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P9: SEWAGE FOR CIVILS
(MATLAB functions, plotting
You have been asked to design a pump for pumping treated effluent at a sewage treatment facility. The pump must remove the effluent at the fastest rate possible without causing a pipe to burst or overflowing the effluent handling tank. The motor that y9ou are using runs at 60 rpm. The piston head is 6 inches in diameter. Given this, select r so the average output of the pump is no larger than 420 in3/s due to the speed at which the effluent can be handled. Exceeding this value will overflow the tank. Also select l so that the instantaneous velocity of the flow is not more than 1400 in3/s or the pipe will burst due to excess pressure.
The piston used has a diameter of 6 in. The average flow rate of the pump is the area of the piston multiplied by the distance it travels, 2*r, given by the equation
ave_flow = piston_area*2*r.
To determine the value of r, plug in the maximum allowed average flow and the piston area. Then solve for r. The solution should be rounded down to a half inch increment. For example, 4.9 would be rounded to 4.5. The rounding can be hand coded if needed.
The equations you will need to solve the problem are listed below. Note that ω is the angular velocity of the shaft, t is the current time, and x is the displacement of the piston.
To determine the value of l, test four values. The first value should be at least 0.5 inches larger than r and should be increased by increments of 2.0 inches. For each value of l, plot the flow rate as a function of time for one rotation of the pump. Each of the plots should appear in the same figure on the same axis. The plot must contain axis labels with units, title, and a legend. Use visual inspection of the plot to select the value of l that will not exceed the maximum instantaneous flow rate.
Diagram of the pump.
There should be three files for this problem. Two should contain functions. The other should have a script that accomplishes all the tasks given below.
1. Given the information above, determine r.
2. Create a plot to determine the smallest l that can be used without exceeding the maximum instantaneous flow rate. The plot must contain the flow rate for four different values of l. It also must contain axis labels with units, title, and a legend.
3. Use the selected values to generate plots of the position and velocity of the piston every 0.01 seconds over one rotation of the shaft. The plot must contain axis labels with units and a title. These plots should appear in different figures.