External Problem 2: Dimensional analysis and similarity The viscous torque T produced on a disc rotating in a liquid depends upon the characteristic dimension D, the rotational speed N, the density pand the dynamic viscosity u. a) Show that there are two non-dimensional parameters written as: T and a, PND² b) In order to predict the torque on a disc of 0.5 m of diameter which rotates in oil at 200 rpm, a model is made to a scale of 1/5. The model is rotated in water. Calculate the speed of rotation of the model necessary to simulate the rotation of the real disc. c) When the model is tested at 18.75 rpm, the torque was 0.02 N.m. Predict the torque on the full size disc at 200 rpm. Notes: For the oil: the density is 750kg/mand the dynamic viscosity is 0.2 N.s/m. For water: the density is 1000 kg/m' and the dynamic viscosity is 0.001 N.s/ m² . IN =1gm

External Problem 2: Dimensional analysis and similarity The viscous torque T produced on a disc rotating in a liquid depends upon the characteristic dimension D, the rotational speed N, the density pand the dynamic viscosity u. a) Show that there are two non-dimensional parameters written as: T and a, PND² b) In order to predict the torque on a disc of 0.5 m of diameter which rotates in oil at 200 rpm, a model is made to a scale of 1/5. The model is rotated in water. Calculate the speed of rotation of the model necessary to simulate the rotation of the real disc. c) When the model is tested at 18.75 rpm, the torque was 0.02 N.m. Predict the torque on the full size disc at 200 rpm. Notes: For the oil: the density is 750kg/mand the dynamic viscosity is 0.2 N.s/m. For water: the density is 1000 kg/m' and the dynamic viscosity is 0.001 N.s/ m² . IN =1gm

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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External Problem 2: Dimensional analysis and similarity
The viscous torque T produced on a disc rotating in a liquid depends upon the
characteristic dimension D, the rotational speed N, the density pand the dynamic
viscosity u.
a) Show that there are two non-dimensional parameters written as:
PND?
and a, =
b) In order to predict the torque on a disc of 0.5 m of diameter which rotates in oil at
200 rpm, a model is made to a scale of 1/5. The model is rotated in water.
Calculate the speed of rotation of the model necessary to simulate the rotation of
the real disc.
c) When the model is tested at 18.75 rpm, the torque was 0.02 N.m. Predict the
torque on the full size disc at 200 rpm.
Notes: For the oil: the density is 750 kg/m and the dynamic viscosity is 0.2 N.s/ m² .
For water: the density is 1000 kg/ m² and the dynamic viscosity is 0.001 N.s / m².
IN =1 kgm

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