The dynamic viscosity u and density p of water may be assumed constant, as follows: u =0.0013 kg/m.s; p = 1000 kg/m3. The information contained in the Moody diagram is

also described by the Colebrook-Whiteequation: \frac{1}{\sqrt{f}}=-2.0 \log _{10}\left(\frac{\varepsilon / D}{3.7}+\frac{2.51}{R_{e} \sqrt{f}}\right) In this equation, the usual notation applies.(a)Briefly explain why it is difficult to find f from the Colebrook-White equation usingnormal algebraic methods, even when the relative roughness and Reynolds number(10 marks)are known. (b)Check the validity of the equation using the data you were assigned in Part 1 of the(15 marks)assignment. \text { (c) At large Reynolds numbers, the term } \frac{2.51}{R_{e} \sqrt{f}} \text { 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 ɛ/D = 0.003 and Re = 4 x 107and comment on whether or not you think this is a valid approximation for these(10 marks)values.