l.
For a two-dimensional irrotational flow in the x-y plane, the velocity component in the x-direction is given by vx -x. Obtain expressions for the stream function (sye)u and the velocity potential (phy)q if it is given that sye(u) 0 for y and phy 0 at the origin. What type of flow pattern is represented by this

A reinforced concrete rectangular section of size 300 mm x 600 mm (effective) is reinforced with 4 bars of 20 mm dia on the tension side. Determine the safe uniformly distributed load that the beam can carry over a simply supported effective span of 8 m. The grade of concrete and steel used are M 20 and Fe 415 respectively. For the given environmental exposure, the effective cover to reinforcement is 50 mm.

For the system shown in Figure a small block of mass m and a smooth irregular shaped block of mass both free to move, are placed on a smooth horizontal plane. Find the minimum velocity to be imparted to the smaller block so that it reaches the highest point of the larger block.

src='./qimages/7929-1c.jpg'>
Figure

Draw the Bending Moment diagram for the CD portion only for the beam shown in Figure

src='./qimages/7929-1d.jpg'>

Figure
An excavation is made in a soil whose porosity is 30% and the specific gravity of soil solids 2.6. A 1·5 m thick layer of this soil is subjected to an upward seepage head of 2·0 m. Find out what factor of safety exists against the piping (boiling). If a factor of safety of 2 is needed against the piping, what depth of gravel is required to be placed above the soil layer 1 Assume the unit weight of gravel to be the same as that of the soil and negligible loss of head in the gravel layer.

2.
Check the stability requirements for a cantilever type retaining wall of the dimensions as shown in Figure to retain the levelled earth for a height of 4 m above G.L. The safe bearing capacity of soil available at a depth of 1·2 m below the G.L. is 165kN/m2.The angle of repose of soils 30° and the coefficient of friction between the soil and concrete is 0.52. The unit weight of the soil is 18 kN/m3.


src='./qimages/7929-2a.jpg'>



The details of the subsoil conditions at a site are shown in Fig together with the details of the soil properties. The ground water level is 1.2 m below the upper surface of the silt. It can be assumed that the gravel has a degree of saturation of 50% and that the silt layer is fully saturated. plot the total vertical stress, neutral stress(pore pressure and effective vertical stress over the entire depth of subsoil up to the rock layer.Also, determine the effective vertical stress at a point 1.0 m above the rock layer.

src='./qimages/7929-2b.jpg'>

A square foundation has to be constructed on a thick deposit of uniform cohesionless soil with angle of internal friction, phy =34°. The depth of foundation is 1·2 m. The water table is at a great depth and its effect can be neglected. The allowable design load of the footing with a factor of safety of 3 is 700 kN. Determine the size of the foundation. Given phy Nc =52.6, Nq =36·5 and Ny =37.0 and unit weight of soil, Y=18 kN/m3.

3.
Two moving loads of 100 kN each are moving from left to right on the truss shown in Figure Calculate the maximum load in member BG due.to the moving loads.


src='./qimages/7929-3a.jpg'>

Figure

A reinforced concrete beam of rectangular section has a width of 230 mm and an effective depth of 500 mm. The effective covers to tension and compression reinforcements are 40 mm and 30 mm respectively. The
beam is reinforced with 3 bars of 20 mm dia in tension and 3 bars of 16 mm dia in compression. Find the limiting moment carrying capacity of the beam. The grade of concrete used is M 20 and steel grade is Fe 415.

Steady, two-dimensional, fully developed laminar flow of a fluid (mass density dynamic viscosity) is taking place on an infinite plate inclined at an angle of 30 degrees from the horizontal. The thickness of the fluid layer is h and the top surface has atmospheric pressure. Obtain an expression for the average flow velocity in the direction of flow.

4.
Water flows through a 1.0 m diameter pipe which has a roughness height, of 0.1 mm. What will be the maximum possible flow rate if the head loss is to be limited to 5 m per km Use the following equation for the friction factor
0.25
f
log10(e/3.7D+5.7/R power 0.9)

A submarine is travelling at a large depth in the sea (seawater p =1030 kg/m3 coefficient(Mu)= 1·15 x 10-3 with a speed of 5 m/s. It is
desired to estimate the drag force on the submarine by conducting experiments in a freshwater tank on a scaled model of the submarine. If the length scale is 1 25, what should be the speed in the model If the drag force on the model is measured as 1000 what is the drag force on the submarine?

The following results were obtained from a series of consolidated undrained triaxial tests on specimens of saturated clay. Determine the shear strength parameters (both effective stress and total stress) of the soil.


src='./qimages/7929-4c.jpg'>



5.
Sketch the variation of shear stresses for the cross-sections of the beams shown in Figure at the point of maximum shear force.



src='./qimages/7929-5a.jpg'>


Figure


A 5 mm diameter nozzle is discharging a vertically upward jet of water with a velocity of 10 m/s at the nozzle. What is the maximum height to which this jet will reach? If a flat plate weighing 1·5 N is balanced on the jet, what will be its height from the nozzle?

A pretensioned prestressed concrete beam, 250 mm wide and 450 mm deep, is prestressed with wires (area 42.0 mm2) located at a constant eccentricity of 50 mm and carrying an initial stress of 1 kN/mm2. The span of the beam is 12 m. Calculate the percentage losses of stress in the wires using the following data:
Modulus of Elasticity of steel Es 200 kN/m2
Modulus of Elasticity of concrete Ec 40 kN/m2
Coefficient of shrinkage 280 x 10-6
Coefficient of creep 1·6



In Figure an inclined plane is kept at an angle of 45° from horizontal plane at the bottom edge of a smooth wall. A uniform ladder of length l and mass M rests on the inclined plane against the wall such that it is perpendicular to the incline. What is the minimum coefficient of friction necessary so that the ladder does not slip on the incline?


src='./qimages/7929-5d.jpg'>



A site with a large areal extent underlain by 10 m thick, horizontal deposit of dry sand over bed rock, initially at a relative density of was compacten to a final relative density of The sand was
characterised with the maximum and minimum void ratios of 1-0 and
respectively_ Find the surface settlement following compaction

6.
Three metal cubes are arranged as shown in Figure The central metal cube is subjected to a uniform compressive stress of 1000 N/mm2. Cillr.nlate the volumetric strain of cube if displacement is restrained about the-x-a-xis-.
Al
l1 =l2 =l3
E1 =E3 1.2 x 10 power 5 N/mm2
E2 2.1 x 10 power 5 N/mm2
N1=N3 =0.20
N2 0.3



src='./qimages/7929-6a.jpg'>



Figure

A 500 mm diameter concrete pile is to be driven in a clayey soil. The design capacity of the pile is 500 kN. The soil conditions are shown in Figure Determine the length required for the pile for the above design capacity. (Assume alpha =0·75)

src='./qimages/7929-6b.jpg'>


Figure

Determine the shear reinforcement required-for: a reinforced-concrete. beam ofT-shaped cross-section with a flange width of 1500 mm, a flange thickness of 100 mm, a web width of 300 mm and an effective depth of 600 mm. The beam is reinforced with 8 bars of 25 mm on the tension side and 4 bars of 16 mm on the compression side. The reinforcements continue uninterrupted into the supports. The beam supports a factored
u.d.l. of 80 kN/m over a clear span of 10 m. The grade ofconcrete is M 20 and steel is Fe 415. The shear strength of concrete is given below:
Percentage of Steel Permissible Shear Stress for
M 20 in N/mm2
2.10 0.797
2.12 0.799
2.14 0.802
2.16 0.804
2.18 0.806
2.20 0.808


7.
A hydraulic jump is formed in a 2 m wide rectangular channel carrying water at a flow rate of 2 m3/s. It was found that the velocity head after the jump is only of that before the jUmp. What are the pre-jump and post-jump depths?

Design a simply supported beam with an effective span of 8 m-carrying a factored u.d.I. of 10 kN/m. The compression flange is restrained laterally along its entire length and the yield stress of steel is 250 MPa
The properties of ISMB 300 section are given below
Area 5870 mm2
D=300 mm
bf 140 mm
tf 13.1 mm
tw =7.7 mm
Ixx 8985.7 cm4
rxx 124mm
ryy 28.6 mm

The coordinates of two points on the virgin compression line below: are as
sigma1' 400 kPa, e1 0.8; sigma2 800 kPa, e2 0.75
In the-field, a 3 m thick normally consolidated layer of this soil subjected to construction load and the average effective vertical stress increased from 250 kPa to 450 kPa. Determine
the compression index and initial void ratio of the clay layer,
the consolidation settlement of the layer, and (iii)the load increment to cause 25 mm final consolidation settlement to occur and the corresponding void ratio


8.

A long column is initially straight and hinged at both ends. Consider, least moment of inertia Young's· modulus homogeneous material and centre-to-centre distance of hinge support L. Prove that the critical load for the column will be

Wc pi*pi*E*I/L2
pi 22/7

A simply supported beam of homogeneous cross-section and material is subjected to axial and transverse loads as shown in Figure Calculate the total stresses at points 1 and 2 of the section-C as shown in the figure. J.O

src='./qimages/7929-8a-ii.jpg'>


Flow of air (mass density 1·2 kg/m3 dynamic viscosity 1.8 x 10-5 takes place over a rectangular flat plate kept parallel to the flow direction. The flow velocity is 10 m/s and the length of the plate is such that the Reynolds number is critical at the trailing edge (i.e., the boundary layer is laminar throughout). The width of the plate is half of its length. The plate is then rotated by 90° in its plane so that the flow is now taking place along the shorter side. Find the ratio of the drag forces under these two flow situations.
Why are the characteristic curves needed for a turbine What are the various types of characteristic curves Show a typical constant head -characteristic curve between unit speed and unit powel fOi a Pelton wheel turbine.

A circular copper bar is carrying a tensile load of 200 kN as shown in Figure Calculate the displacement of point B of the copper bar. 1"0 2
Cross-sectional area of the copper bar 5000 mm2
Cross-sectional area of each of the steel bars 5000 mm Length of the copper bar 3.0 m
Length of each of the steel bars 1.0 m
Esteel=210GPa, Ecopper=120GPa


src='./qimages/7929-8c.jpg'>

Figure