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 pND? and 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 mnodel 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/m For water: the density is 1000 kg m and the dynanmic viscosity is 0.001 Ns/m. kgm 1N 1

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 pND? and 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 mnodel 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/m For water: the density is 1000 kg m and the dynanmic viscosity is 0.001 Ns/m. kgm 1N 1

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

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
PND
and 2
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/m
For water: the density is 1000 kg/ m and the dynamic viscosity is 0.001NS/m.
kg.m
1N 1

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