$(30$ pts $)$ The figure below shows a circular butterfly gate, $4$ ft in diameter, which is pivoted about a horizontal axis passing through its diameter. Compute the torque vector, T $($magnitude and direction$),$ required to keep the gate in the closed position shown. The specific weight of the water in the tank shown is $=9\mathrm{.}81k\frac{N}{m^3}.T=784\mathrm{.}2902$lbfe