Reference no: EM132292509

The aim of this assignment is to demonstrate the students' ability to produce a technical engineering report investigating steady fluid flow phenomena in open channels, using both laboratory experiments and computer simulations. As such, the assignment comprises two components:

• Part A. It is concerned with laboratory investigation of two methods of measuring open channel flow and hydraulic jumps.
o A.I . Crump weir
o A.2. Broad crested weir

• Part B. It involves a computer model of gradually varied flow in an open channel (M2 backwater profile).

Part A

This part investigates the phenomenon of rapidly varied steady flow in an open channel. This will be based on a laboratory experiment comparing the measurement of flow using a crump weir with that using a broad crested weir, and will also investigate hydraulic jumps occurring downstream from the two weirs, and matching the experimental results obtained from those from theory. Estimates will also be made of the loss of specific energy of the flow over the two weirs. The experimental procedures and required analyses are outlined below:

1. Verify that the hydraulic bench unit (water tank and pump) has enough water and is connected to the 1423 flume water intake.

2. Measure the channel dimensions (width and depth), and ensure that the slope (So) of the flume is cero (So = 0%),

3. Install the crump weir at about 800mm downstream from the point at which the water leaves the stilling filter.

4. Turn on the pump of the hydraulic bench, and adjust the flow to its maximum by opening the valve. The water should not overflow from the channel.

5. Obtain the depth of the flow at the following locations by using the depth gauge provided. The depth is the result of the difference of two readings: bottom bed and water surface.

a. Some 100mm upstream of the weir (y1)
b. At the lowest depth at the bottom of the weir (y2)
c. Just before the jump (y3)
d. After the jump where the water is in tranquil flow (y4)

6. Estimate the length of the jump (L), i.e. the distance between y3 and y4

7. By using the Pitot tube measure the velocity head (if possible) at the same four locations, comment on any difficulties experienced.

8. Measure the flow rate by using the volume gauges built into the hydraulic bench, and the stop watch provided. It is suggested to record the time that takes to deliver 5 litres of water.

Please note that the tank starts filling when the plug (rubber ball) is blocking the outlet.

In order to reduce the uncertainty and improve the results, measure the flow rate at least 3 times and obtain an average.

Calculate the mean flow in m³s^-1

9. Decrease the flow rate by closing slightly the valve and repeat the procedure from point 5. Verify that the depth upstream of the weir decreases at least 5 mm. And repeat this procedure at least 5 times more, every time with a different discharge.

Calculation Procedure

a- For the very first value of volumetric flow rate (Q), calculate the critical depth (y,) and critical energy (E_c).

b- Using that value of volumetric flow rate per unit width (q), evaluate the specific energy for a range of theoretical depths up to a maximum of 200 mm. Plot these values in a dimensionless form: (y/yc) versus (E/yc). On the same curve, plot the values of the E1 and E2 calculated from the measured y1 and y2 dimensionless form, for the same discharge.

• Explain how the graph has been generated and investigate the phenomenon of rapidly varied steady flow in an open channel along with the characteristics of a free hydraulic jump.
• Briefly list the equipment used.
• Experimental set up.
• Tabulated results.
• Raw measurement
• Fully annotated plots and description of it.

c- Now using the whole S experimental results; calculate the ratio y4/y3, and the Froude number (Fr) just before the jump in each case. Using this calculatedFr, calculate the theoretical value of y4/y3. Plot y4/y3 against Fr for both experimental and theoretical results. For fully annotated plots and description of it, including equation for Froude number.

d- Discuss your results, assessing their validity and reliability, comment on the accuracy and draw the relevant conclusions.
• How valid the equations.
• What were the assumptions for the equations when derived, what human and lab errors were present, accuracy of instruments used etc.
• Draw conclusions.
• For wider implications.

e- For each case, calculate the flow force across the gate, the head loss across the jump.

A.2. Broad Crested Weir
Repeat the procedures outlined in A.1 using the broad crested weir in the same position as the crump weir was.

a. Calculate the loss of specific energy across each weir and through each hydraulic jump.

b. Calculate the Drag Coefficient of the weir

c. In your conclusion compare the performance of the two weirs as measuring systems for the flow in open channels and discuss this with reference to published work on each weir.

d. Suggest which weir would be used if you needed an accurate measure of irrigation water delivered to an area or a large agricultural business
e. Comment on the use of hydraulic jumps to reduce the energy in open channel flows.

Part B. Gradually Varied Flow Simulation

This part requires you to produce a "simple computer model" (using EXCEL) to establish water level profiles in a proposed channel (delivery canal to a reservoir, terminating with a free outfall) using the direct step method.

The channel, rectangular in cross-section, with a width b=0.050m, is required to carry a minimum discharge (Q) of 0.001 m³/s. The channel has a bed slope S_o = 0.0010, constructed at a minimum elevation of 1.0m above Ordnance Datum (OD) at the downstream end of the channel. The channel will be lined with neat a cement surface having a Manning's friction factor rt = 0.011.

If the critical depth (ycr) is assumed at the outfall (x=0), obtain the minimum length that the channel needs upstream to attain the normal depth (y_n). Use the direct step method to determine the water level profile along the channel(backwater curve), assuming gradually varied flow. It is recommended to use Δy = 0.001 m.

Plot this profile to scale. You will need to illustrate two calculations steps in your report, and then use a spreadsheet (e.g. MS Excel) to obtain the full flow profile.

dy/dx = (So - Sf)/(1-Fr²) or dE/dx = (So - Sf)

S_f = v²n²/R^4/3 and Fr = v/√gh

GVF Direct Step Method

1. Identify the condition of the flow

2. Identify the type of transition and subsequently the corresponding profile

3. Identify the control depth, and determine if the calculations go upstream or downstream from control section, setting that point as chainage x=0

4. Assume a depth increment (Δy).

5. Determine the geometrical characteristics of two consecutives cross sections (control depth and the control depth with the increment): hydraulic area (A), wetted perimeter (P) and hydraulic radius (R)

6. Determine the velocity (V²/2g) and the total energy head (E) of the section.

7. Determine the friction slope (Sf): Sf = v²n²/R^4/3

8. Calculate the energy head increment (ΔE) between consecutives sections.

9. Find the mean friction slope value: Sfmean = (Sfi + Sfi+1)/2

10. Find the horizontal increment (Δx) from ΔE/Δx = so - Sf mean

11. Accumulate Δx as x = ∑ⁿ_i=1Δxi

12. Determine the bed and water surface levels:

Bed level = OD + xS_o

Water surface level = Bed level + y

13. Repeat the process from step 5, until Sfmean = ) or until it changes its signal

Fill the table below with the results obtained from the procedure suggested above.

a) Description of how the spreadsheet was constructed

b) Show two calculation steps

c) The actual spreadsheet of the rectangular channel

d) Plot the variation of the water surface and bed level with respect to the length, starting at the outfall (x=0)

e) Final answer on length