What is the efficiency of a spinning garden sprinkler at a given speed?

[morry]

sprinkler efficiency (urgent

Ok, I have an exam on monday and both my lecturers and tutor have gone walkabouts. So you guys are my last resort. Thanks. :)

Anyway:
Water is discharged from a a garden sprinkler from two nozzles and opposite ends of an arm. Its the type that spins around and sprays water on your garden.

I have calculated the torque exerted when its stationary but the second part of the question confuses me.

It asks for the work done per second when spinning at speed "u". No worries.
But then it asks for the efficiency of the device at that speed.

Then asks for the value of "u" for maximum power.

I don't understand how to find the efficiency of this, can someone explain how I would go about it?

 

[Astronuc]

Its hard to say what is meant by efficiency - which presuambly would be work output/energy input.

On the other hand, from the torque, one can presumably determine what total work could be performed (100% efficency) as compared to what work is actually done based on when spinning with speed "u", and the ratio of "work actually done to work that could be theoretically done" is the efficiency.

 

[morry]

I understand what youre saying, but I don't know how to work this out.

I have calculated the torque it puts out, but how would I work out the theoretical part?

Thanks Astronuc.

 

[Astronuc]

Well

$$dW\,=\,\vec{F}\,\cdot\,d\vec{s}\,=\,F_\perp\,ds\,=\,\,F_\perp\,r\,d\theta$$

and

$$dW\,=\,\tau\,d\theta$$

So find the maximum work for the given torque.

Do you have the kinetic energy from the tip moving with speed "u", which should equal $\omega\,r$.

The power is also just $\vec{\tau}\,\cdot\,\vec{\omega}$

 

[morry]

Thanks astronuc. I know what youre on about now.

I had the exam this morning and I think I did quite well. No questions on sprinkler efficiency though. :)