Problem $06\mathrm{.}056-$ Sprinkler with unequal arms

Water enters vertically and steadily at a rate of $35\frac{L}{s}$ into the sprinkler with unequal arms and unequal discharge areas. The smaller jet has a discharge area of $3c{m}^2$ and a normal distance of $r_1=50cm$ from the axis of rotation. The larger jet has a discharge area of $5c{m}^2$ and a normal distance of $r_2=36cm$ from the axis of rotation.

Take the density of water to be $1000k\frac{g}{m^3}=1k\frac{g}{L}.$

Problem $06\mathrm{.}056.$a $-$ Rotational speed of the sprinkler

Disregarding any frictional effects, determine the rotational speed of the sprinkler in rpm$.$

The rotational speed of the sprinkler is $$ rpm$.$