Consider a two-dimensional, laminar flow around a circular cylinder. Using Thwaites' correlation method, determine the separation angle for these two different velocity distributions given below. (a) From potential flow, the velocity distribution is given by, = 2Uo sin(%) U (x) 2Uo sin () (b) From actual experimental measurements by Hiemenz, the velocity distribution is given by, U (x) U(1.814f - 0.271f3 - 0.0471f5) In the equations above, Uo is the free-stream velocity, R is the radius of the cylinder, x is the arc length along the cylinder's surface, and 2 = x/R is the dimensionless arc length.

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.

The higher the astm grain-size number, the coarser the grain is. a)-true b)-false

The short distance from the objective lens to the object causes problems at high magnification. which of the following is the most serious? a. cleaning the object surface b. positioning the object c. reflection from the object surface. d. illumination of the object