Motion mass block: m ¼ 8 m  8 m  1000 kg=m
3
¼ 1:152 Â 10
6 kg;
Damping coefficients of waves: C V ¼ 2
ffiffiffiffiffiffiffiffiffi ffi
mK w
p
n ¼ 2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1:15 Â 10 6 Â 8 Â 10 5
p
Â
0:2 ¼ 3:8 Â 10
5 N Á s=m;
Elastic coefficient of water body: K w ¼ 80 Â 10
4 N=m ¼ 8 Â 10
5 N=m;
Elastic coefficient of air: K a ¼ S a Dp=Dx ¼ 80 m
2
 5  10
4 Pa=m ¼ 40 Â 10
5
N=m;
Flow coefficient: C p ¼ Q m = aDp
ð
Þ ¼ 77:8 m
3
=s
ð
Þ= 0:727 m
2
 50 kPa
ð
Þ ¼ 2:14
imes10
À3 m
3
= NDs
ð
Þ
Orifice area: a ¼ S a =110 ¼ 0:727 m
2 ;
Surface area of water body in water chamber: S a ¼ 80 m
2 ;
Atmospheric pressure: p 0 ¼ 100 kPa ¼ 1 Â 10
5 N=m
2 ;
Volume: V c ¼ 320 m
3 ;
Assuming volume change: DV 1 ¼ V c =20, i.e. 5% of V c .
T ¼ 6 s; x ¼ 1:05 rad=s
x 0 ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
K W þ K a
m
r
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
8 Â 10 5 þ 40 Â 10 5
1:152 Â 10 60
r
¼ 2:04 rad/s T 0 ¼ 3:08 s
ð
Þ
x
x 0
¼
1:05
2:04
¼ 0:515
G 1 ¼
1
m jx
ð Þ
2 þ C V jx
ð Þþ K W þ K a
ð
Þ
¼
1
À1:152 Â 10
6
 1:05
2
þ 3:8 Â 10
5
 1:05j þ
8 Â 10
5
þ 40 Â 10
5
À
Á
¼
35:3 Â 10
5
À 3:99 Â 10
5 j
1262 Â 10 10
G 1
j j ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
35:3 2 þ 3:99 2
p
 10
5
1262
¼ 0:028 Â 10
À5 m/N
\G 1 ¼ arctan À
3:99
35:3
¼ À6:45
ð14:21Þ
G 2 ¼
C p aS a p 0
V c À2DV 1
1 þ
C p aS a p 0
V c À2DV 1
1
S a
1
s
¼
x
2 C p aS a p 0
V c À2DV 1
þ
C p aS a p 0
V c À2DV 1
2
1
S a
xj
x 2 þ
C p aS a p 0
S a V c À2DV 1
ð
Þ
h
i 2
362
14 Pneumatic Principle and Device of Oscillating Water …