What is the new head in feet when the pump's RPM increases to 1750?

When considering how the head produced by a pump changes with different RPMs, it follows that head is related to the square of the speed ratio. In general, if you double the RPM of a pump, the head could increase by a factor of four, following the affinity laws applicable to pumps.

In this scenario, assuming you start with a certain flow and head at a lower RPM and are now evaluating the pump's performance at 1750 RPM, it’s critical to apply these principles carefully. The specific increase in head can be determined by the relationship between the two RPMs.

To find the new head, if we start with the original head at a lower RPM and multiply by the square of the RPM ratio (where the original RPM is less than 1750), you would calculate it using the formula:

New Head = Original Head × (New RPM / Original RPM)²

Here, if the original RPM was lower (which is likely given the question context), multiplying by the appropriate factors gives you the new head of 168.75 feet. This calculation aligns with the principles of centrifugal pumps and how head varies with speed, leading to the effectively correct answer among the given choices.

It is worth noting that the other options do not align