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

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

Explain briefly step by step process?




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


Explain briefly step by step process?


(i) Find the charge in the volume defined by 0 < y < 2 and 0 < z < 2 , if theVolume charge density is rho_{v} = 60y * z ^ 2 * mu * C / (m ^ 3)
Verify the Stokes's theorem for the following vector F=2 rho z hat a rho +; 3z sin varphi hat a varphi -4 rho cos p hat a z over the range z = 1 , 0< p < 2, 0 < varphi < 45 degrees .

Velocity profile of a liquid is shown below:

                                                

If the shear stress per unit surface area on the rigid plate over which the liquid flows is measured to be 0.083 N/m2.

1.    Calculate the viscosity of the liquid .

2.    What is the maximum velocity at the free surface if the plate is tilted by an angle of 60o to the horizontal plane and the liquid is allowed to down freely keeping the same film thickness? There is no pressure gradient in the direction of flow. Density of the liquid is 887 kg/m3.





Heat is flowing through an annular wall of inside radius ‘Ri’ and outside radius ‘Ro’. The thermal conductivity varies linearly with the temperature from ki at Ti and ko at To. Find the temperature profile and develop an expression for the heat flow through the wall at r = Ro


1. Under what situation shall engineers use jacking at one end only and from both
ends in prestressing work?
3. In incremental launching method of bridge construction, what are the measures
adopted to enhance sufficient resistance of the superstructure during the launching
process?
4. In bridge widening projects, the method of stitching is normally employed for
connecting existing deck to the new deck. What are the problems associated with this
method in terms of shrinkage of concrete?

15. What are the three major types of reinforcement used in prestressing?


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