Using Cubic Splines to Determine Characteristics and Efficiency of a Pump
By D.M. Griffin, Jr.
About this worksheet:
Determines a pump operation point in terms of head and discharge, operation efficiency, suitability of a selected pump, and input horsepower to the pump
Example of a pump system, applicable to civil engineers, environmental engineers, etc.
Performs cubic splines, conservation of mechanical engergy between water surfaces in tanks, Darcy-Weisbach equation, final system head curve equation, plotting, efficiency, etc.
This worksheet provides you with an example of a problem where you need to determine a pipe operation point in terms of head and discharge, operation efficiency, suitability of the pump chosen, and input horsepower to the pump. This worksheet also provides you with an example of PTC Mathcad's ability to work with data initially stored in Excel and exported into a PTC Mathcad worksheet. This worksheet also shows you how to obtain smooth curves by using cubic splines for each curve. Cspline is a function in Mathcad that you can use to create cubic splines to pass a smooth curve through data points.
The next section of the worksheet defines the system parameters which include the length of pipe, elevation of point 1 and 2, conservation of mechanical energy between water surfaces in tanks, pressure head terms, velocity, friction, and minor losses. You can also calculate the pipe friction using the Darcy-Weisbach equation. The worksheet shows you how to calculate for minor loss constants for system elements more specifically by defining Tee, check valve, exit, and entrance. You are also shown how to calculate the final system head curve equation.
The curves are then plotted for the operating characteristics which include:
Pump characteristics data
Power data points
Efficiency data points
System head curve
Operating point of pump
From there, you are shown how to evaluate the maximum efficiency and the input_hp. This worksheet shows you how you might also summarize the data you have obtained from this type of problem and concludes that the system head intersects the middle of the pump characteristic which is good. The pump efficiency ends up being 76% and the point of maximal efficiency is 87%.
This worksheet provides you with step by step notation and calculation for this problem. All formulas, data, images, graphs, solutions, and summaries are included to aid and guide you through your own calculation process.