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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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