Final Answer:
The flow delivered to elevate circuit pressure to the pressure control setting and maintain it at that pressure for Ti is determined by the equation Q = (Pc - Pi) * Cv * sqrt(Ti), where Q is the flow, Pc is the pressure control setting, Pi is the initial pressure, Cv is the valve flow coefficient, and Ti is the time duration.
Step-by-step explanation:
The flow delivered (Q) is calculated using the formula Q = (Pc - Pi) * Cv * sqrt(Ti). This equation considers the pressure control setting (Pc), initial pressure (Pi), valve flow coefficient (Cv), and the square root of the time duration (Ti). The term (Pc - Pi) represents the pressure difference, indicating the change required in pressure. The Cv factor accounts for the valve's efficiency in controlling flow. Multiplying these factors by the square root of the time duration helps incorporate the time element into the equation.
In the given equation, subscript c denotes the pressure control setting, subscript i denotes the initial pressure, and subscript v represents the valve flow coefficient. The square root of time (Ti) is crucial, as it influences the rate of change in pressure over time. This equation is fundamental in process control systems, ensuring that the flow delivered corresponds to the desired pressure control setting and is sustained for the specified time duration.
In summary, the formula Q = (Pc - Pi) * Cv * sqrt(Ti) provides a comprehensive calculation for determining the required flow to elevate circuit pressure to the pressure control setting and maintain it for a specified time duration. Each component in the equation plays a crucial role in accurately estimating the flow needed for effective pressure control in the system.