The pressure head at point a is measured at 25 m head of

Question

Assignment - 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 as shown in Figure 1 has been constructed in order to convey water from two supplies (A and F) to a number of delivery points. A pump has been installed in the line between F and E in order to boost the pressure as water flows from F to E.

The details of each pipe are given in the table below:

Pipe	AB	BC	CD	DE	EF	FA	AG	GC	GB
Length (m)	200	400	240	160	700	100	150	500	190
Diameter (mm)	100	50	100	250	250	200	200	100	50
Roughness (mm)	0.15	0.1	0.15	0.0.6	0.0.6	0.2	0.2	0.15	0.1

The head added by the pump is a constant 30 m

TASKS:

a) Use the linearisation method to solve for the unknown discharges in each pipe.

b) The pressure head at point A is measured at 25 m (head of water). Assuming the network is situated on a level grade estimate the pressure head in metres at each pipe junction (B, C, D, E, F & G)

HINT: The pump has the opposite effect (opposite direction) to the friction loss in pipe FE.

Question 2 - Surge Tank

The question below can be completed by minor modification of the code written for that question.

A hydroelectricity plant is supplied from a reservoir via a pipeline 4.5 km long and 2.6 m in diameter. The pipeline terminates at its downstream end in a control valve. This pipeline is cast iron (lookup roughness)

Under normal operating conditions the hydro plant runs with a steady discharge of 15 + N₁ cumecs, where N₁ is the second last digit of your student number.

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.

Surge Tank Design Criteria:

Unrestricted on inlet (F_S = 0)

Maximum allowable water height = 4.0 + N₂ m above level in reservoir.

(Where N₂ is the last digit in your student number)

For example if your student number is Q1528616 then:

The steady discharge is = 15 + 1 = 16 m³/s

Max allowable water height is = 4.0 + 6 = 10 m

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 15 + N₁ m³/s to Q = 0)

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 surge tank in the tutorial problem reaches a maximum height of approx  11.8m  during complete closure.

Question 3 - Cut Throat Flume

A Cut-throat flume is to be constructed for measuring flow at a certain location of an irrigation channel. The shape of the channel cross-section is rectangular with a width of 2.5 m and the Manning roughness n is of 0.025.

The maximum flow rate (Q_max.) in the channel is 0.1 + (0.05 x N₁) m³/s

The bed slope of the channel S_o is 0.001 + (0.0001 x N₂)

Where, N₁ is the second last digit and N₂ is the last digit in your student number.

For example if your student number is 0008006549 then

Max. Q = 0.1 + (0.05 x 4) = 0.3 m³/s

S_O = 0.001 + (0.0001 x 9) = 0.0019

Flume Design Criteria:

• Flume length (L) = 1.5 m
• Floor of flume is above channel bed
• Total Width (B) must be less than channel width, see figure 7-26 in Reading 16.1
• The ratio of H_a:L should be less than 0.4
• Maximum upstream afflux = 0.1 + (y_n x 1.25) metres

The flume will discharge under free flow condition, which means you need to ensure that there will be no submergence at the downstream end, and eventually the flow at the downstream will be at normal depth y_n.

Use the method and equations described in the selected reading 16.1 for the Module 16.

Your tasks:

a) Design the flume in terms of Length, Width and floor height, a proposed methodology is as follows:

• Determine the normal flow depth
• Guess a flume width and determine appropriate coefficients
• Calculate H_a & H_b at max Q
• Determine a flume floor height (above bed) that ensures free flowing conditions but will not exceed the allowable upstream afflux
• Check against design criteria and revise width and floor height if required

b) Draw a sketch of your flume showing dimensions from TOP and SIDE views

c) Draw a rating curve (Q vs H_a) for the design range of the flume

d) Briefly discuss why a flume might be more appropriate than other forms of flow measurement for this situation

 References-

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

Marriott, M. 2009, Nalluri and Featherstone's Civil Engineering Hydraulics. 5th Edition, Wiley- Blackwell.

Kraatz. D.B. & Mahajan I.K. 1975, Small Hydraulic Structures, FAO Irrigation and Drainage Paper 26/2. FAO, Rome.