The lawn sprinkler shown is supplied water with a flow rate of Q. Neglect fricti

Question

The lawn sprinkler shown is supplied water with a flow rate of Q. Neglect friction in the pivot, assume a steady state angular speed, and assume you're solving for shaft torque: Explain each term given and show which terms go to zero. Write the resulting equation. (r times F_s) + integral_sys M (r times g) partial differential m + T_shaft - integral_cv r times (2 omega times v_xyz + omega times (omega times r) + alpha times r) rho partial differential Forall = partial differential/dt integral_cv r times v_xyz rho partial differential Forall + integral_cs (r times v_xyz) rho (v_xyz middot partial differential A) This term is the angular acceleration. Since the angular velocity is not changing with time, this term is zero. Done for you above

Explanation / Answer

1)This is the viscous force term arises due to non ero viscosity of the fluid.

2)Themost common body force is that of gravity, whch eert a downward force on each differential element.This is the gravitational force acting on the fluid element.

3)This is the shaft torque term.

4) This is the coriolis force term, it is an inertial force arises due to motion of relative to the reference frame.

5)The centrifugal fore term, the centrifugal force always points radially out ward from the axis of rotation and it is independent of the motion of the particle of the rotating frame.

7)This term arises due to rate of mass change of the sprinkler.

8)The time rate of change of the linear mometum of the content of the control volume.For steady flow this term is zero.

9)The net flow of the linear momentum out of the control surface by mass flow.

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