Given v1 = 45 sin(ωt + 28°) V and v2 = 50 cos(ωt – 30°) V. Determine the phase angle between the two sinusoids. Please report your answer so the magnitude is positive and all angles are in the range of negative 180 degrees to positive 180 degrees. The phase angle between v1 and v2 is:

Compute the pressure drop of 30°c air flowing with a mean velocity of 8 m/s in a circular sheet-metal duct 300 mm in diameter and 15 m long. use a friction factor, f 0.02, and pair = 1.1644 kg/m a. 37.26 pa b. 25.27 pa n c. 29.34 pa d. 30.52 pa

Air flows over a heated plate àt a velocity of 50m/s. the local skin factor coefficient at a point on a plate is 0.004. estimate the local heat transfer coefficient at this point.the following property data for air are given: density = 0.88kg/m3 , viscosity 2.286 x 10 ^-5 kgm/s , k = 0.035w/mk ,cp = 1.001kj/kgk. use colburn reynolds analogy.

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