$4.)$ At Point $A,$ water is flowing through a pressurized pipe $($the direction of flow is into

the page$).$ A manometer is connected to the pipe to measure the pressure, as

shown below. Atmospheric pressure is $100$ kPa absolute$,$ but this manometer is

not open to the atmosphere. Instead, it is connected to a tank of mercury, and we

know the gage pressure at the top surface of the mercury in the tank $($Point $C)$ is

$10$ kPa $.$ The manometer also contains a volume of air in between the water and

mercury, as shown. Assume the density of water is $1,000k\frac{g}{m^3},$ and the density

of mercury is $13,500k\frac{g}{m^3}.$ The entire system is at a temperature of $28C.$

a$.(10$ points$)$ Find the density of the air in the manometer at Point $B,$ in $k\frac{g}{m^3}.$

Hint: The pressure of the air inside the manometer is not equal to

atmospheric pressure, and the air's density is not the same as the standard

value at sea level shown on your equation sheet. You will need to find the

density a different way, based on the information you know or can calculate

from the problem. Assume the air behaves as an ideal gas.