Q1 A straight and horizontal pipeline with diameter of 0.8m conveys crude oil (density is 950 kg/mº.
kinematic viscosity is 1.2 x 10-5 m2/s). The pipe wall is assumed to be smooth and the
corresponding friction factor can be found from the Moody Diagram (in the Supplementary
Information sheet). To maintain the oil flow rate, pressure boosters are distributed every 20 km
along the pipeline.
(a) If the oil flow rate is 0.45 m/s, determine the flow state and the amount of pressure that
needs to be raised at each pressure booster.
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Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Slip occurs via two partial dislocations because of (a) the shorter path of the partial dislocation lines; (b) the lower energy state through partial dislocations; (c) the charge balance.

For a gate width of 2 m into the paper, determine the force required to hold the gate abc at its location.