This set of Distillation Design Quiz focuses on “Numerical Method – Newton Raphson Method”.
1. In matrix language, The Newton Raphson equation is
a) Ji Yif = -Fk
b) Ji Xif = -Fk
c) Ji Kif = -Fk
d) Ji Tif = -Fk
Explanation: In matrix language, The Newton Raphson equation is Ji Xif = -Fk,, here i represents the number of gas rows and j similarly columns of liquid.
2. What is Fk?
Explanation: As Fk= (f1 f2 f3 ……fn)T, Fk is Vector , Matrix and Factor are correlated by an empirical correlation of total functions and temperature.
3. A square nXn matrix is called
a) Jacobin Matrix
b) Raphson Matrix
c) Newton Matrix
d) 2N Matrix
Explanation: A square n X n matrix is called Jacobin Matrix, where the number of row properties are equal to number of column properties.
4. For any instance, XK+1 is
a) Xk + h
b) Xk + t
c) Xk + X
d) Xk + X1
Explanation: For any instance XK+1 is Xk + h, where h is the common difference and Xk is the previous calculated value of series.
5. Independent variable are in the range of
a) Tmin< Tj > Tmax
b) Tmin> Tj > Tmax
c) Tmin< Tj > Tmax
d) Tj < Tmax
Explanation: Independent variable are in the range of Tmin < Tj < Tmax, i.e. the maximum temperature should be less than initial and greater than the final temperature.
6. In quasi Newton Method, Sk represents the
a) Vector factor
b) Scalar factor
c) Separation factor
d) Correction factor
Explanation: In quasi Newton Method, Sk represents the Scalar factor, while function quantiles such as temperature and pressure relations are called as vector ones.
7. Solve cos x = 2x?
Explanation: Solving f(x) = 0 then f(x) = cos x − 2x, x0 = 0.5, x1 = 0.45063, x2 = 0.45018, x3 = 0.45018, the root is x = 0.45018.
8. Find XK+1? If Xk = 0.5, consider a difference of 5 stages
d) Can’t be calculated
Explanation: For XK+1 = Xk + h = 0.5+ 5 = 5.5.
9. The first assumption of the NR Method is
a) Assume K=0
b) Assume Xi = 0
c) Assume F(x) = 0
d) Assume F’(x) = 0
Explanation: The first assumption of the NR Method is assume K=0, as we assume k=0, then we calculate F(x) = 0 and then F’(x) = 0.
10. Jacobin equation is solved using the
a) Matrix Multiplication
b) LU Factorization
c) Elimination Method
d) Follow up method
Explanation: Jacobin equation is solved using the LU Factorization method, where we eliminate the lower and upper triangle matrix resulting in a singular matrix.
Sanfoundry Global Education & Learning Series – Distillation Design.
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