By George Emanuel
The second one version of Analytical Fluid Dynamics offers an improved and up to date remedy of inviscid and laminar viscous compressible flows from a theoretical point of view. It emphasizes simple assumptions, the actual elements of circulate, and the fitting formulations of the governing equations for next analytical therapy.
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Extra resources for Analytical Fluid Dynamics
2a) for continuity transforms into Dρ -------- + ρ ∇ • w = 0 Dt and continuity is invariant under the transformation, as mentioned earlier. 6 ANGULAR MOMENTUM EQUATION Consider a particle of mass m at an arbitrary position r . As a result of an applied force F , the particle experiences a moment, m r × F , which is a vector called the torque, that is perpendicular to r and F . For the angular momentum of a fluid particle, we similarly encounter the moments r × σ and r × F b as a result of the applied surface and body forces.
We will prove this assertion for continuity shortly. However, the linear momentum equation is a vector relation and therefore is not invariant. It is for this reason that a noninertial system is discussed in terms of Newton’s second law. 1. 13) where the four rightmost terms provide the acceleration of the noninertial system due to its translational and rotational motion relative to the inertial system. ] Thus, in a noninertial frame the momentum equation has the form Dw d 2 R d ω rot -× r ρ -------- + --------2- + 2 ω rot × w + ω rot × ω rot × r + ----------Dt dt dt where the acceleration can be written as ↔ = – ∇p + ∇ • τ + ρ F b 38 Analytical Fluid Dynamics Dw w2 ∂w -------- = ------- + ∇ ------ + ω × w Dt ∂t 2 Observe that the del operator is associated with the inertial system.
The shear and dilatational stresses are caused by the attractive and repulsive forces between molecules and the collisional relaxation of the rotational and vibrational energy modes of polyatomic molecules, respectively. Ultrasonic absorption measurements show µb to be zero for a low-density monatomic gas, in accordance with kinetic theory. For certain polyatomic molecules, such as CO2, µb can be much larger than µ. In any case, the second law of thermodynamics requires µb ≥ 0, as will be shown in Chapter 3.
Analytical Fluid Dynamics by George Emanuel