Asimple supported beam at x0 = 0 and xn = l with a uniform load w and the

vertical deflection v(x) is described by the boundary value problem

d

2

v

dx2

=

x−l

3ei

wx, v(0) = 5, v(l) = 100

where l is the length of the beam, e represents the young’s modulus of the material from which

the beam is fabricated and i is the second moment of area of the beam’s cross–section. suppose

l = 15 m, e = 210 kn/m

2

, i = 370.5 m2

and w = 9.8 kn/m. use the shooting method to

approximate the vertical deflection, v(x) with the step size, h = 3, the first guess, z0 = 10 and

the second guess, z0 = 5.

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at -20°c. air approaches the tube bank in the normal direction at 0°c and 1 atm with a mean velocity of 4 m/s. the tubes are arranged in-line with longitudinal and transverse pitches of sl- st 1.5 cm. there are 30 rows in the flow direction with 15 tubes in each row. determine (a) the refrigeration capacity of this system and (b) pressure drop across the tube bank. evaluate the air properties at an assumed mean temperature of -5°c and 1 atm. is this a good assumption?

Air is compressed isentropically from an initial state of 300 k and 101 kpa to a final temperature of 1000 k. determine the final pressure using the following approaches: (a) approximate analysis (using properties at the average temperature) (b) exact analysis

What is a monomer? how do they form a ploymer from the view point of chemical bonding?