Find ix, iy, and j for the following shapes. in addition, find the radius of gyration (r) with respect to the x axis and y axis for each shape given, r = sqrt(i/a).

the radius of gyration is primarily used in axially loaded members such as columns when we worry about the column bending from being too long.

Water in a partially filled large tank is to be supplied to the roof top, which is 8 m above the water level in the tank, through a 2.2-cm-internal-diameter pipe by maintaining a constant air pressure of 300 kpa (gage) in the tank. if the head loss in the piping is 2 m of water, determine the discharge rate of the supply of water to the roof top in liters per second.

For each of the following process: a) sketch the p-v diagram, b)sketch t-s diagram, c) sketch t-v diagram, d) sketch the boundary work on one of the diagrams (a, b or c) and e) sketch the reversible heat transfer on one of the diagrams (a, b or c): 1- isobaric process from compressed liquid to superheated vapor 2- isothermal process from compressed liquid to superheated vapor 3- isentropic process from compressed liquid to superheated vapor

With increases in magnification, which of the following occur? a. the field of view decreases. b. the ambient illumination decreases. c. the larger parts can be measured. d. the eyepiece must be raised.