Design of spilway gate

8/13/2019 Design of spilway gate

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MINI DESIGN PROJECT 1:

DESIGN OF A SPILLWAY GATE OF A DAM

by Nicodemus Paul (1166125)

Friday, February 5, 2010

MEC E 330 LAB H2 (Wednesday)

University of Alberta


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February 5, 2010 MEC E 330 LAB H2 Paul, Nicodemus

Mini Design Project 1 1166125

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Objective

Design the spillway gate of a dam to contain water above the spillway crest, while providing a

convenient method to open the gate in case of flood.

Given Data

Elevation of spillway crest = 2090.0 ft Normal high-water elevation = 2110.0 ft Span of piers = 30.0 ft Working fluid is water.

Assumptions

The length of the gate does not exceed the span of the piers. The top of the gate is not required to exceed the normal water level. The bottom of the gate does not extend below the spillway crest elevation. The working fluid is incompressible. Atmospheric pressure acts equally on both sides of the gate. Compared to water, atmospheric pressure does not vary significantly with elevation. Acceleration due to gravity is constant: g =32.174ft

s2

Atmospheric conditions are constant: T = 293 K; P =1 atm The density of the water is constant: "=998 kg

m3


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Schematic

Roadway

Spillway Gate

20.0 ft ytop

Hinge

y yhinge

ybottom Spillway Crest

x

The spillway gate has a maximum length of 30.0 ft into the page.


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Analysis

In the event of a flood, water must be discharged as quickly as possible in order to prevent

damage to the dam structure. When open, a larger gate area will produce a greater flow rate.

Thus, a flat rectangular plate is used. The length of the gate is restricted by the span of the piers

(30.0 ft). The height of the gate is restricted by the height of the spillway crest (2090.0 ft) and

the normal water level (2110.0 ft).

L = 30.0 ft

H = 2110.0 ft " 2090.0 ft = 20.0 ft

A = L# H = 30.0 ft( ) 20.0 ft( ) = 600 ft2

It is necessary to determine the total force applied by the water. According to Pascals Law, the

pressure at a depth hbelow the free surface is

P =Patm + "gh

Atmospheric pressure acts on each side of the gate and is therefore neglected. The net pressure

applied to the gate is

P=

"gh

By the definition of pressure, the resultant force is given by the product of the pressure at the

centroid of the surface and the area of the surface,

FR= P

cA

The centroid of the surface is given by

yc =1

A

ydAA

"

The resultant force acts through the centre of pressure. Employing the Parallel Axis Theorem,

yp = y c +Ixx,c

ycA


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For a vertical rectangular plate whose top edge is horizontal and at the free surface,

yc =1

2y top +y bottom( )

FR = P0 + "g s+ b /2( )sin#[ ]ab ="gLH2

2

yp =s +b

2+

b2

12 s+ b /2 + P0/ "gsin#( )[ ]

=

2H

3

Plugging in values,

yc=

1

2 20.0 ft+

0( )

FR=

998kg

m3"

#$

%

&'

0.062428lbmft3

1kg

m3

"

#

$$$

%

&

'''

1 lbf

32.174 lbmft

s2

"

#

$$$

%

&

'''

32.174ft

s2"

#$

%

&'30.0 ft( ) 20.0 ft( )

2

2

yp =2 20.0 ft( )

3

yc = 10.0 ft

FR = 3.74" 105lbf

yp = 13.3 ft

Thus, the resultant force of the water has a magnitude of 3.74105lbf and acts at a distance of

13.3 ft from the free surface. If the hinge is placed in the same position on the opposite side of

the gate, there is no net moment. In the event of a flood, the water level will rise, causing the

line of action of the resultant force to shift upward. This will produce a moment about the hinge

axis, causing the gate to swing open and allow water to flow.


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However, in the event of a low water level, the line of action of the resultant force will lower.

This would also cause rotation about the hinge axis. To prevent undesired discharge, a stop

should be placed at the bottom of the gate, on the side opposite to the reservoir.

Drawings

MH=0"

FR H FH

Fy

Figure 1: Free body diagram of gate. Reservoir at normal water level.

y

x


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MH


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Conclusions

The spillway gate of a dam was designed, given the normal reservoir level (2110.0 ft) and the

elevation of the spillway crest (2090.0 ft). In order to expedite discharge in the event of a flood,

the area of the gate was maximized. Considering the pier span of 30.0 ft, the gate was given a

length of 30.0 ft and a height of 20.0 ft. At a normal reservoir level, the water was found to

apply a force of 3.74105lbf to the gate at a distance of 13.3 ft from the free surface. In order to

balance forces and moments, the hinge was placed directly opposite to the resultant force.

The design assumptions are reasonable. Water is known to be an incompressible fluid.

Atmospheric conditions vary based on location. If the dam is built in Canada, lower

temperatures and icing conditions must be considered. Nevertheless, the principal quantities

used in the design of the gate, such as the acceleration due to gravity and the density of water, do

not vary widely with respect to environmental conditions. Overall, this model is robust.

The design is feasible and efficient. In the event of a flood, no human action is required.

Effectively, the additional weight of the water causes the spillway gate to open until the normal

level is restored. Due to its maximal area, the gate provides an optimal flow rate, reducing

potential damage to the dam structure.

In order to proceed with the design, detailed stress analysis must be completed. This will

allow for material selection and detailed design.

References

[1] Cengel, Y.A. (2010), Fluid Mechanics: Fundamentals and Applications, 2nd ed., pp. 76-

78 and pp. 88-93.


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Nomenclature

A Area of the gate

FH Force applied by hinge

FR Resultant force

Fs Force applied by stop

Fy Vertical force applied to gate

g Acceleration due to gravity

h Depth below free surface

H Height of the gate

Ixx,c Second moment of area about thex-axis passing through the centroid of the area

L Length of the gate

P Pressure

Patm Atmospheric pressure

Pc Pressure at the centroid

ybottom y-coordinate of bottom of the gate

yc y-coordinate of centroid of the gate

yhinge y-coordinate of hinge

yp y-coordinate of centre of pressure (from free surface)

ytop y-coordinate of top of the gate

! Density

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Design of spilway gate