## Question 1

A pipe network as shown in Figure 1 has been constructed in order to convey water from two reservoirs (G & H) to a number of delivery points.

The details of each pipe are given in the table below. You may also neglect all minor losses that may occur in the system.

Pipe | AB | BC | CD | DE | EF | FA | AE | FH | EG |
---|---|---|---|---|---|---|---|---|---|

Length (m) | 220 | 500 | 250 | 150 | 550 | 150 | 200 | 300 | 450 |

Length (m) | 200 | 150 | 150 | 100 | 150 | 175 | 200 | 225 | 200 |

Roughness (mm) | 0.15 | 0.1 | 0.06 | 0.25 | 0.06 | 0.15 | 0.15 | 0.25 | 0.06 |

- a) Use the
**linearisation method**to solve for the unknown discharges in each pipe of the network - b) The pressure head at points H & G is given in terms of metres head of water. Assuming the network is situated on a level grade estimate the pressure head in metres at each pipe junction (A, B, C, D, E, F )

**HINT:** The partial loop from H to G can be analysed as a normal loop once you account for the difference in energy (water level) between the reservoirs.

## Question 2

A hydroelectricity plant is supplied from a reservoir via a 2.5 m diameter pipeline. The initial stage of this pipeline is 2.35 km long and terminates in a control valve which opening is regulated to match electricity demand.

A surge tank (Fs = 1.0) with diameter of 8 m is situated immediately upstream of this valve in order to cope with sudden changes in valve opening. Under normal flow conditions the pipeline is discharging 2160 ML/day (25 cumecs) and the water level in the surge tank is 17.5 m below the level of water in the reservoir.

Your task is to model this pipeline when the valve is suddenly partially closed reducing the flow to (10+2*N)% of the original rate.

where N = 5

Model the flows within the pipe and surge tank using the numerical solution technique (equations 12.21 & 12.22) described by Marriott (Nalluri and Featherstone) in Section 12.4. From your model produce plots of

- a) the variation of water level in the surge chamber relative to the reservoir level
- b) the variation of velocity in the tunnel,

Plot each of these over a time of at least three upsurges (surge level peaks).

### Question 3

An irrigation scheme is fed from a river via a diversion channel. The irrigation channel is 4 m wide and is roughly faced with cemented rubble giving an estimated value of 0.028 for the Manning n. The bed slope is 0.002.

The discharge into the channel is controlled by a vertical sluice gate. The depth upstream of the gate is a constant 2.5 m, and the maximum discharge is 15 m^{3}/s.

Prepare a rating curve for the sluice gate (yG vs Q) and for the normal depth downstream of the jump (yn vs Q). Indicate the discharge at which the gate changes from a freely discharging condition to a drowned condition.

### References

Chadwick, A., Morfett, J. And Borthwick, M. 2004, Hydraulics in Civil and Environmental Engineering. 4^{th} Edition E & F N Spon.

Marriott, M. 2009, Nalluri and Featherstone’s Civil Engineering Hydraulics. 5^{th} Edition, Wiley-Blackwell.

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