Question

.Emergency Coolant Injection from an Accumulator Tank (8 marks) Consider an accumulator tank with a cross sectional area of A,-10m, and a height of H-6m, initially filled with 5m of water as shown in the figure. The top of the tank is closed and filled with air at an initial pressure of P, 1,101 kPa At time -Os, the water starts to discharge from an opening at the bottom of the tank with an opening area of A2 0.001m2. The pressure at the tank nozzle remains constant at atmospheric pressure, P 101 kPa. The Bernoulli equation is given by 2and the ideal gas law for the air in the tank is given by PaVg constant, where vg is the total gas volume above the liquid. a) Calculate the initial discharge velocity, V2i, at t -0, and the final discharge velocity, V2s, when the liquid level reaches h- 1 m. State any assumptions made. Use g -9.81 m/s. (4 marks) b) Using the average discharge velocity, VavE (Vai+ V21)/2, estimate the amount of time, t*, in seconds needed for the liquid level to fall from h -5 m to 1 m. (2 marks) c) Is the amount of time calculated, t, expected to be greater or less than the actual amount of time needed for h to fall from 5 to 1 m? Why? (2 marks) -5.0 m H#6.0m V.

Answer 1

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