When measuring small pressure differences with a manometer, often one arm of the manometer is inclined to improve the accuracy of reading. $($The pressure difference is still proportional to the vertical distance and not the actual length of the fluid along the tube.$)$ The air pressure in a circular duct is to be measured using a manometer whose open arm is inclined $45\backslash$deg from the horizontal, as shown in the figure. The density of the liquid in the manometer is $0\mathrm{.}77$ kg$/$L$,$ and the vertical distance between the fluid levels in the two arms of the manometer is $12$ cm$.$ Determine the gage pressure of air in the duct and the length of the fluid column in the inclined arm above the fluid level in the vertical arm. An illustration of a duct connected to a manometer to determine the gage pressure of air in the duct.The illustration has a spherical storage on the left labeled duct. It is filled with air and is connected to a U$-$tube manometer with an open arm. Both the arms of the tube are filled with water and the open arm is inclined $45$ degrees from the horizontal. The vertical distance between the fluid levels in both arms of the manometer is $12$ centimeters. The length of the liquid column in the inclined arm of the manometer is labeled L$.$The gage pressure of air in the duct is Pa$.$The length of the fluid column is cm$.$