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Part B It is proposed to introduce a surge shaft to protect supply tunnel from pressure rise that propagates towards the supply reservoir as shown in Figure 1. The supply tunnel is 1.25 m in diameter has a friction coefficient of 0.008. The length of the supply tunnel is 500 m from the supply reservoir and under steady flow condition, the full flow to turbine is 3.0 m/s. In the initial design it is decided to construct a surge shaft of 3.75 m in diameter. Supply reservoir surface level Hydraulic gradient Supply reservoir Supply tunnel area di diameter Sures sha area diameter Penstock Castrol valves Tailace Discharge Turbine Lower reservoir Figure 1 Schematic of a surge shaft layout The governing equation for surge shaft control is given by, th, +2=0 g dt The friction head loss is given by, 1 d2g h = = 41 Hydraulic Engineering Laboratory Department of Civil Engineering, Faculty of Engineering Technology (1) Obtain the govering equation for water level fluctuation in surge shaft in the case of a sudden complete valve closure. Consider the continuity of flow at the surge shaft junction. The sudden complete valve closure makes flow in penstock zero. (i) If friction resistance in supply tunnel is ignored, determine how far the water level in the surge shaft would rise above supply reservoir surface level. (iNow, if friction resistance in supply tunnel is incorporated in the analysis, determine the solution using a numerical method. What is the maximum rise of water level in the surge shaft in this case? (iv) Discuss the accuracy of the solution based on the time step selected in the numerical computations (v) Compare the water level fluctuations in swge shaft in (i) and (ii) and provide a very brief commentary (vi) Introduce a possible function to the solution obtained in (ii) to simulate the condition in (iii). Part B It is proposed to introduce a surge shaft to protect supply tunnel from pressure rise that propagates towards the supply reservoir as shown in Figure 1. The supply tunnel is 1.25 m in diameter has a friction coefficient of 0.008. The length of the supply tunnel is 500 m from the supply reservoir and under steady flow condition, the full flow to turbine is 3.0 m/s. In the initial design it is decided to construct a surge shaft of 3.75 m in diameter. Supply reservoir surface level Hydraulic gradient Supply reservoir Supply tunnel area di diameter Sures sha area diameter Penstock Castrol valves Tailace Discharge Turbine Lower reservoir Figure 1 Schematic of a surge shaft layout The governing equation for surge shaft control is given by, th, +2=0 g dt The friction head loss is given by, 1 d2g h = = 41 Hydraulic Engineering Laboratory Department of Civil Engineering, Faculty of Engineering Technology (1) Obtain the govering equation for water level fluctuation in surge shaft in the case of a sudden complete valve closure. Consider the continuity of flow at the surge shaft junction. The sudden complete valve closure makes flow in penstock zero. (i) If friction resistance in supply tunnel is ignored, determine how far the water level in the surge shaft would rise above supply reservoir surface level. (iNow, if friction resistance in supply tunnel is incorporated in the analysis, determine the solution using a numerical method. What is the maximum rise of water level in the surge shaft in this case? (iv) Discuss the accuracy of the solution based on the time step selected in the numerical computations (v) Compare the water level fluctuations in swge shaft in (i) and (ii) and provide a very brief commentary (vi) Introduce a possible function to the solution obtained in (ii) to simulate the condition in (iii)