Pressure Regulators are devices which maintain a preset pressure level in a system regardless of changes in upstream or downstream pressure.
A pressure regulator typically consists of a valve, a diaphragm or other sensing element, and a set of springs that determine the pressure level at which the valve opens and closes. When the upstream pressure exceeds the set pressure, the valve opens, allowing fluid to flow through and reducing the pressure downstream. When the downstream pressure drops below the set pressure, the valve closes, preventing additional flow and maintaining the desired pressure level.
In the context of rocketry, pressure regulators are used to ensure the pressure inside tanks and other fluid components remain at a desired value, even if environmental conditions such as temperature, combustion chamber pressure, or pressurant tank pressure change.
Mechanical pressure regulators do not function ideally if the mass flow rate of the fluid which moves through it increases. As mass flow rate increases, the regulated downstream pressure will drop below the set point. This phenomenom is known as droop.
Droop is very significant when dealing with the high flow rates that are often seen in liquid rocket feed systems. Droop will make it very difficult to accurately regulate the pressure without knowing the mass flow rate of the fluid itself.
If the mass flow rate of the fluid is known, in addition to the upstream pressure, then a datasheet from the manufacturer of the regulator should allow you to estimate the downstream pressure.
If the datasheet does not have enough information, the droop effect can be approximated linearly using this equation:
represents the droop, or the difference between the setpoint and the acual downstream pressure. is a constant representing the ratio between mass flow rate increase and pressure drop. is the mass flow rate of the fluid moving through the regulator.
With some experimentation, the value of can be determined for a particular setpoint and upstream pressure. Note that will be different if the upstream pressure changes or if the setpoint moves.
This approximation also has a very limited operating range, as the actual droop curve is not linear.