HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 221

The result is 0.149836.., i.e., y = 0.149836. • It is known, however, that there are actually two solutions available for y in the specific energy equation. The solution we just found corresponds to a numerical solution with an initial value of 0 (the default value for y, i.e., whenever the solution field is empty, the initial value is zero). To find the other solution, we need to enter a larger value of y, say 15, highlight the y input field and solve for y once more: The result is now 9.99990, i.e., y = 9.99990 ft. This example illustrates the use of auxiliary variables to write complicated equations. When NUM.SLV is activated, the substitutions implied by the auxiliary variables are implemented, and the input screen for the equation provides input field for the primitive or fundamental variables resulting from the substitutions. The example also illustrates an equation that has more than one solution, and how choosing the initial guess for the solution may produce those different solutions. In the next example we will use the DARCY function for finding friction factors in pipelines. Thus, we define the function in the following frame. Special function for pipe flow: DARCY (ε/D,Re) The Darcy-Weisbach equation is used to calculate the energy loss (per unit weight), hf, in a pipe flow through a pipe of diameter D, absolute roughness ε, and length L, when the flow velocity in the pipe is V. The equation is Page 6-20