Civil Engineering Practice 2
Semester 2, 2006
Assignment 3
You have been asked to design a cylindrical steel pipe to carry water under pressure over a horizontal distance of 2,500 metres, subject to the following design criteria:
• The inlet pressure pin is 800 kPa and the outlet pressure pout is 300 kPa
• The pipe must weigh no more than 500 kg per metre
• The tangential stress on the outside of the pipe must not exceed 2,000 kPa
• The flow quantity along the pipe must be maximised
Use non-linear programming methods to determine the optimal values for the internal pipe radius ri (m) and the external pipe radius re (m) in order to satisfy the above design criteria. Assume the density of steel is 7,860 kg/m3.
Tangential stress on the outside of a cylindrical pipe is given by
Where pi is the maximum fluid pressure inside the pipe, and
The total head loss H (m) along a horizontal pipe with an inlet pressure pin (kPa) and an outlet pressure pout (kPa) is given by
Where w is the unit weight of water = 9.81 kN/m3
The flow quantity Q (m3/sec) along a pipe of length L (m) with a total head loss H (m) and diameter D (m) is given by the Darcy Weisbach equation as follows:
where f is the friction factor for the pipe; in this case f = 0.001 sec2/m.
Note: some starting values for decision variables may not give a solution, so try a range of different starting values.
20 marks
參考答案:看不懂啊!