Page 210 - Excel for Scientists and Engineers: Numerical Methods

CHAPTER 8 ROOTS OF EOUATIONS 187

makes the expression have a value of 0.288, and calculate the concentrations
of A, B and C at equilibrium.

9. For the gas-phase chemical reaction
A + B + C +2D
the equilibrium constant expression for reaction is

K= [c1[D12 = 15.9 atm at 400°C.
[A1 [Bl
A reaction mixture is prepared in which the initial concentrations are [A] = 1
atm, [B] = 2 atm, [C] = 0, [Dl = 0. From mass balance and stoichiometry,
the concentrations at equilibrium are [A] = 1 - x, [B] = 2 - x, [C] = x, [D] =
4x 3
2x, from which the expression for K is . Find the value of x that
X’ -3xi-2
makes the expression have a value of 15.9, and calculate the partial pressures
of A, B, C and D at equilibrium.

10. The Reynolds number is a dimensionless quantity used in calculations of
fluid flow in pipes. The Reynolds number is defined as

where Di is the inside diameter of the pipe, V is the average velocity of the
fluid in the pipe, p is the fluid density and p is the absolute viscosity of the
fluid. For flow in pipes, a Reynolds number of less than 2000 indicates that
the flow is laminar, while a value of greater than 10,000 indicates that the
flow is turbulent. For a pipe diameter of 5 cm, and fluid of density 1 g/cm3
and viscosity of 1 centipoise, find the minimum velocity that results in
turbulent flow.

1 1. Find the value of the (1,l) element of the following matrix that gives a
determinant value of zero.
0.75 0.5 0.25

[ 0.5 1 0.51
0.25 0.5 0.75
Which elements in the matrix cannot be changed in order to give a
determinant of zero?

12. Use the Bairstow custom function to find all of the roots of the polynomial