《高等流体力学》第二章例题

系统总动量变化率 (pir)+ (pu ir)+ (pueui)+.(pu ruord80z fril ap 1 a +-(pu,r)+-(pun)+-(pu.)+pr Oi+ncin+lt如+n2186 t r ar r06 ar r a0 az Du =p-rOro86z Dt 柱坐标中=l,en+le+e, 06 于是 Du a a, ue a L-+ 06 Que +ugee +ue) +u Or ragaz De +. ue oue+u z +0) ar r a8 +u au u ou,+u c)e t 06 az

系统总动量变化率 [ ( ) ( ) ( ) ( )] 1 1 { [ ( ) ( ) ( )] [ ]} r z r z r z ur u ur u u u ru r z t r z u u u u u ru u r u u r u u r z t r r r z t r r z Du r r z Dt                           + + +             = + + + + + + +         = 柱坐标中 , , r r r z z r e e u u e u e u e e e         = + + = = −   2 ( )( ) ( ) ( ) ( ) r z r r z z r r r r r z r r r z z z z z r z z Du u u u u e u e u e Dt t r r z u u u u u u u u e t r r z r u u u u u u u u u e t r r z r u u u u u u u e t r r z                      = + + + + +         = + + + − +         + + + + +         + + +     于是

微元体所受的表面力 or(rp,)+agta(rp )]dededr l 06 (ro2)+=+on+-(ro0)le+ 06 ()+2n+2()E}mk 06 微元体所受的重力 FB=pgrord00z=(pg, e,+pgee+pge ror800z

[ ( ) ( )] {[ ( ) ( )] [ ( ) ( )] [ ( ) ( )] } S r z r rr zr r r r z z rz zz z p F rp rp d dzdr r z r r e r z r r e r z r r e drd dz z z                              = + +       = + − + +       + + + +       + +    微元体所受的表面力 微元体所受的重力 ( ) F gr r z g e g e g e r r z B r r z z = = + +          

依据动量定理 ①D。,O m08++[(m)+aaV lr t a0- az r Pg +-(ro)+ 00-0w+y(ro 06 +u dug u, ue 06 P8a+-[(ro)+ 00+0+(rod 06 az L + 06 n8:+0 rO.)+ +—(r 00 az

依据动量定理 1 [ ( ) ( )] r z Du p g rp rp Dt r r z        = + + +    2 1 [ ( ) ( )] 1 [ ( ) ( )] 1 [ ( ) r r r r r z r x rr zr r r z r r z z z z z r z z rz u u u u u u u u t r r z r g r r r r z u u u u u u u u u t r r z r g r r r r z u u u u u u u t r r z g r r z                                        + + + −        = + + − +        + + + +        = + + + +        + + +       = + +  ( )] z zz r z    +  