Exercise

The pressure$-$viscosity relationship of a given gas is given as:

$\backslash$table$[[$P$,$ psi,$400,800,1200,1600,2000,2400],[,cp,0\mathrm{.}0117,0\mathrm{.}0125,0\mathrm{.}0132,0\mathrm{.}0146,0\mathrm{.}0163,0\mathrm{.}0180]]$

a$)$ Using the data, prepare a finite difference table

b$)$ Using a second degree polynomial that satisfies the constraints at $400,800,$ and $1200,$ calculate the viscosity at $1000$ and the error

c$)$ Using a second degree polynomial that satisfies the constraints at $1600,2000,$ and $2400,$ calculate the viscosity at $1000$ and the error

d$)$ Which of the calculated values is more accurate. Explain