Question

An equal percentage valve has

• A. high sensitivity at high flow rates
• B. high sensitivity at low flow rates
• C. low sensitivity at high flow rates
• D. low sensitivity at low flow rates

Hint:

For an equal percentage valve:
$\text{Sensitivity} \propto \text{Flow rate}$.
Low flow = Low sensitivity (stable fine tuning).
High flow = High sensitivity (fast response).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks about the sensitivity characteristics of an equal percentage control valve at different operating flow rates.

Step 2: Key Formula or Approach:
The flow characteristic of an equal percentage valve is mathematically defined by the differential equation:
\[ \frac{dq}{dx} = \beta q \] where:
$q$ is the flow rate,
$x$ is the valve stem position (fractional opening), and
$\beta$ is a constant.
The sensitivity of the valve is defined as the rate of change of flow with respect to valve opening ($\frac{dq}{dx}$).

Step 3: Detailed Explanation:

• According to the relationship:
\[ \text{Sensitivity} = \frac{dq}{dx} = \beta q \]
• This shows that the valve's sensitivity is directly proportional to the current flow rate ($q$).

• At low stem openings (low flow rates), $q$ is small, so the sensitivity ($\frac{dq}{dx}$) is very low. This allows fine, precise adjustments of flow in the low-flow regime.

• At high stem openings (high flow rates), $q$ is large, so the sensitivity ($\frac{dq}{dx}$) is very high. Large changes in flow occur for small adjustments in stem position.

• Therefore, an equal percentage valve exhibits high sensitivity at high flow rates.

Step 4: Final Answer:
An equal percentage valve has high sensitivity at high flow rates.