# Thermofluids Assignment

Part 1

For this part of the assignment, you are allocated one set of data, Table 1 and Appendix 1. This is to ensure you have an individual set of data.

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 Data Set h1 (m) h2 (m) D1 (mm) D2 (mm) Q (l/s) η (%) (A)  1.5 (B)  20 (C)  300 (E)  600 (F)  500 (G)   85 (H)  2.0 (J)  18 (K ) 250 (L )  650 (M)  460 (N)  80 (P)  2.5 (R)  24 (S) 400 (T)  700 (U)  610 (V )  75

Table 1

A storage reservoir supplies water to a pressure turbine, Figure 1, under a head of h2. When the turbine draws Q of water the head loss in D1 mm diameter supply line amounts to 2.5m (assume this value in all cases for this assignment).  Determine the pressure intensity at the entrance to the turbine.                                                                                               (20 marks)

If a negative pressure of 30 KN/m2 exists at the D2 mm section of the draft tube h1 below the supply line, estimate the energy absorbed in the turbine in kW neglecting all frictional losses between the entrance and the exit of the turbine.                                                            (20 marks)

Hence find the output of the turbine assuming an efficiency of η %.                          (5 marks)

Hint:

You may assume that the conservation of energy between sections 2 and 3 can be written as:

Where Et is the energy absorbed by the machine/unit weight of water flowing.

Total energy absorbed by the machine, that is, the input energy = Et x W

Where W = weight of water flowing through the turbine per second.

Efficiency, η = Output/Input

Part 2.

For this part of the assignment, you are allocated one value from each of the categories defined below, Table 2 and Appendix 1. This is to ensure you have an individual set of data.

 Data Set Pipe diameter, D (m) (a)  0.2 (b)  0.25 (c)  0.3 Pipe relative roughness ε/D (r)  0.002 (s)  0.004 (t)  0.006 Volumetric flow rate Q (m3/s) (w)  0.01 (x)  0.02 (y)  0.03

Table 2

The dynamic viscosity μ and density ρ of water may be assumed constant, as follows: μ = 0.0013 kg/m.s; ρ = 1000 kg/m3.

The information contained in the Moody diagram is also described by the Colebrook-White equation:

In this equation, the usual notation applies.

• Briefly explain why it is difficult to find f from the Colebrook-White equation using normal algebraic methods, even when the relative roughness and Reynolds number are known.                                                                        (10 marks)

(b)      Check the validity of the equation using the data you were assigned in Part 1 of the assignment.                                                                                                 (15 marks)

(c)       At large Reynolds numbers, the term      in the above equation is often set to zero. Estimate f using both the Moody chart (annotate Figure 2 to show how this is derived), and the modified equation, for the case where ε/D = 0.003 and Re = 4 × 107 and comment on whether or not you think this is a valid approximation for these values.                                                                                                            (10 marks)

Presentation: This mark will be awarded based on the legibility and professionalism of the presentation.                                                                                                                    (20 marks)

The results chart on Page 5 MUST be submitted with all calculations.

Figure 2

Note:

• All working out must be shown.

• Marks will be lost for untidy work.

• You may write your answers by hand, or you may type them. You will not be penalised for writing your answers by hand, as long as they are neat and properly laid out.

editor. It will take you longer, but will be a good investment in time, as you will find it

useful at some point during your studies.

• All work found to have been plagiarised will be reported to the University and will be forwarded for consideration as Misconduct and you will be penalised accordingly.

Results Chart of Summary of Numerical Answers

(This Chart MUST be submitted with your work)*

 Name: Student Number:

 PART 1 Enter the values of  your Data Set h1 (m) h2 (m) D1 (mm) D2 (mm) Q (l/s) η (%)

 PART 2 Enter the values of your Data Set Pipe diameter, D (m) Pipe relative roughness ε/D Volumetric flow rate Q (m3/s)

 Quantity Student’s value Tutor’s Comment V1 (m/s) V2 (m/s) P2 (kN/m2) Et (m) W (KN/s) Output (kN) f from Moody chart f Modified

(*) All calculations carried out to obtain the values entered in the results table above MUST be included as part of your submission.  Values entered above should have the units indicated.

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