Question

Pressure head characteristic of a mine fan and a mine characteristic curves are shown in the figure below: 

Match the points with their corresponding nomenclatures

• A. P = 1, Q \(\rightarrow\) 2, R \(\rightarrow\) 3
• B. P = 2, Q \(\rightarrow\) 3, R \(\rightarrow\) 1
• C. P = 3, Q \(\rightarrow\) 1, R \(\rightarrow\) 2
• D. P = 1, Q \(\rightarrow\) 3, R \(\rightarrow\) 2

Hint:

In fan curves, always remember that the stall point corresponds to the lowest flow, the operating point is where the fan is working optimally, and the shut-off head corresponds to the highest head with zero flow.

Answer 1

The Correct Option is C

The problem involves understanding the characteristics of a mine fan in relation to its operating point, stall point, and theoretical shut-off head. These points are typically identified from the fan curve. 
Step 1: Understanding the nomenclature. 
\( P \) represents the stall point, which is the point at which the fan no longer produces any pressure or head. At this point, the quantity of air flow is zero.
\( Q \) represents the operating point, which is the point where the fan is operating under normal conditions, with both pressure and flow rate.
\( R \) represents the theoretical shut-off head, which is the head corresponding to zero flow. This point typically occurs at the extreme right of the fan characteristic curve.
Step 2: Analyzing the graph. 
Point \( P \) is where the fan curve intersects the horizontal axis, indicating zero flow (stall point).
Point \( Q \) is where the fan is operating normally, showing the maximum head for a given flow (operating point).
Point \( R \) is where the curve reaches the highest head value corresponding to zero flow (shut-off head).
Conclusion: The points match as follows: \( P = 3 \), \( Q \rightarrow 1 \), \( R \rightarrow 2 \).