308-12-16 - 12 A gate having the shape shown is located in...

12. A gate having the shape shown is located in the vertical side of an open tank containing
water. The gate is mounted on a horizontal shaft. (a) When the water level is at the top of
the gate, determine the magnitude of the fluid force on the rectangular portion of the gate
above the shaft and the magnitude of the fluid force on the semicircular portion of the gate
below the shaft. (b) For this same fluid depth, determine the moment of the force acting on
the semicircular portion of the gate with respect to an axis which coincides with the shaft.
(c) Clearly sketch the hydrostatic pressure distribution on the vertical gate.
Shaft
6 m
3 m
Fluid
Side view
of gate
Rectangular part
F
rect
=ρgAh
c
=(999)(9.807)(6)(6)(3)=1058097 N
Semicircular part
) m 3 (
π 3
4
m 6 R
π 3
4
m 6 h
c
+ = + =
=7.273 m
I
xc
=0.1098R
4
N 007344 1 ) 273 . 7 ( (3) π
2
1
7) (999)(9.80 gAh ρ F 2
c semi
= = =
m 359 . 7
) 273 . 7 ( ) 3 (
2
π
0.1098(3)
m 273 . 7
Ay
I
y y
2
4
c
xc
c semi
= + = + =
Moment acting on semicircular part
M=F
semi
(y
semi
-6 m)=(1007344)(7.359-6)
M=1369483 N·m =1.37 MN·m
13. A 3-m long curved gate is located in the side of a reservoir containing water as shown.
Determine the magnitude of the horizontal and vertical components of the force of the water
on the gate for a gate radius of R=2 m and a fluid depth of 6 m.