A device used to control flow by varying the opening is a:

The correct response is that a gate valve is a device specifically designed to control the flow of fluids in a system by varying the size of the opening through which the fluid passes. Gate valves operate by raising or lowering a gate that obstructs or allows flow, thus enabling precise control over the volume of liquid or gas that can pass through the valve. This type of valve is particularly effective for on/off flow control, though it can also be used for throttling, depending on how it is positioned.

In contrast, the other devices mentioned serve different functions. A pressure-stat is used to monitor and control pressure levels within a system rather than flow rates. A humidistat is designed to control humidity levels in an environment, dealing specifically with moisture content rather than fluid flow. Similarly, a thermostat regulates temperature, ensuring a system maintains a set point, but does not directly vary flow. Each of these devices plays a critical role in their specific applications, but for the specific purpose of controlling flow by adjusting the opening, the gate valve is the appropriate choice.