Please use SI units a heres the student number 220024286
UNIVERSITY OF KWAZULU NATAL: MECHANICAL ENGINEERING
ENME2FM FLUID MECHANICS I SUMMATIVE ASSESSMENT 1
EXAMINERS: Prof G Snedden and Mr T Velthuysen TIME: No time limit
DATE: 1 March 2022 TOTAL MARKS: 35
Additional Instructions:
This assignment counts 20% towards your final mark. No collusion will be tolerated. Your submission, via Moodle, should include a title page with your Name and Student number and the UKZN anti plagiarism declaration without which, no mark will be assigned.
Submission Deadline: 17:00 on the 17th May 2022
Submissions after this deadline will be rejected.
Neglect all losses other than pipe friction. g = 9.81 m/s2
Remember to use the European formulation for the Darcy equation:
h?? = 4??????2/2????
ASSIGNMENT 1
Theory
Multiple pipes
Multiple pipe systems arise where there is branching of the pipes. For simplicity we will examine the flow in three pipes to indicate the principle of the flow and the method of solution. Further branching is best dealt with by computer programs which are more convenient for solving the large number of simultaneous equations that arise. Only frictional losses are usually of any significance and minor losses (including the velocity head in the pipe) are neglected.
Consider the above figure, where flow in three pipes between three reservoirs is described. Flow will obviously take place from reservoir A through pipe 1 towards junction J. At the junction, flow will continue through pipe 3 towards reservoir C. But what will be the flow direction in pipe 2? Will it be towards reservoir B or from reservoir B towards the junction?
The flow direction will depend on the total head at the junction. If it is higher than that at the surface or reservoir B, then flow in pipe 2 will be towards reservoir B. For flow toward J, the total head at J must be less than that at the reservoir B, i.e. below the surface level of reservoir
B. Unless it is obvious which way the fluid is flowing in pipe 2 we must guess, and if in the ensuing calculations ridiculous values result then we know our choice was incorrect. Note that the total head line and hydraulic grade line are coincident since the velocity head in a pipe is neglected.
If zj is the elevation of the junction and Hj is the total head at the junction then the total head at A:
????/ ??2
???? = ???? + ??/2?? + ???? + h??1
But ????2/ is neglected, and putting ???? = ????/???? + ???? then 2??
From A to J: ???? = ???? + h??1
From J to B: ???? = ???? + h??2
From J to C: ???? = ???? + h??3
From Continuity:
Now for each pipe: ??1 = ??2 + ??3
h?? = 4??????2/2???? = 32??????2/??2????5
Therefore putting h??1, h??2 and h??3 in terms of ??1, ??2 and ??3 the four resulting equations may be solved simultaneously for ????, ??1, ??2 and ??3.
To effect the solution by hand can be very tedious, so one can simply use a trial value of ???? in the first three equations and solve for ??1, ??2 and ??3. The values can be substituted into the continuity equation to check if they satisfy that equation and then to adjust the value of ???? accordingly. ??1 -(??2 + ??3) can be plotted against ???? and the solution is found where the graph crosses the ???? axis.
Question 1 [15]
Student Number: 2ABCDEFGH
Therefore, if your student number is 216007895, H=5, G=9 and F=8 for example.
L1 = 3+H [km]
L2 = 2+H [km]
L3 = 2+5H [km]
zA = 500 [m] ZB = 250 [m]
ZC = 100 [m]
d1 = 250+10F [mm] d2 = 180+10G [mm] d3 = 250+10H [mm]
As the engineering in charge of developing the new branch of the city water reticulation system you have been asked to design the pipe network system to integrate a new water reservoir into the existing system that consists of a water reservoir (C) connected to the main water supply dam (A).
The new reservoir (B) has been sited by the civil engineers and is to be connected with a pipe of length L2.
i) What flow rates will result in each branch of the pipe? [10]
ii) If the population near B grows and more water is needed, what can you propose as a change to the water reticulation system to increase the flow rate to B? Back up your ideas with a calculation. [5]
Assume f = 0.008 for all pipes.
Question 2 [7]
Applications where a regular amount of fluid is drawn from a pipeline, such as an irrigation system are handled as follows. Consider the pipe shown below: The flow rate entering the pipe is Q0 with velocity V0 and the fluid is drawn off at a rate of q [(m3/s)/m] length of pipe. This draw off rate can be assumed if the tapping points are close together.
At a distance l from the inlet where the fluid velocity is V and as the cross-sectional area A of the pipe is constant, we get:
?? = ??0/??0 = (??0 - ????)/??
Now
h?? = 4??????2/2???? And hence for an incremental length of pipe dl,
4????2/2????)????
??h?? = (
i) Determine the total loss for a closed pipe of length L with a fluid draw off of q. [5] ii) Compare this result to the stand Darcy equation for loss in a pipe. [2]
Question 3 [13]
?H = 80+10F [m]
L1 = 400G [m]
L2 = 400H [m]
All pipe diameters D = 150+10G [mm] Assume f = 0.008 for all pipes.
A farmer has two dams connected by a pipe. His irrigation system requires a flow rate of 2000 l/hour to irrigate his crops effectively.
i) Determine the flow rate in Pipes 1 and 2.
ii) What is the pressure head (Hj) that the irrigation system junction?
Neglect all losses other than pipe friction.