Engineering Mathematics

Order Instructions/Description

Assessment Brief
You are a Chemical Engineering Student undergoing industrial training in a company. You are part of a team carrying out design of a system which will transport fluid. You are given two tasks which involve flow determination and shaft design. The details of the two tasks are presented thus:
Task 1:
The company is interested in using a widening pipe to transport fluid from location A to another location B. The pipe will be full with the flowing fluid during operation. The area of the pipe cross section at location A is A and this section is at an elevation z. It is expected that the fluid will flow with velocity v and pressure p.  It is assumed that the system will have geometry and parameters similar to the one presented in Fig 1.
You are required to consider the rate of change of momentum from location A to B, the forces acting due to the effect of surrounding pressure and changes in elevation and employ calculus to:
Derive a relationship between velocity, pressure, elevation and density along the pipe.
What assumption(s) did you make on the fluid properties?
If the pipe is to be horizontal and the flow of the fluid is reversed such that at location B, the velocity, pressure and diameter are 1.5 m/s,138 kPa and 0.15 m, respectively. You are required to:
Determine the pressure the fluid will possess at another location of the pipe where the diameter is 100 mm assuming that there is no loss of energy.


Fig 1

Task 2
Given that you need a pump to support the flow described above and the pump is to be driven by a steel shaft loaded as shown in Fig 2. It is anticipated that there is a point of elastic-plastic boundary along the section AB located at P where the shaft integrity is critical. If the shaft has modules of rigidity G = 80 GPa, yield stress τyield = 160 MPa, You are required to:

Derive an expression for the torque TAB in terms of P.
Determine the distance P which is the elastic-plastic boundary.


Fig 2

Submission of work
Your completed work for assignments must be handed in on or before the due date. You must keep a copy or backup of any assessed work that you submit.  Failure to do so may result in your having to repeat that piece of work.
Electronic submission:
This is normally done via WOLF. Any special instructions will be available on the upload tag or within the assessment brief.
Paper submission:
Your assignment should be handed in at the student office on the ground floor of MI building. It should have a barcoded front cover (available via eVision) and be neatly presented, preferably in a suitable plastic cover.   Any item handed in must have, clearly written on the front:
your name and student number
the module number, title and the module leader’s name
the date of submission

Penalties for late submission of coursework
Standard University arrangements apply. ANY late submission will result in the grade 0 NS being allocated to the coursework.
Procedure for requesting extensions / mitigating circumstances
This is done via eVision. Further information can be found at
Retrieval or Failure
Where a student fails a module (less than 40% for undergraduate modules, less than 50% for postgraduate modules) they have the right to attempt the failed assessment(s) once, at the next resit opportunity (normally July resit period).  If a student fails assessment for a third time they have a right to repeat the module.
Return of assignments
Assignments will be normally returned within three working weeks.
If you have any questions regarding your feedback you normally have two working weeks from the date you receive your returned assessment and/or written feedback or receive your exam results to contact and discuss the matter with your lecturer.
Cheating is any attempt to gain unfair advantage by dishonest means and includes plagiarism and collusion. Cheating is a serious offence. You are advised to check the nature of each assessment. You must work individually unless it is a group assessment.
Cheating is defined as any attempt by a candidate to gain unfair advantage in an assessment by dishonest means, and includes e.g. all breaches of examination room rules, impersonating another candidate, falsifying data, and obtaining an examination paper in advance of its authorised release.

Plagiarism is defined as incorporating a significant amount of un-attributed direct quotation from, or un-attributed substantial paraphrasing of, the work of another.

Collusion occurs when two or more students collaborate to produce a piece of work to be submitted (in whole or part) for assessment and the work is presented as the work of one student alone.
For further details see: