applied numerical analysis.pptx

7/29/2019 APPLIED NUMERICAL ANALYSIS.pptx

http://slidepdf.com/reader/full/applied-numerical-analysispptx 1/12

APPLIED NUMERICAL ANALYSIS

BATCH 10



PROBLEM 1



SOLUTION

(a) Finding out the entropy corresponding to a specific

volume of 0.108 using Linear Interpolation



SOLUTION

(b) Using Quadratic Interpolation

x0 = 0.10377

x1 = 0.11144

x2 = 0.1254

f(x0) = 6.4147

f(x1) = 6.5453f(x2) = 6.7664



SOLUTION

b1 = 17.027394b0 = 6.4147

b2 = -54.98245573



SOLUTION

Substituting b0, b1, b2, x0, x1 and x2,

f 2(x) = 6.4147 + 17.0273794(x-0.10377)

– 54.98245573(x-0.10377)(x-0.11144)

where x = 0.108

f 2(0.108) = 6.487525876 kJ / kg Kwhich is the entropy



SOLUTION

(c) Finding out the specific volume corresponding toan entropy of 6.6 kJ / kg K using InverseInterpolation

Substituting f 2(x) = 6.6 in the formula derived usingQuadratic Interpolation

f 2(x) = 6.4147 + 17.0273794(x-0.10377)

– 54.98245573(x-0.10377)(x-0.11144)



SOLUTION

We get, x = 0.1147707903 which is the specificvolume

Substituting f 1(x) = 6.6 in the formula derived forlinear interpolation,

We get, x = 0.1162393607 which is the specificvolume



PROBLEM 2

During a survey, you are required to compute the area of the

field shown in figure. Use Simpson’s rules to determine the area.



SOLUTION

DISTANCE (NORTH TO SOUTH) ORDINATE (WEST TO EAST)

0 0

200 600

400 880

600 950

800 1100

1000 1600

1200 1900

1400 21001600 2300

1800 2600

2000 2950

2200 3150



SOLUTION

DISTANCE (NORTH TO SOUTH) ORDINATE (WEST TO EAST)

2400 3200

2600 3200

2800 3150

3000 3000

3200 2800

3400 2700

3600 2600

3800 25254000 2525

4200 2430



SOLUTION

Use Simpson’s 1/3 rd rule for the first 18 segments and Simpson’s 3/8the rule for the remaining 3 segments.

Area1 = (3600 – 0) [0 +4(600+950+1600+2100+2600+3150+3200+3000+2700) +

2(880+1100+1900+2300+2950+3200+3150+2800+2600)]/4 =7917333.333 sq. ft

Area2 = (4200 – 3600)[2600+3(2525+2525)+2430]/8

= 1513500 sq. ft

Total = 9430833 sq. ft

applied numerical analysis.pptx

Documents