A pumping system with two different static lifts is shown....

A pumping system with two different static lifts is shown. Each reservoir is supplied by a line consisting of $1000 \mathrm{ft}$ of 6 -in. cast-iron pipe. Evaluate and plot the system head versus flow curve. Explain what happens when the pump head is less than the height of the upper reservoir. Calculate the flow rate delivered at a pump head of 85 ft.

Key Concepts

Pump Performance Curve

The pump performance curve shows the relationship between the head the pump can generate and the corresponding flow rate delivered. This curve is crucial for system design as its intersection with the system head curve determines the operating point of the pump. It indicates how the pump will perform under various load conditions.

Friction Loss in Piping

Friction loss refers to the energy loss due to friction as the fluid flows through the pipe. This loss is influenced by factors such as pipe length, diameter, material roughness, and flow velocity. In pump system analysis, these losses are typically represented by a term that increases with the square of the flow rate, and they are added to the static head to form the total required head.

Pump Operating Conditions and Shutoff

The operating condition of the pump is determined by where its performance curve intersects with the system head curve. When the pump head is less than the static head (that is, the elevation difference), no flow can occur because the pump lacks the necessary energy to overcome the gravitational potential of the upper reservoir. This situation effectively represents a shutoff condition or no flow scenario, highlighting the importance of meeting the minimum head requirements to ensure proper operation.

System Head Curve

The system head curve is a graphical representation that relates the total head required by the system to the flow rate. It includes constant elevation components (static head) and variable losses such as friction loss in the pipes. This curve is essential in matching the pump’s performance characteristics with the demands of the system to determine the operating point.

Static Lift

Static lift is the vertical distance that the pump must overcome to raise the fluid from a lower reservoir to a higher one. It establishes a baseline head requirement regardless of flow, and if the pump’s head is less than this required elevation difference, the system will not be able to deliver fluid to the upper reservoir.

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