Engineering Answers

9)Find Laurent series expansion of the function 1/ z²+z-6 in the regions

1<|z-1 <4 and |z-1|> 4.

8)Show that u(x, y) = 4y + 3x²y-y³ is harmonic and find its conjugate harmonic function v(x, y).

7) Show that the function f(z)={(z̅ )^2,Z≠0. ; 0,Z=0 satisfies Cauchy-Rieman equations at z=0.Does f'(0) exists?

3) Find Laplace transform of the function f(t)={t, 0≤t<1 ; 2-t,1≤t≤2 and f(t+2)=f(t)

2. What is “preset” during installation of bridge bearings?

6. Sometimes the side of concrete bridges is observed to turn black in colour. What is the reason for this phenomenon?

17. When branch pipelines are connected to main pipelines, sometimes Y-junctions or fitting branched pipelines to main pipelines by formation of holes in main pipelines are used. Which one is a better choice?

19. What is the purpose of carrying out water absorption test for precast concrete pipes?

1. In soil compaction test, if a test result exceeds 100%, should engineers accept the result?

The ratio of specific heats is k=Cp/Cv=R, a constant. Combine these two expressions and show that Cv=R/(k-1) and Cp=kR/(k-1)