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A HOLLOW CYLINDER 1m IN DIAMETER AND 2 m HIGH WEIGHS 3825 N.
(A) HOW MANY kN OF LEAD WEIGHING 110 kN/m
3
MUST BE FASTENED TO THE OUTSIDE
BOTTOM OF THE CYLINDER TO MAKE IT FLOAT WITH 1.5 m SUBMERGED IN WATER?
(B) HOW MANY kN OF LEAD IF IT IS PLACED INSIDE THE CYLINDER?
SOLUTION :
(A) FASTENED TO THE OUTSIDE BOTTOM OF THE CYLINDER
∑ F
y
BF
C
+ BF
L
= W
C
+ W
L
γ
fluid
V
d
fluid
V
d
= γ
C
V
C
L
V
L
( 9. 81 kN/m
3
π( 1 m)
2
( 1. 5 m)
4
) + ( 9. 81 kN/m
3
)(V
L
) = 3. 825 + ( 110 kN/m
3
)(V
L
V
L
= 0. 0772 m
3
W
L
= 0. 0772 m
3
( 110 kN/m
3
W
L
= 8. 489 kN
(B) PLACED INSIDE THE CYLINDER
∑ F
y
BF
C
= W
C
+ W
L
γ
fluid
V
d
= γ
C
V
C
L
V
L
( 9. 81 kN/m
3
π( 1 m)
2
( 1. 5 m)
4
) = 3. 825 + W
L
W
L
= 7. 732 kN
A CUBE 2.2 ft ON AN EDGE HAS ITS LOWER ON AN EDGE HAS ITS LOWER HALF OF SG = 1.6 AND
UPPER HALF OF SG = 0.7. IT RESTS IN A TWO-LAYER FLUID, WITH LOWER SG = 1.4 AND UPPER
SG = 0.8. DETERMINE THE HEIGHT H OF THE TOP OF THE CUBE ABOVE THE INTERFACE.
SOLUTION :
∑ F
y
BF
1
+ BF
2
= W
A
+ W
B
BF = γ
fluid
V
d
BF
1
- 4 lb/ft
3
2 ft
2
- 2 ft − h
BF
2
- 4 lb/ft
3
2 ft
2
h
W = γV
W
A
= ( 62. 4 lb/ft
3
)( 1. 6 )( 2 ft)
2
( 1. 1 ft)
W
B
- 4 lb/ft
3
2 ft
2
- 1 ft
( 62. 4 lb/ft
3
)( 1. 4 )( 2 ft)
2
( 2. 2 ft − h) + ( 62. 4 lb/ft
3
)( 0. 8 )( 2 ft)
2
(h) =
- 4 lb/ft
3
2 ft
2
- 1 ft
- 4 lb/ft
3
2 ft
2
- 1 ft
- 2 ft − h
h
- 1 ft
- 1 ft
- 08 − 1 .4h + 0 .8h = 1. 76 + 0. 77
h = 0. 917 ft
FROM THE FIGURE BELOW, IT IS SHOWN THAT THE GATE IS 1.0 m WIDE AND IS HINGE AT THE
BOTTOM OF THE GATE. COMPUTE THE FOLLOWING:
(A) THE HYDROSTATIC FORCE IN kN ACTING ON THE GATE
(B) THE LOCATION OF THE CENTER OF PRESSURE OF THE GATE FROM THE HINGE,
(C) THE MINIMUM VOLUME OF CONCRETE (UNIT WEIGHT = 23.6 kN/m
3
) NEEDED TO KEEP THE
GATE CLOSED POSITION.
SOLUTION :
(A) THE HYDROSTATIC FORCE IN kN ACTING ON THE GATE
F = γhA
F =
- 81 kN/m
3
( 1 m)( 1 m)( 2 m)
F = 19. 62 kN
(B) THE LOCATION OF THE CENTER OF PRESSURE OF THE GATE FROM THE HINGE
e =
I
g
Ay̅
; I
g
bh
3
e =
( 1 m)( 2 m)
3
( 1 m)( 2 m)( 1 m)
e =
d = 1 − e
d = 0. 667 m
(C) THE MINIMUM VOLUME OF CONCRETE
M
A
T( 3 m) = 19. 62 kN( 0. 667 m)
T = 4. 36 kN
∑ F
y
T + BF = W
T + γ
fluid
V
d
= γ
concrete
V
o
- 36 kN + ( 9. 81 kN/m
3
)(V
O
) = ( 23. 6 kN/m
3
)(V
O
V
O
= 0. 316 m
3
