Water leaves a penstock (the flow path through a hydroelectric dam) at a velocity of 100 ft/s. How deep is the water behind the dam (in ft). Neglect friction. [h = 155 ft]

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.

Asolid steel sphere (k=63.9 w m-1 k-1 , ? =7832 kg m-3 , c=0.523 kj kg-1 k-1 ), 100 mm in diameter is initially at a uniform temperature of 500o c and is suddenly quenched in a large oil bath for which t? = 100o c and h = 3200 w m-2 k-1. estimate the time required for the sphere to cool to 200o c and to 110o c

The load on a bolt consists of an axial pull of 10 kn together with a transverse shear force of 5 kn. the bolt material has a yield strength of syt syc 100 mpa. find the diameter of the bolt at factor of safety n-0.5, n 1 and n-2 using maximum shear stress theory