Fluids eBook: Viscosity

Ch 1. Basics					Multimedia Engineering Fluids
Mass Density	Ideal Gas Law	Viscosity	Surface Tension	Vapor Pressure

FLUID MECHANICS - CASE STUDY
		Introduction
Rotational Cylindrical Viscometer		Students are given a simple device called a rotational cylindrical viscometer, as shown in the figure, and asked to determine the viscosity of an unknown liquid. The outer cylinder is fixed while the inner cylinder is rotating at a constant angular speed of ω by applying a torque T.

		Questions
		Derive an equation for the viscosity in terms of angular velocity, ω, torque, T, submerged inner cylinder height, L, inner cylinder radius, R_i, and outer cylinder radius, R_o. Calculate the viscosity value when ω = 55 rev/min, T = 0.9 N-m, L = 0.3 m, R_i = 0.12 m and R_o = 0.13 m.

		Approach
		Assume the velocity profile between the container and the rotating cylinder is linear. Neglect the end effects and bottom surface of the cylinder. Assume the liquid is a Newtonian fluid. Assume the force (F) is perpendicular to its moment arm (r), hence the torque is given by T = Fr.