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# ahhhulen - NOMENCLATURE Symbol b l A B h P V L t tav U r...

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NOMENCLATURE Symbol Definition SI Units μ Viscosity kg / m.s ρ Density kg / m 3 ρb Density of the ball kg/ m 3 ρl Density of the fluid kg/ m 3 A Constant for a given viscometer m 2 / s 2 B Ball constant m 2 / s 2 h Distance btw upper and lower marks m P Pressure drop kg / m.s 2 V Volume m 3 L Length m t Time of fall s t av Average time s U Thermal velocity m/s r Capillary tube radius m 1

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1. INTRODUCTION The problem is how to measure the viscosity of fluids and the objective is to find viscosity to use it in engineering calculations. Viscosity of aqueous glycerol solutions at different temperatures and concentrations are measured with three measurement methods in this experiment. These methods are Capillary Flow Method, Falling Ball Method, and Rotating Shaft Method. Firstly, background information about experiment is given below. Then, three measurement techniques will be explained which are applied in the laboratory . 1.1. Viscosity Viscosity is a measure of the resistance to flow when a shearing force is applied on the fluid. The viscosity is constant regardless of shear stress or shear rate according to Newton’s Viscosity Law (F/A=-µ.dU/dX). Fluids, which obey Newton’s Viscosity Law, called Newtonian fluids. For a Newtonian Fluid, the relationship between the shear stress and velocity gradient is linear as it is shown in figure1.1. Non-Newtonian fluids can be defined as fluids with a viscosity, which is not constant, but varies according to the shear rate or the shear stress applied.¹ Fig 1.1 Newtonian Fluids behaivour For a newtonian fluid, the force per unit area is proportional to the velocity gradient and the proportionality constant is called absolute viscosity (µ). The SI unit of absolute viscosity is the pascal second (1 Pa s= 1 kg m -1 s -1 ). The absolute viscosity is usually called dynamic viscosity. The rate of change of velocity with respect to distance measured perpendicular to the direction of flow and represented by dV/dx. The equation is τ =-µ dV/dx. The term τ is shear stress. τ is measured in newtons per square meter (Force/Area) in SI units. The ratio of the absolute viscosity to the density of a fluid is the kinematics Velocity gradient Shear Stress Newtonian fluids 2
viscosity and represented by ν. The equation is ν = µ/ρ. The kinematics viscosity unit is square meters per second in SI units. ¹ 1.2. Viscosity Measurement Techniques 1.2.1. Capillary-Flow Method This method is also called Ostwald-Fenske method which uses the Hagen-Poiseuille equation to determine the fluid viscosity. Capillary-flow viscometers measure the time of flow of a fixed volume of fluid through a small orifice under the influence of gravity at a controlled temperature in a fluid bath Hagen – Poiseuille equation, L P r dt dV × × = μ π 8 4 Volumetric Flowrate (Eq. 1.1) Rearranging; VL t gh r 8 4 × × × = ρ π μ = A ρ t (Eq.1.2) ∆P = the pressure difference t = the time required for fluid to fall from the upper mark to the lower mark h = the distance between the upper and the lower fixed marks 1.2.2. Falling Ball Method

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ahhhulen - NOMENCLATURE Symbol b l A B h P V L t tav U r...

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