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Q1a. To investigate the sliding stability of this reservoir by controlling its friction coefficient if the water level goes up to h=6.0m behind it (see Figure 1)

The catchment of this reservoir (shown in Figure 1) has recently experienced prolonged rainfalls leading to flooding in the area. As a result of this flooding water level has risen behind the reservoir. Your tasks as follows:

Q1a. To investigate the sliding stability of this reservoir by controlling its friction coefficient if the water level goes up to h=6.0m behind it (see Figure 1). You can communicate your inspection results by stating “the reservoir will be stable because of (you should explain the reason)” OR “the reservoir will not be stable because of (you should explain the reason)”.                                                                                              

  • The dimensions of this reservoir are: a=2:00 m; b=8:00 m; c=6.00 m
  • The current friction coefficient of the reservoir is ƞ = 0.21.
  • The unit weight of concrete is 26.6kN/m3 and rests on a solid foundation.
  • No fluid uplift pressure along the base.
  • Carry out the calculations for a unit length of the reservoir (L=1.0m).

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Q1b. If the friction coefficient of the reservoir increased to ƞ =0.55 by redesigning the reservoir, calculate the maximum water rise behind the reservoir in order to keep the current stability (i.e. ƞ =0.55).

  • In your design you need to consider b=4a and c=3a.
  • The unit weight of concrete is 26.6kN/m3 and rests on a solid foundation.
  • No fluid uplift pressure along the base.
  • Carry out the calculations for a unit length of the reservoir (L=1.0m).

 

figure 1

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  1. 2.      Q2. There is currently a broad crested weir in downstream channel of the above reservoir’s steep spillway (see Figure 2) with the height of 90cm. Is this height enough to cause a hydraulic jump in the channel? You can communicate the results by stating “the Hydraulic Jump will occur and the height is enough because of (you should explain the reason)” OR “the Hydraulic Jump will not occur and the height should increase to (you need to specify the new height)”.                                                                         

Note:

  • The downstream open channel is rectangular.
  • The cannel can carry a flow of 10 m3/s per meter of its width.
  • The Froude number before the weir (point (1) shown in Figure 2) is Fr=3.
  • Carry out the calculations for a unit width of the channel.

 

Figure 2

 

Q3.

  1. 3.      Two sharp-ended pipes of diameter D1 = 50mm, and D2 = 100mm, each of length 100m, are connected in parallel between the reservoir in Figure 1 and another reservoir (shown in Figure 3) in its downstream. The water level difference between the two reservoirs is H = 10m, as illustrated in Figure 3. If the Darcy coefficient is f = 0.008 for both pipes, calculate the flow rate in each pipe 

 

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These are the equations that are to be used in the assignment:

 

Flow in pipe

Bernoulli                                                                                             

Continuity                                                                                          

Momentum Equation                                                                   

Darcy-Weisbach friction loss                                                        or

Minor losses                sudden enlargement              

sudden contraction                

Flow in open channel

Manning                                                                                                                                                                   

                                                                                                              

                                                                                                               

Colebrook-White                                                                            

                                                                                                               

                                                                                                                 ;

                                                                                                               

                                                                                                               

Conjugate depth                           

Flow over bump                                                                              

Energy loss                                                                                        

 

Hydraulic Jump                                                                                

                                                                                                               

Hydrostatics and energy loss

Hydrostatic Pressure                                                                     

Weight Density                                                                                

Force                                                                                                    

          

                                                                                                               

Centre of pressure on submerged surface                          

                                                                                                              

Friction Coefficient                                                                          FH=ƞ.FV

 

Linear Interpolation                                                                       

 

Table 1

Shape

Dimensions

Location of the centroid, G

Second moment of area, IG

Rectangle

Breadth L

Height D

D/2 from base

L D3/12

Triangle

Base length L

Height D

D/3 from base

L D3/36

Circle

Radius R

Centre of the circle

π R4 / 4

Trapezoid

Height D

Long Breadth L1

Short Breadth L2

   

 

Table 2 - Variation of the length of a hydraulic jump Lj with F1

F1

<1.7

1.7

2.0

2.5

3.0

4.0

5.0

7.0

14.0

20.0

Lj

Undular jump

4.0D2

4.4D2

4.8D2

5.3D2

5.8D2

6.0D2

6.2D2

6.0D2

5.5D2

                                                                


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