A12m rectangular column has a cross section that is 20cm tall and 10cm wide. assume these line up with the standard y and x axis, respectively. the column is fixed at the bottom and pinned at the top. additionally, a pin is attached halfway up the column that restricts movement in the x direction. what is the buckling stress that will cause the column to fail and what are the slenderness ratios associated with column? assume the material is a36 steel. (hint: think of how the pin in the middle of the column affects the length in the associated direction and what are the supports for each condition? )

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?

Afluid flows with a velocity field given by v=(x/t)i.. determine the local and convective accelerations when x=3 and t=1.

Burgers vector is generally parallel to the dislocation line. a)-true b)-false