(Solved): 1) Calculate the density and specific weight (in BG units) of air at a gauge pressure of \( 100 \m ...

1) Calculate the density and specific weight (in BG units) of air at a gauge pressure of \( 100 \mathrm{psi} \) and a temperature of \( 100^{\circ} \mathrm{F} \). Assume standard atmospheric pressure. 2) A dirigible has a volume of \( 90,000 \mathrm{~m}^{3} \) contains helium under the following atmospheric conditions: \( \left[\right. \) pressure \( =101 \mathrm{kPa}(\mathrm{abs}) \) and temperature \( \left.=15^{\circ} \mathrm{C}\right] \) Determine the density and total weight of the helium. 3) A 25-mm-diameter shaft is pulled through a cylindrical bearing as shown in the figure below. The lubricant that fills the gap between the shaft and bearing is an oil having a kinematic viscosity of \( 8.5 \times 10^{-4} \mathrm{~m}^{2} / \mathrm{s} \) and a specific gravity of \( 0.95 \). If the force, \( P \), required to pull the shaft at a velocity of \( 3 \mathrm{~m} / \mathrm{s} \) is \( 10 \mathrm{~N} \), determine the height of the gap between the bearing and the shaft. Assume that the velocity distribution is linear.