Problem $4$: A $20-$story office building has plan dimensions of $100$ feet by $60$ feet and is positioned at a $45-$degree angle to a $\backslash (20-\backslash$mathrm$\{$mph$\}\backslash )$ wind. All the windows are fixed. The building has double vestibule$-$type swinging doors on the $\backslash (60-\backslash$mathrm$\{$ft$\}\backslash )$ walls, and the walls are constructed with tightfitting curtain walls. The doors have approximately $\backslash (1/8\backslash )-$inch gaps.

$1.$ Calculate the pressure differences for each wall due to wind and stack effect on the first, fifth, fifteenth, and twentieth floors. Assume the temperature difference $\backslash ($ t$\_\{$i$\}-$t$\_\{$o$\}\backslash )$ is $\backslash (40^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ).(1$ point$)$

$2.$ Considering the air infiltration through the door gaps, estimate the total air change rate per hour $\backslash ((\backslash$mathrm$\{$ACH$\})\backslash )$ for the building. Assume the gap around each door is continuous and the infiltration rate can be calculated using the orifice flow equation. $(1$ point$)$

$3.$ Calculate the total heat loss through infiltration for the building for one day. Use the following assumptions: indoor temperature is maintained at $\backslash (70^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ),$ outdoor temperature is $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ),$ and the specific heat capacity of air is $\backslash (0\mathrm{.}24\backslash$mathrm$\{$Btu$\}/\backslash$mathrm$\{$lbm$\}\backslash$cdot$\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ).(1$ point$)$

$4.$ Evaluate the impact of varying wind speeds on the ACH and heat loss. Perform calculations for wind speeds of $\backslash (10\backslash$mathrm$\{$mph$\},20\backslash$mathrm$\{$mph$\}\backslash ),$ and $30$ mph $.$ Discuss how the results change with different wind speeds. $(1$ point$)$

$5.$ Consider the building's height and temperature gradient's impact on the neutral pressure level. Perform calculations to determine how the neutral pressure level shifts if the temperature difference is $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ instead of $\backslash (40^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ).$ Discuss how this shift impacts overall pressure differences and infiltration rates. $(1$ point$)$

$6.$ Analyze the effect of building orientation on wind pressure. Calculate the pressure differences and ACH if the building is rotated to be parallel to the wind direction. Discuss the implications of building orientation on energy efficiency. $(1$ point$)$