A compacted base aggregate sample has λ (%) air void by the total volume of the sample. The specific gravity of the aggregate is SG. The water content of the sample is w (%). It is known the density of water is rhow gram/cm3 . What is the dry density of this sample, rhodry in terms of λ, SG, and rhow? Refer to the derivation for zero air void density?

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.

Calculate the bore of a cylinder that has a stroke of 18 inches and an extension time of 6 seconds at a flow rate of 4 gal/min.

Derive the correction factor formula for conical nozzle i=-(1+ cosa) and calculate the nozzle angle correction factor for a nozzle whose divergence hal-fangle is 13 (hint: assume that all the mass flow originates at the apex of the cone.