Hydrostatic Forces on Inclined Plane · PDF fileChapter 2 Hydrostatics ... Rm. E119B...
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10/28/2010 1 Chapter 2 Hydrostatics Hydrostatic Forces on Surfaces Zerihun Alemayehu Rm. E119B Hydrostatic Forces on Inclined Plane Hydrostatic Trust
Transcript of Hydrostatic Forces on Inclined Plane · PDF fileChapter 2 Hydrostatics ... Rm. E119B...
10/28/2010
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Chapter 2 Hydrostatics
Hydrostatic Forces on Surfaces
Zerihun Alemayehu Rm. E119B
Hydrostatic Forces on Inclined Plane
Hydrostatic Trust
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Hydrostatic Forces on Inclined Plane
Hydrostatic Forces on Vertical Plane
The distance between centroid and center of pressure GC = Ig/Ah
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Hydrostatic Forces on Vertical Plane
When the surface is not symmetrical about the vertical centroidal axis.
Hydrostatic Forces on Curved Surfaces
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Hydrostatic Forces on Curved Surfaces
Where Av is the vertically projected area of the curved surface; or Fx = pressure intensity at the centroid of a vertically projected area (BD) x vertically projected area
Hydrostatic Forces on Curved Surfaces
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Pressure Diagram
Pressure Diagram
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Tensile Stress in a Pipe
P e
T1
T2
F cp
c r
1 m
F = p. 2r . 1
For small pressureT1 is smaller than T2, but for large pressure we can assume T1 = T2
T1 + T2 = F=2pr Since T1 + T2 =2T, T = pr Where, T is the tensile force per metre length of pipe
Zc = Pc/
Tensile Stress in a Pipe
• For wall thickness t, the circumferential stress,
For an allowable tensile stress all, the required wall thickness t will be:
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Tensile Stress in a Pipe
• For large pressure variation, i.e. Zc = Pc/ 10r
From Fh = 0 : T1 + T2 = F = 2p.r M2 = 0 : 2rT1 – 2pr(r-e) = 0 Finally, we get:
Example (1)
kNF
Ay
ApF
6.1569
)4*4(*)1*10*9810(
)sin(
Find: Force of block on gate
m
Ay
Iyycp
133.0
)4*4*10(
12/4*4 3
F
kNF
kN
FF
FF
M
gb
gwgb
gbgw
378.104
6.15692
133.0
2
133.0
2133.0
0
,
,,
,,
Fw,g Fb,g
0.133
2
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Example (2)
m
Ay
Iyycp
4641.0
)24*464.6(
12/6*4 3
N
AyApF
000,318,1
)6*4(*)30cos33(*9810
)sin(
kNR
kN
FR
FR
M
A
A
A
05.557
1318)42265.0(
6
4641.03
)4641.03(6
0
F
RA
3-0.4641
6
Find the reaction at A
Example 3
3m 4m
45o
Determine the total hydrostatic force and the center of pressure
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Example 3 Solution
Example 3 Solution
Total hydrostatic pressure = F = whc.A
hc = yc Sin 45o
yc = 3/Sin 450 + 4r/3 = 5.94 m
Therefore, hc = 4.20 m
Area of gate , A = r2/2 = x 42/2 = 25.13 m2
Thus, F = 9.81 x 4.20 x 25.13 = 1.035 MN
And hcp = ycp Sin 45o = 4.33 m
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Example 4
A C
B B
6 m
Hinge
kN
AyF CBx
6.176
1*6*3*9810
Determine the magnitude and direction of the force acting on the quarter circle gate of 1 m long.
F = 328.84 kN
ycp
Fy
Fx
F
y
Example 5 A 3 m diameter roller gate retains water on both sides of a spillway crest as shown in the figure below. Determine (i) the magnitude, direction and location of the resultant hydrostatic thrust acting on the gate per unit length, and (ii) the horizontal water thrust on the spillway per unit length.
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Example 5 solution
Example 5 solution
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Example 5 solution
Example 5 solution
