A simple hydroelectric plant includes a reservoir, surge tank and turbine set. If friction is proportional to the square of the velocity, the oscillatory motion of the level in the surge tank following sudden complete turbine shut down is described by the equation0)(222=+±ZdtdZdtZdβα; in which Z is the height at any instant of the surge tank level with reference to the reservoir level and α and β are constant. The surge tank diameter is 30m, pipeline diameter is 4.5m, and the length of the pipeline from the reservoir to surge tank is 720m. At the instant when the turbines are completely shut down, the flow along the pipeline is 42.4 m3/s and the level in the surge tank is stationary, 0.9m below the level in the reservoir.

(a) Derive the expression of α and β, and find out the values of α and β.

(b) If friction is negligible, derive an expression for the time response and the maximum rise of the water level in the surge shaft.

Answer rating: 100% (QA)

Answer a From the given information we know that Z 09 m Q 424 m3s D 45 m L 720 m Thus we can calculate the value of and as follows 2LlogDd Q2D where d ... View the full answer