QI. The dynamics of a gravity tank in the figure below are given by the following equation dt -) PA Where u is the velocity of liquid. L the length of the exit pipe. A the cross-sectional area of the pipe and a is the friction coefficient. All parameters other than u and k are constant. You are required to: - Linearize the model around the steady state - Write the model in terms of deviation variables c. Write the transfer function between the input (h) and the output (u) d. Determine the parameters of the process e. Sketch the response of the system to a step of magnitude 7