(Solved): 6 (a) Careful calculation of the total dynamic head (TDH) is one of the most important factors in ...

6 (a) Careful calculation of the total dynamic head (TDH) is one of the most important factors in selecting the proper size of a pump. Make a list of all aiding and opposing elements that encountered in the pumping systems in Figure Q6(a). (6) Figure Q6(a) Q6 cont'd overleaf/ (b) A small hydropower plant had a number of Francis turbines installed in 1928. The plant is now under review for modernisation. Each of the existing turbines generates $300\mathrm{kW}$ at $250\mathrm{rpm}$ at an available head of $7.9\mathrm{m}$ for a flow rate of $5.8{\mathrm{m}}^3/\mathrm{s}$. The diameter of the draft tube is $1.34\mathrm{m}$ and the outlet area of the turbine runner is the same as the crosssectional area of the draft tube. Your task is to appraise the current performance and evaluate a number of different turbine replacements, all to operate under the same head, flow rate, and speed. Assume for all turbines a typical best efficiency of $95\%$ and a combined efficiency of all other components of $94\%$ for power conversion or transmission. The density of water is $1000\mathrm{kg}/{\mathrm{m}}^3$. Typical specific speed ratios are: (i) Evaluate the current performance of the installed turbines compared to that expected by a typical turbine under the given operating conditions. (3) (ii) Evaluate the choice of turbine type given the head it operates at and the power it provides. (iii) Discuss whether a multi-jet Pelton Wheel with a specific speed per jet of $N_s=N(P/?{)}^{1/2}/(\mathrm{gH}{)}^{5/4}=0.02$ would have been a better choice. Calculate the number of jets required to generate the same output. (iv) Would a Kaplan turbine with a specific speed of $\mathrm{Ns}=0.36$ be an appropriate choice? (v) Would a Kaplan turbine with a specific speed of ${\mathrm{N}}_{\mathrm{s}}=0.6$ be an appropriate in the given operating conditions? (vi) By how much could the available head be increased by increasing the diameter of the draft tube by $10\%$ ? Would it be worth doing? (4)