Experimentally, it has been observed for single crystals of a number of metals that the critical resolved shear stress, τcrss, is a function of the dislocation density, rhod, as where τ0 and a are constants. for some metal, the critical resolved shear stress is 2.33 mpa at a dislocation density of 2.64 × 104 mm-2. if it is known that the value of a for this metal is 2.46 × 10-3 mpa-mm, compute the τcrss (in mpa) at a dislocation density of 1.08 x 106 mm-2.

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.

Hydraulic fluid with a sg. of 0.78 is flowing through a 1.5 in. i. d. pipe at 58 gal/min. the fluid has an absolute viscosity of 11.8 x 105 lbf-sec/ft2. is the flow laminar, turbulent or within the critical range? give both a numerical reynolds number and a term answer.

Water at the rate of 1 kg/s is forced through a tube with a 2.5 cm inner diameter. the inlet water temperature is 15°c, and the outlet water temperature is 50°c. the tube wall temperature is 14°c higher than the local water temperature all along the length of the tube. what is the length of the tube?