbol Equivalence pascal (SI) Pa 1 Pa = 1 N/m2 bar bar 1 bar = 105 Pa atmosphere (standard) atm 1 atm = 101 300 Pa meter of water mH2 O 1 mH2 O = 1 000g Pa millimeter of mercury mmHg kilogram-force per square centimeter (TS) kgf/cm 1 mmHg = 13 600g Pa 2 1 kgf/cm2 = 104 g Pa p p gag p atm p abs 0 Fig.

Positive stresses that act upon the foreground faces of an elemental cube. 1. Foreground faces are those where the normal vector is aligned to a coordinate axis and background faces those where the normal vector is in the opposite direction to a coordinate axis. 2. 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 .