Guide pour Extended essay

Problem Based Learning

Fluid Mechanics I

MEL III

PROBLEM 03-MELIII

mEASURING VISCOSITY OF DIFFERENT FLUIDs using ball drop method

I. Abstract

Viscosity is one of the most significant property of fluids, which dictate a lot about the fluid behavior when it is deformed by the action of shear stress. In this experiment we will determine the viscosity of different fluids by measuring the amount of time it takes steel balls to travel through given distances through the liquids and then compare them with the original values.

ii. INTRODUCTION

        Fluid mechanics is the study of how fluids react to forces. It has various applications, it is used to study pollution dispersion, forest fires, volcano behavior, oceanography etc.

In this experiment we will be dealing with a major property of fluids, known as Viscosity.

Viscosity is a quantity that expresses the magnitude of internal friction in a fluid, as measured by the force per unit area resisting uniform flow, or it is a resistance to gradual deformation by shear stress or tensile stress. Viscosity describes how a fluid resists forces, or more specifically shear forces. Since fluids are composed of many molecules that are all moving, these molecules exert a shear force on one another. Fluids with low viscosity have a low resistance to shear forces, and therefore the molecules flow quickly and are easy to move through such as water, Fluids with high viscosity flow more slowly and are harder to move through such as honey. For liquids, it corresponds to the informal concept of "thickness" for example, syrup has a higher viscosity than water. Viscosity is the property of a fluid which opposes the relative motion between two surfaces of the fluid that are moving at different velocities. In simple terms, viscosity means friction between the molecules of fluid. When the fluid is forced through a tube, the particles which compose the fluid generally move more quickly near the tube's axis and more slowly near its walls; therefore some stress (such as a pressure difference between the two ends of the tube) is needed to overcome the friction between particle layers to keep the fluid moving. For a given velocity pattern, the stress required is proportional to the fluid's viscosity.

[pic 1]

           Figure 1: Behavior of fluid placed between two plates

A fluid that has no resistance to shear stress is known as an ideal or inviscid fluid. Zero viscosity is observed only at very low temperatures in superfluids. Otherwise, all fluids have positive viscosity and are technically said to be viscous or viscid. A fluid with a relatively high viscosity, such as pitch, may appear to be a solid.

iii. Characterisitcs of fluids

A fluid is a substance that is continuously deformed when acted upon by shearing stress of any magnitude. Both liquids are gases are termed as fluids. Some characteristics of fluids are described below:

1. Density

The density of a fluid is its mass per unit volume, represented by (ρ).

 [pic 2]

1. Specific Volume 

It is the volume per unit mass of a fluid, so it is also equal to the reciprocal of density.

[pic 3]

1. Specific weight

It is defined as the weight per unit volume of a fluid.

[pic 4]

1. Specific Gravity 

It is the ratio of density of a fluid to the density of water at some specified conditions.

[pic 5]

1. Viscosity

It is basically the resistance to flow for a fluid. It is also known as absolute viscosity or dynamic viscosity for Newtonian fluids, Viscosity of a fluid is highly affected by temperature. For the liquids it increases with the increase in temperature whereas it decreases for the case of gases. Fluids for which the shearing stress is directly related to rate of shearing strain are known as Newtonian fluids, whereas the fluids for which shearing stress is not directly related with shearing strain are known as non-Newtonian fluids, hence the term apparent viscosity is used for these type of fluids. Viscosity is only mildly dependent on pressure and its effect is highly neglected.

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 Figure 2: Viscosity as a function of temperature.

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Figure 3: Variation of shearing stress with rate of shearing strain for several types of fluids, including common non-Newtonian    fluids.

Bingham is neither a fluid nor a solid, such a material can withstand a finite non-zero shear stress without motion therefore it is not a fluid, but when a yield stress is exceeded is flows like a fluid hence it is not solid as well.

1. Melting Point

It is the constant temperature at which a pure substance melts (change in state from Solid to Liquid). For pure water it is 0.[pic 8]

iv. METHODOLOGY

Drag Force: For objects that have basic geometries, for example, spheres, the drag on the object can be determined with known equations. In principle, the force F required to drag a sphere of radius rat velocity v through a fluid of viscosity  can be calculated.[pic 9]

[pic 10]

This equation is known as Stokes’ Law and is valid only for laminar flow, where the flow of the fluid can be treated as consisting of layers, each layer having a well defined velocity.

Gravitational Force:

A sphere of density ρs falling in a stationary fluid of density ρl feels a gravitational force given by:

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