50°F water is being pumped from a reservoir to an upper tank whose surface is 100 feet higher. Both surfaces are open to the atmosphere. The system will be operated in Leadville, Colorado where g 32.12 ft/s². The system consists of the following: 800 feet of 3-nom sch 40 commercial steel pipe. An inward projecting entrance. A projecting exit. Six 90° standard flanged elbows. Four straight-through 0° gate valves. Two swing check valves. 7-in. Bell & Gossett Series 1531 1½AC centrifugal pump. A 3500 rpm impeller speed was originally selected because the system would operate very close to the point of peak efficiency while delivering approximately 210 gpm. The following pages include the pump performance curve for the 7-in. Bell & Gossett Series 1531 1½AC pump operating at an impeller speed of 3500 rpm, and a table with values of the pump head delivered versus the flow rate when the 7-in. pump is operated at 3500 rpm. Create a MATLAB program that will use Newton’s method to find the volume rate of flow in the pipe when the valves are fully-open and a 7-inch Bell & Gossett Series 1531 2AC is being used to pump 50°F water from the reservoir to the tank. The MATLAB program will only be used for problems in US units where water will be pumped from a lower reservoir to a higher reservoir. There will always be an inwardly projecting entrance, a projecting exit, 90° standard flanged elbows, straight-through 0° gate valves, and swing check valves. Commercial steel pipe will always be used. Notes about the MATLAB program that will be created: The input will be values of the pipe’s inside diameter in inches, the pipe length in feet, the elevation difference of the reservoirs in feet, the number of elbows, the number of gate valves, the number of swing check valves, the gravitational acceleration g in ft/s², the density of the liquid in lbm/ft³, the viscosity of the liquid in lbm/ft-h, and the pump’s impeller speed in rpm. Use a MATLAB function to evaluate the total head loss in the pipe. Use the Swamee-Jain friction factor and the Hooper 2K method to compute the minor loss coefficients. Assume K will always include the coefficients for an inwardlyprojecting entrance and a pipe exit. The MATLAB function’s arguments will include the following: 1) The volume rate of flow in cubic feet per second (ft³/s) 2) The pipe’s inside diameter in feet 3) The length of the pipe in feet 4) The density of the water in slug/ft³ 5) The viscosity of the water in slug/ft-s 6) The gravitational acceleration in ft/s² 7) The number of elbows 8) The number of straight-through 0° gate valves 9) The number of swing check valves Use a MATLAB function to determine the head added by the pump. The MATLAB function’s argument will include: 1) The pump’s impeller speed in rpm 2) The volume rate of flow through the pump in gallons per minute (gpm) The program will need an initial estimate for the flow rate in the pipe. Examine the pump curve and pick something sensible, but don’t pick the answer! Use MATLAB program to find the flow rate in the system, in gpm, when the valves are fully open and the impeller speed is (a) 3500 rpm and (b) 3200 rpm. Submit PDF copies of your answer, the MATLAB program (including any MATLAB functions you created), and the MATLAB m-files themselves.
50°F water is being pumped from a reservoir to an upper tank whose surface is 100 feet higher. Both surfaces are open to the atmosphere. The system will be operated in Leadville, Colorado where g 32.12 ft/s². The system consists of the following: 800 feet of 3-nom sch 40 commercial steel pipe. An inward projecting entrance. A projecting exit. Six 90° standard flanged elbows. Four straight-through 0° gate valves. Two swing check valves. 7-in. Bell & Gossett Series 1531 1½AC centrifugal pump. A 3500 rpm impeller speed was originally selected because the system would operate very close to the point of peak efficiency while delivering approximately 210 gpm. The following pages include the pump performance curve for the 7-in. Bell & Gossett Series 1531 1½AC pump operating at an impeller speed of 3500 rpm, and a table with values of the pump head delivered versus the flow rate when the 7-in. pump is operated at 3500 rpm. Create a MATLAB program that will use Newton’s method to find the impeller speed needed to generate a 180 gpm volume rate of flow in the pipe when the valves are fullyopen and a 7-inch Bell & Gossett Series 1531 2AC is being used to pump 50°F water from the reservoir to the tank. The MATLAB program will only be used for problems in US units where water will be pumped from a lower reservoir to a higher reservoir. There will always be an inwardly projecting entrance, a projecting exit, 90° standard flanged elbows, straight-through 0° gate valves, and swing check valves. Commercial steel pipe will always be used. Notes about the MATLAB program that will be created: The input will be values of the pipe’s inside diameter in inches, the pipe length in feet, the elevation difference of the reservoirs in feet, the number of elbows, the number of gate valves, the number of swing check valves, the gravitational acceleration g in ft/s², the density of the liquid in lbm/ft³, the viscosity of the liquid in lbm/ft-h, and the volume rate of flow in gpm. Use a MATLAB function to evaluate the total head loss in the pipe. Use the Swamee-Jain friction factor and the Hooper 2K method to compute the minor loss coefficients. Assume K will always include the coefficients for an inwardlyprojecting entrance and a pipe exit. The MATLAB function’s arguments will include the following: 1) The volume rate of flow in cubic feet per second (ft³/s) 2) The pipe’s inside diameter in feet 3) The length of the pipe in feet 4) The density of the water in slug/ft³ 5) The viscosity of the water in slug/ft-s 6) The gravitational acceleration in ft/s² 7) The number of elbows 8) The number of straight-through 0° gate valves 9) The number of swing check valves Use a MATLAB function to determine the head (in feet) added by the pump at a specified volume rate of flow and impeller speed. The MATLAB function’s argument will include: 1) The pump’s impeller speed in rpm 2) The volume rate of flow through the pump in gallons per minute (gpm) The program will need an initial estimate for the impeller speed: just use 3500 rpm. Use MATLAB program to find the impeller speed needed, in rpm, when the valves are fully open and the desired volume rate of flow is 180 gpm. Submit PDF copies of your answer, the MATLAB program (including any MATLAB functions you created), and the MATLAB m-files themselves.