《空气动力学》（双语版）Chapter 2 Aerodynamics：Some Fundamental Principles and Equations

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Based on the argument above, the integral of V· ds can be expressed as volume flux through fixed control surface Further Vv can be expressed as the rate at which fluid volume is leaving a point per unit volume +号x△-如AM△x4y ax 2)4y a+ax2y△2 ·尝y|-影字△

Based on the argument above, the integral of can be expressed as volume flux through fixed control surface. Further, can be expressed as the rate at which fluid volume is leaving a point per unit volume.   S V dS   V  

The average value of the velocity component on the right- hand x face is l+(a/ax)(△x/2) The rate of volume flow out of the right-hand x face is L+(au/ax)△2)△ That into the left-hand x face is Lu-(o/Ox)x/2)y△Az The net outflow from the x faces is (O/ax)△△y△ z per unit time

The average value of the velocity component on the right￾hand x face is u +(u x)(x 2) The rate of volume flow out of the right-hand x face is u +(u x)(x 2)yz That into the left-hand x face is u −(u x)(x 2)yz The net outflow from the x faces is (u x)xyz per unit time

The net outflow from all the faces in x, y, z directions per unit time IS I(Ou/ax)+(Ov/av)+(Ow/ Oz)xAyA The flux of volume from a point is lim outflow flux-inflow flux [(Ou)ax)+(Ov/ay)+(Ow/az)AxAyAz →0 △x△y△z lim outflow flux -inflow flux (Ou/Ox)+(Ov/ay)+(Ow/az) →0

The net outflow from all the faces in x,y,z directions per unit time is (u x)+(v y)+(w z)xyz The flux of volume from a point is   x y z u x v y w z x y z V outflowflux inflow flux V      +   +      = − → ( ) ( ) ( ) lim 0 lim ( ) ( ) ( ) 0 u x v y w z V outflowflux inflow flux V =   +   +   − →

2.4 Continuity equation e In this section, we will apply fundamental physical principles to the fluid model, More attention should be given for the way we are progressing in the derivation of basic flow equations o Derivation of continuity equation Step 1. Selection of fluid model A fixed finite control volume is employed as the frame for the analysis of the flow Herein, the control surface and control volume is fixed in space

2.4 Continuity equation In this section, we will apply fundamental physical principles to the fluid model. More attention should be given for the way we are progressing in the derivation of basic flow equations. Derivation of continuity equation Step 1. Selection of fluid model. A fixed finite control volume is employed as the frame for the analysis of the flow. Herein, the control surface and control volume is fixed in space