$(25$ pts $)$ Jet$-$A is used to fuel jet engines on commercial aircraft and is often stored in large tanks at airports prior to being transferred into trucks that refuel the planes. Occasionally the tanks must be cleaned, requiring an operator entrance through a $2m2m$ hatch shown below. Note that the tank is vented to atmosphere so that there is no overpressure.

Air Vent

a$.$ Using the figure provided above, create a free body diagram for the approximately rectangular hatch, showing all the forces and sketching the pressure distribution created by the Jet$-$A on the hatch$-$label the slope of the distribution using fluid properties. $(5$ pts $)$

b$.$ If the tank holds a maximum fluid level of $5$ meters, determine the resultant pressure force on the hatch by the Jet$-$A for this level of fuel. $(10$ pts$)$