Milling Journal - Q4 2008 - (Page 31) • 1,250=14X + 950 – 9.5X • 1,250-950=14X - 9.5X • 300=4.5X • 300/4.5=X=66.67 • X=66.67 % of wheat A • 100-66.67=33.33% wheat B of mixture. Proportion reflects the part per one unit of the mixture. For many people it seems easy to interchange one for the other. For example, 20 units out of 100 is 20% or a 0.20 proportion. Notice the values differ by a factor of 100. Identify Known and Unknowns • The proportion contained in the mixture is 1.00. • X = proportion of wheat A in the mixture • (1-X) = proportion of wheat B in the mixture Develop an Equation Using the Blending Formula in Figure 1, complete the equation using the known information forming a single equation with one unknown. 1*12.5=14X + 9.5*(1-X) QM*AM = Q1*A1 + Q2*A2 Solve for X: This I’ll leave to you. Conclusion Understanding the solution to the simple blending problem can aid in dealing with many problems from blending wheat to blending flour and properly blend off grade flour to the proper protein or ash level. It is also the beginning step needed in the understanding and development of cumulative ash curves used to monitor mill and wheat performance. Best of luck with your blending challenges! Dr. Jeff Gwirtz is CEO of JAG Services Inc., an international milling consulting company based in Manhattan, KS. He is also an associate professor in the Department of Grain Science and Industry at Kansas State University, also in Manhattan. He can be reached at 785341-2371 or jeff@ jagsi.com. “Understanding the simple blending problem solution can aid in dealing with many problems from blending flour and properly blend off grade flour to the proper protein or ash level.” Check Your Answer Our calculation indicates that 66.67% of the mixture is wheat A, with a protein content of 14%. The remainder of the mixture or 33.33% of the mixture is wheat B with a protein content of 9.5%. Once again using the formula in Figure 1, calculate the units of protein contributed by each wheat (QN*AN) divided by the total units of product, which in this case is 100. • (Q1*A1) = 66.67*14 • (Q2*A2) = 33.33*9.5 = 316.64 • (QN*AN) = 1,250.0–933.38 = 316.62 • Q 100 = 66.67 + 33.33 • (QN*AN)/ ÓQ = 1,250/100 = 12.50% Another Solution Instead of using percentage in the calculation you may use proportions. The end result is not any different, as long as you keep the units aligned and uniform within the problem. A percent as used in the calculation above reflects the parts contributed by each material per 100 parts Response No. 311 MILLING JOURNAL Fourth Quarter 2008 31 http://www.vortexvalves.com http://www.vortexvalves.com
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