20071518

20071518 2 .

.

(x,y) ( 2.1). , . x y .

, . x y .

, px, py, ps , , , ax, ay x, y (x, y) 0

.

() () . yx .

. 2 , 3 1 3 .

. .

0 , .

Newton 2 Euler .

(surface force) (body force) ( 2.2). , y y . (x, y, z) p y

2.2 .. y/2 y . y .

x z ,

2.2 F .

, 0

. , 0 .

(gradient) del . 8.2

p -p f.

. , 0 Newton 2 . a . (f - jr) . .

Pascal . , . p y

. , , .Derive the pressure equation of the compressible fluid for the constant temperature and varying temperature.

.

.

. ln . .

. ()

(-0.00651 K/m). , .

, .

Derive the moments of inertia of simple areas about centroidal axis for the figures such as follows

[ 2.6] (gate) CDE( 2.12) CD (hinge)E P . O.8 . . (a) , (2.5.2) . (b) , (c) P

2.12

, 2.12

x y , y = 4 x = O, y = 6.5 x=3

a, b , a, b 1 x y .

,

(2.5.2)

(b) . (2.5.8)

x , . (2.5.11)

, O.32 ft .(c) , CD

[ 2.7] [ 2.14(a)] . 2,500 . .

. () [ 2.14(b)] , . 0 [ 2.14(c)]. . . 3,000N . 2.14(d) () . y , y , 0

. 2 3 . Newton-Raphson( B.5) ().

y . , y=2.5 y . , y=2.196m .

[ 2.8] (gravity dam) . . 2.15 . 2.5 , . 1ft . , , (foundation pressure) ( )(hydrostatic uplift) . , ()(hydrostatic head) 1/2 , 0 . , . , . () () . , , . 0

. 2.15

. , . ,

, . () . 0 .

. 3 . () 3 .

.

. . 2.18 3 . x . x

x . , x . x x . . x (y ) , x (y ) .()(closed body) , () , () 2.19 , 0 . x B C . B C ,

.

30[ 2.10] . 2m . 8 1 . xz , () y .

yz , 2-(4/3 )(2)m .

[ 2.11] (2.22). . 1m . (a) (b) .

.(CD () A .)

AB

.

(b) ABC CD . BC CD BCD 0.

.

2 9,806 Pa.

.

, () . r () . e .

.

2.25

0 . ,

0 . () . . . ()(center of buoyance) . () , . . ( ) () .

.

, , . 2.26 . , W V

.

()(hydrometer) . 2.27 . a .

(2.72)

, . .

, .

. , (2.7.2) (2.7.3)

. . [ 2.15] 1Mkg 2.32 . 2.0m 0.5m . y-y (rolling) x-x (pitching) .

2.32

[ 2.17] 66, 2 ( 2.35). () . .

. 0 (2.9.2)

p = 0 for y = 0, x = 4.5; so p0 = 2.25. Then, for y = 0, along the bottom . ,

When a free surface occurs in a container that is being rotated, the fluid volume underneath the paraboloid of revolution is the original fluid volume. The shape of the paraboloid depends only upon the angular velocity with respect to the axis (Fig. 2.37). The rise of liquid from its vertex to the wall of the cylinder is, from Eq. (2.9.6), for a circular cylinder rotating about its axis. Since a paraboloid of revolution has a volume equal to one-half its circumscribing cylinder, the volume of the liquid above the horizontal plane through the vertex is

. , . . ( 2.37) () (2.9.6)

. 1/2

2.37 ,

. . .