In this study, we will detail the physics of a solenoid-actuated butterfly valve. We will then develop a comprehensive formula to describe the pressure drops across valves in a system of many valves. We then use this formula to perform a case study of a network of three valves subject to the laminar flow. We then analyze the system as each of the valves is subjected to external noise with the intent to understand the behavior of the system as one valve is disturbed. Additionally, we capture chaotic dynamics of the system, showing that chaos can be induced in this system. The findings of the work show that a general formula of many valves can be used in simulating a system of three valves. Additionally, it is shown that when each of the valves is subjected to an external disturbance, the other ones behave different in each case.