A relief valve is installed on the bottom of a pressure vessel. The entrance to the valve is 4.5 inches diameter, and the exit (which discharges in the horizontal direction, 90 degrees from the entrance) is 5 inches in diameter. The loss coefficient for the valve is 4.5 based on the inlet velocity. The fluid in the tank is a liquid with a density of 0.8 g/cm^3. If the valve opens when the pressure at the valve reaches 150 psig. Determine:
a: The mass flow rate through the valve, in lbm / s
b: The net force (magnitude and direction) exerted on the valve
c: Determine the location (orientation) of a cable that is to be attached to the valve to balance the net force. (Note that a cable can support only a tensile force)