A sprinkler has 2 arms each of radius R20 cm and outlet area

A sprinkler has 2 arms each of radius R-20 cm and outlet area A-30 mm2. The inlet flow rate is Q1 liter/second. The frictional torque applied to the nozzle varies with the speed of rotation and is given by 0.024) where is the angular velocity of the nozzle (in rad/s). Find the angular velocity of the nozzle for the flow rate given. (note that although the nozzles are spinning the control volume will be stationary so you can use absolute velocities in your calculations) (2) 12 Nozzle exit area= A Flow out Tshaft Flow out \\ 0

Solution

Inlet flow rate(Q1)=1l/s=0.001cumic m per sec

Therefore, outlet flow rate(Q2)= Q1/2=0.0005m^3/s (from each nozzle)

A(area of each nozzle)=30(mm)^2=0.00003m^2

V(velocity of flow)=Q2/A=0.0005/0.00003=16.67m/s

w(angular velocity)=V/R=16.67/0.2 =83.33 radian/s