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
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
, 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