Hydraulics - Open Channel and Pipeline Flow
Objectives
1. Evaluate and apply the equations available for the description of open channel flow
2. Solve simple pipe networks using an appropriate method
3. Apply rigid and elastic water hammer theory to the analysis of pipeline systems
4. Design a range of hydraulic structures including: fixed and movable crest weirs; gated control structures; pipe conveyance structures; spillways and energy dissipation structure; critical flow measuring flumes; gulley control structures; weir and culvert type structures using the minimum specific energy concept.
Question 1 - Pipe Network
A pipe network system as shown in Figure 1 supplies water from two reservoirs (G & H) to a number of delivery points. The Table shows the details of each pipe.
The pressure head at points H & G is given in terms of metres head of water (Figure1). You may neglect all minor losses that may occur in the system.
|
Pipe
|
AB
|
BC
|
CD
|
DE
|
EA
|
AF
|
FD
|
GC
|
HA
|
|
Length (m)
|
160
|
350
|
280
|
560
|
190
|
230
|
210
|
125
|
125
|
|
Diameter (mm)
|
200
|
200
|
180
|
180
|
185
|
185
|
160
|
250
|
250
|
|
Roughness (mm)
|
0.09
|
0.10
|
0.07
|
0.12
|
0.13
|
0.14
|
0.16
|
0.08
|
0.08
|
a) Use the linearisation method to solve for the unknown discharges in each pipe of the network.
b) 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, A, B, C, G can be analysed as a normal loop once you account for the difference in energy (water level) between the reservoirs.
- Nodes H and G do NOT have node equations
- you only need to remove node equations if you have too many equations
- You should end up with 3 loops
Question 2 - Surge Tank
A hydroelectricity plant is supplied from a reservoir via a pipeline 1.8 km long and 3 m in diameter. This pipeline is made of cast iron (k=0.25 mm) and terminates at its downstream end in a control valve. The water level at the reservoir is maintained at a constant 25 m above the inlet end of the pipeline.
You have been given the task of determining the size of the surge tank which is to be installed at the downstream end of this pipeline and immediately upstream of the valve. This tank must be designed in order to deal with the surge that would occur when the valve downstream of the tank is closed completely and instantaneously.
Model the flows within the pipe and surge tank using the numerical solution technique (equations & 12.22) described by Marriott (Nalluri and Featherstone) in Section 12.4. You should use a time step of 5 seconds or smaller and account for the change in f with velocity.
Task:
a) Determine the minimum surge tank size (nearest ½ m) to satisfy the max. allowable height
For the case of complete closure (Q changes from (10 + 1 × N1) m3/s to 0 m3/s)
b) Plot the water level in the surge tank (relative to reservoir) over time for at least 2 upsurges
c) Plot the velocity in the pipeline over the same period (different set of axes).
HINT- The initial water level in the tank is below the level in reservoir by distance of hf at full flowing condition
Question 3 - Control Structure
A reservoir supplies water to an irrigation scheme via a diversion channel. The channel is 2 m wide and is constructed of concrete with Manning n 0.016. The bed slope of the channel is 0.0017. The discharge into the channel is controlled by a vertical sluice gate (Cc = 0.61).
The water depth in the upstream of the gate is maintained at a constant depth of 2.9 m, and the maximum allowable discharge to the diversion channel is 12 m3/s. The depth on the downstream side of the gate is at normal depth.
You have been asked to develop the rating curve for the sluice gate (YG vs Q). Table below is incomplete tasks for this rating curve.
|
Q
|
Yg
(free flowing)
|
Yg
(for submerged)
|
Yn or Y3
|
|
(m3/s)
|
(m)
|
(m)
|
(m)
|
|
1
|
0.110
|
??
|
0.431
|
|
2
|
0.222
|
??
|
0.701
|
|
3
|
0.337
|
??
|
0.943
|
|
4
|
0.455
|
??
|
1.171
|
|
5
|
0.575
|
??
|
1.392
|
|
6
|
0.698
|
??
|
1.607
|
|
7
|
0.824
|
??
|
1.819
|
|
8
|
??
|
??
|
??
|
|
9
|
??
|
??
|
??
|
|
10
|
??
|
??
|
??
|
|
11
|
??
|
??
|
??
|
|
12
|
??
|
3.121
|
??
|
Your Tasks:
(a) Calculate the missing gate openings for free flowing condition and normal depth in the table.
(b) Determine at what discharge the gate changes from freely flowing to submerged conditions (to the nearest m3/s)
(c) Calculate the new gate opening (YG) for those discharges for where the gate is submerged by the depth downstream of the gate.
(d) Plot the rating curves (show both the free flowing and altered part where the gate is submerged)