Here are some more thoughts on the vortex mystery for you. Suppose there
is a trough that extends from the cylindrical tank tangentially as
diagrammed in Fig. 1.
. . . . . . . . . .
. . . . . . . . .
. . Key:
. o .
. . o - Drain
. . . - Side of tank
. . .
Fig. 1 - Tank with tangential extension and drain
As the water is drained from the tank in Fig. 1 the water in the trough
accelerates linearly left to right. When it arrives at the cylinder
boundary its linear motion is changed into circular motion. In Fig.1 -
water on balance goes from no angular momentum to substantial clockwise
angular momentum. There must indeed be a counter-clockwise torque exerted
on the tank. In fact, that torque is exerted at the far left end of the
trough by water pressure due to the higher water height at the left as
compared to the right side of the trough. The trough is off center so
torque is obtained.
A similar circumstance exists if there are vertial screw type vanes in the
tank which impart an angular momentum to the water is it moves downward.
The vanes, connected to the tank, apply opposed angular momentum to the
tank and thus to the earth.
If water is drained from an oblong cross-section tank, like a bath tub,
then given any initial angular momentum near the drain, the tub acts like
the tank haiving a tangential extension. It can actually create water
angular momentum by action with the earth.
Now, consider the perfectly cylindrical tank with no vanes. Though the
water having a small initial angular velocity falls in spirals, thus
accelerating its angular velocity and increasing its kinetic energy through
the acceleration by gravity, it actually exerts torque on the tank in its
direction of motion (due to finite viscosity). It thus *loses* angular
momentum before going down the drain. This viscous coupling to the bottom
of the tank is amplified by the increased speed of the fluid near the hole.
A tank on axial bearings would actually accelerate angular motion in the
direction the water goes down the drain. Any angular momentum exhibited by
the vortex must be there initially, and some of that is lost by transfer to
the tank bottom.
In all cases the overall angular momentum is conserved.
Regards,
Horace Heffner
