A $150$ mm diameter pipe is fitted with a double nozzle with the geometry shown. At section $(2)$ the exit diameter of the nozzle is $80$ mm and at section $(3)$ the exit diameter is $100$ mm$.$ The pipe and both nozzles lie in the same vertical plane. A steady discharge of $0\mathrm{.}05$ m$3/$s of water from the pipe at section $(1)$ emerges as jets from the nozzles into the surrounding atmosphere. Energy losses in the flow may be assumed to be negligible.$($a$)$ Calculate$($i$)$ the flow rate at each nozzle exit, $($ii$)$ the water pressure section $(1).($b$)$ The double nozzle fitting is attached to the pipe by a bolted flange. The fitting has a material mass of $5$ kg and the water volume within it is $0\mathrm{.}005$ m$3.$ Calculate the magnitude and direction of the resultant force applied to the group of flange bolts for the flow conditions described above.