Four reservoirs are to be linked to a nozzle by sections of straight pipeline carrying water at…
Four reservoirs are to be linked to a nozzle by sections of straight pipeline carrying water at 20°C. The five pipelines meet at a single junction point as shown in Figure 1. Water will always flow from the highest reservoir and will always exit at the nozzle. Flow direction in the intermediate reservoirs is unknown, i.e. water could exit from the pipe into one, two or three middle reservoirs or enter from one, two or three
ENGG2500–Term 1, 2020–Assignment – 1
middle reservoirs into the pipe. Entry and exit losses are not negligible and must be taken into account (if applicable assume an appropriate exit loss coefficient). You can assume that the head losses at the pipe junction and at the nozzle exit due to the pipe contraction are negligible.
Figure 1 – Sketch of the pipe system with four reservoirs and a nozzle. (Example figure which may not represent the flow direction for your particular data set; Figure not to scale)
You will be provided with constant values for the following parameters:
Water level in Reservoir 0, H0[m];
Water level in Reservoir 1, H1[m];
Water level in Reservoir 2, H2[m];
Water level in Reservoir 3, H3[m];
Pipe diameter, D0, D1, D2,D3,D4[m];
Pipe length, L0, L1, L2, L3, L4[m];
Relative Pipe roughness ks/D (ks0/D0, ks1/D1, ks2/D2, ks3/D3, ks4/D4) [-];
Entry loss coefficients (K0, K1, K2, K3);
ENGG2500–Term 1, 2020–Assignment – 2
•Nozzle diameter Dn[m].
Each student is being provided with an individual data set. The data set is generated randomly for each student. The individual values of the above parameters will be emailed to each student. The provided values must be used to avoid penalties!
For the provided individual data of reservoir elevations, pipe and nozzle characteristics, compute the flow rate (Q (m3/s)) through the pipeline system. You can limit your calculation efforts to an accuracy to the nearest centimeter (or better) of the total head at the junction. (30 marks)
For the pipe system with four reservoirs and nozzle, sketch the Total Head Lines and the Hydraulic Grade Lines; include the values of total head and piezometric head at every position where local changes in head occur. (12 marks)
Sketch the velocity profile at a cross-section of pipe“0”, i.e. the pipe leading from the highest reservoir to the pipe junction; assume fully developed pipe flow conditions. In addition to the velocity profile add details of the locations with zero, mean and highest flow velocities. (4 marks)
Provide and comment on a complete list of the fluid mechanics concepts/principles and underlying assumptions that you applied for the solution of parts 1 and 2 (use any relevant concepts/principles that you learned in ENGG2500). Provide your answers in a table with three columns named“Fluid mechanics concept/principle”, “Assumptions”, and“Application in assignment”.(14 marks)
The marking of the assignment will be based upon completeness, neatness and logical working. Please explain your working and indicate your calculation steps. Marks will be reduced if you only provide a final value as answer which does not allow the checking of your working. If you used a computer program for your working you need to provide both details about your working steps as well as the formulas and code created. Your sketches should contain all relevant information and the appearance of the sketches must be neat and clear.
Total marks available for each question are given above (in brackets).
For easier marking, 60 marks will be used during marking (and scaled to 30 marks for the course mark).