The figure shows a device
that, an inventor claims, provides a direct measurement of mass flow
rate. The flow to be measured is routed tangentially into the cylindrical
tube (radius R) as shown, flows axially along the tube until it passes
over a set of straight vanes mounted on a shaft that can be rotated
either freely or by applying a torque to the shaft, and then exits from
the system.
The inventor claims he can determine mass flow
directly by two methods: (1) from the angular rate of rotation of the
vanes, (rad/s), when the shaft is allowed
to rotate freely, and (2) from the torque Ts required
to hold the shaft stationary.
Derive
a theory for how this might be done.
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