1. Consider an inlet valve mechanism that is used to fill a water reservoir. The valve...

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1. Consider an inlet valve mechanism that is used to fill a water reservoir. The valve works such that the water filling rate is a function of the gap between the actual water height (h) and the target water height (h*). The valve is produced to provide an inflow that will close the 10% of the gap between h* and h per hour. Additionally, there is a small hole in the reservoir through which some water leaks out. The leakage rate is proportional to the water height, and this hole alone leads to a 5% fall in the water height per hour. Initial height of water is 10 cm, and the target water height is 60 cm. a. Identify the state variables involved in this problem and give the model equation(s) that capture the dynamics of the state variable(s). b. Next give the simulation equations and simulate the model for 10 hours, using a step size dt=0.5, tabulating the water height (h). (You may do it by calculator or using a spreadsheet software, or by computer programming). c. Next solve the model equations analytically in order to find the exact water height value at t=5 and t=10. Compare the exact values with the simulated values you find in (b) 1. Consider an inlet valve mechanism that is used to fill a water reservoir. The valve works such that the water filling rate is a function of the gap between the actual water height (h) and the target water height (h*). The valve is produced to provide an inflow that will close the 10% of the gap between h* and h per hour. Additionally, there is a small hole in the reservoir through which some water leaks out. The leakage rate is proportional to the water height, and this hole alone leads to a 5% fall in the water height per hour. Initial height of water is 10 cm, and the target water height is 60 cm. a. Identify the state variables involved in this problem and give the model equation(s) that capture the dynamics of the state variable(s). b. Next give the simulation equations and simulate the model for 10 hours, using a step size dt=0.5, tabulating the water height (h). (You may do it by calculator or using a spreadsheet software, or by computer programming). c. Next solve the model equations analytically in order to find the exact water height value at t=5 and t=10. Compare the exact values with the simulated values you find in (b)