If a pump’s theoretical manometric head is 30 metres and its measured head is 27 metres, what is its manometric efficiency?

Explanation:

To determine the manometric efficiency of the pump, we need to use the formula for manometric efficiency ( $\eta_m$ ). The manometric efficiency is defined as the ratio of the measured manometric head to the theoretical manometric head.

The formula for manometric efficiency is given by:

$\eta_m = \frac{\text{Measured Manometric Head}}{\text{Theoretical Manometric Head}}$

In this case, the theoretical manometric head is 30 meters, and the measured head is 27 meters.

Substituting these values into the formula, we get:

$\eta_m = \frac{27 \, \text{meters}}{30 \, \text{meters}}$

$\eta_m = \frac{27}{30}$

$\eta_m = 0.9$

Therefore, the manometric efficiency of the pump is 0.9 or 90%, which corresponds to option 3.

Now, let's analyze the other options to understand why they are incorrect:

• Option 1: 0.75 - This value would be obtained if the measured head was 22.5 meters (0.75 × 30 meters), which is not the case here.
• Option 2: 0.85 - This value would be obtained if the measured head was 25.5 meters (0.85 × 30 meters), which is not the case here.
• Option 4: 0.8 - This value would be obtained if the measured head was 24 meters (0.8 × 30 meters), which is not the case here.

All these options do not match the given data, which indicates that the correct answer is indeed option 3.

Important Information:

Understanding manometric efficiency is crucial for evaluating the performance of pumps. Manometric efficiency helps in determining how effectively a pump converts the energy supplied to it into useful work. High manometric efficiency indicates that the pump is effectively converting the input energy into the desired output in terms of head, while low manometric efficiency suggests energy losses within the pump system. The efficiency can be impacted by various factors such as mechanical losses, hydraulic losses, and leakage, which need to be minimized to ensure optimal pump performance. Regular maintenance and proper design can help in achieving and maintaining high manometric efficiency.