Correct Answer: D. 250 GPM
This is a very common problem experienced in the field.
All of the data you require to compute where the pump is on its curve is given.
The problem states the pump is new, the clearances are set correctly and the system is not forcing the pump to operate off of its curve.
You can therefore expect that the pump will be operating on its curve within a few percent accuracy.
There is extraneous data provided, just like in real life that might help solve other problems,
but all we need in this case is the differential pressure across the pump.
This wise customer has installed both suction and discharge gauges. The gauges are new and so they should be fairly accurate.
The gauges are installed at almost the same elevation as the pump so there is no need to compensate for elevation differences.
The differential pressure is discharge pressure minus suction pressure (70.6 – 10 = 60.6 psig.)
To convert the pressure to head you need to multiply the differential pressure by 2.31 and divide by the Specific Gravity (SG).
This calculation should yield 126.9 feet, which we will round off to 127 feet.
Given a head of 127 feet, we enter the given curve on the Y axis (Head) and draw a line perpendicular to the Y axis at that point.
This horizontal line then crosses/intersects the pump’s head flow performance curve based on a 13 inch impeller.
Then: Draw a line perpendicular to the X axis (Flow axis) from the intersection point of the head curve.
That vertical line crosses the flow axis (X) at around 248 GPM, give or take a few GPM.
The flow of 248 GPM is closest to answer D which is 250 GPM.
If you did not compensate for the SG you would have calculated the head at 140 feet which would yield a flow of 200 GPM.
If you had simply taken the discharge pressure and not the differential pressure you have calculated 163 feet which yields shut off head.
If you had used only the discharge pressure, but did compensate for SG you have come up with 147 feet head which would yield 170 GPM.