What Are Spin-Up Effects in Waterwheels and Their Impact on Inertial Damping?

[broegger]

Hi.

Can anyone explain to me what spin-up effects are? The context is a waterwheel that consists of an ordinary wheel with papercups with holes in the bottom suspended along the rim. It is stated that for this wheel there are two sources of damping: ordinary frictional damping and "inertial" damping which is caused by a spin-up effect. This is due to the fact that water enters the wheel at zero angular velocity but is thrown out at non-zero angular velocity through the holes in the bottom of the cups. How does this produce inertial damping?

 

[Andrew Mason]

Hi.

Can anyone explain to me what spin-up effects are? The context is a waterwheel that consists of an ordinary wheel with papercups with holes in the bottom suspended along the rim. It is stated that for this wheel there are two sources of damping: ordinary frictional damping and "inertial" damping which is caused by a spin-up effect. This is due to the fact that water enters the wheel at zero angular velocity but is thrown out at non-zero angular velocity through the holes in the bottom of the cups. How does this produce inertial damping?

F = ma = dp/dt = vdm/dt

So if the water wheel is throwing off mass at a certain rate, there will be an inertial force on the wheel.

AM

 

[arildno]

Since, effectively, the water wheel imparts momentum to the water particles during the contact phase, it follows that the water particles "kick back" on the wheel, according to, for example, Newton's 3.law.
That kick-back is inertial damping of the wheel.

Quantitatively, the net force is typically the product of the mass flow rate and the exit velocity.

.

 

[arildno]

Note:
It is, of course, the TORQUE produced by this force that tends to counter-act the wheel's angular velocity.
In addition, the support structure of the wheel prevents wheel from being displaced as a result of the force from the ejected water particles.