A Bell & Gossett Series e-1531 end-suction pump is to be selected for the system shown in Figure P4.42. The system is designed to move water at 60°F from the lower tank to the upper tank. The system must deliver a minimum of 500 gpm of water from the lower tank to the upper tank when the pump is operating. A tilting disc check valve (α = 5°) is used to prevent the water from flowing backward when the pump is shut off. The total length of straight pipe in this system is 150 ft. The pipe is 4-nom sch 40 commercial steel.
a. Plot the system curve up to 800 gpm.
b. Select a Series e-1531 Bell & Gossett pump for this system.
c. What is the operating point of the pump/pipe system based on the pump you selected in (b)? Specify the capacity (gpm), head (ft), brake horsepower input to the pump (hp), and efficiency of the pump.
The Correct Answer and Explanation is :
To answer your query, I’ll break it down into each part and provide a detailed explanation.
a. Plotting the System Curve (up to 800 GPM)
The system curve represents the relationship between flow rate (GPM) and the head (feet) that a pump must overcome at that flow rate. It is typically plotted by considering the system’s characteristics, such as pipe length, pipe diameter, and the presence of fittings like valves.
To plot the system curve, we need the following parameters:
- Flow Rate (Q): GPM (Gallons per minute) values up to 800 GPM
- Head Loss (H): Calculated using Darcy-Weisbach equation, considering pipe friction losses, static head (difference in height between the tanks), and losses through fittings (including the check valve).
The total head loss in the system is the sum of:
- Static head: The vertical distance between the two tanks, which is constant.
- Friction losses in the pipes, which vary with flow rate and depend on pipe diameter, length, and roughness.
- Minor losses through fittings, like the tilting disc check valve.
To calculate the friction head loss, we can use the Darcy-Weisbach equation for pipe flow, and the loss due to the check valve can be approximated by using standard loss coefficients. Based on the provided pipe size (4-inch, schedule 40 steel pipe), we can apply the appropriate formulas to generate a curve for the system.
Once the head at different flow rates (from 0 to 800 GPM) is calculated, the system curve can be plotted.
b. Selecting the Series e-1531 Bell & Gossett Pump
The Bell & Gossett Series e-1531 end-suction pump should be selected based on its performance curve, which provides the head-capacity relationship for the pump. To select a pump, we match the flow rate of 500 GPM (minimum required flow) with the system curve. The selected pump should provide the required flow and head at the operating point while ensuring it meets the minimum required head to overcome the system’s losses.
We also need to ensure that the selected pump can handle the system’s total head and is efficient at the operating point.
The required parameters for the pump selection would include:
- Flow rate: At least 500 GPM (but consider checking performance for up to 800 GPM)
- Head: The total head the pump needs to overcome (combination of static head, friction losses, and minor losses)
- Horsepower: The brake horsepower input needed for the selected pump at the required flow and head.
c. Operating Point of the Pump/pipe System
Once the pump is selected, the operating point corresponds to the intersection of the system curve and the pump curve. At this intersection, you can determine:
- Capacity (GPM): The flow rate at which the pump operates, typically close to 500 GPM, depending on the system.
- Head (ft): The head the pump operates at, given by the system curve.
- Brake Horsepower (BHP): This is the power input to the pump, which can be calculated from the pump’s performance curve at the operating point.
- Efficiency: This is the pump’s efficiency at the operating point, typically available from the pump’s performance data.
The operating point gives the system’s real-world performance, and it should be within the operational limits of the pump. Based on the pump curve, you will select the point where the head meets the system’s requirements while keeping efficiency and power usage in mind.
Since I cannot access a live system curve or specific pump curve, I suggest using the manufacturer’s pump performance chart to cross-reference with your calculated system curve.