Atrapezoidal river channel section has a basedimension of 30
feet, a liquid depth of 4 feet, and sideslopes of 4 to 1
(horizontal to vertical).
5.1 by integration, determine the locationof the centroid
relative to the channel bottom of this trapezoidalsection.
5.2 by integration, determine the moment ofinertia about a
horizontal axis at the channel bottom. usingthe parallel axis
theorem, determine the moment of inertia about ahorizontal axis
through the centroid.

The mass flow rate of the fluid remains constant in all steady flow process. a)- true b)- false

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.

Abrake has a normal braking torque of 2.8 kip in and heat-dissipating cast-iron surfaces whose mass is 40 lbm. suppose a load is brought to rest in 8.0 s from an initial angular speed of 1600 rev/min using the normal braking torque; estimate the temperature rise of the heat dissipating surfaces.