# Free Report About Theory 3

Type of paper: Report

Topic: Density, Experiment, Ball, Cylinder, Oil, Gravity, Water, Volume

Pages: 10

Words: 2750

Published: 2020/11/07

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## Abstract

The laboratory assignment aims to study the physical properties of fluids and practice the experimental measurements and assessment of errors. The density, specific gravity, and viscosity were measured experimentally and calculated. The experimental errors were assessed by repeating experiments.

## Introduction 3

Experimental 4
Density and specific gravity 4
Rotational Viscometer 6
Falling Ball Viscometer 7
Results 8
Calculations 10
Density 10
Specific gravity 10
Viscosity 10
Conclusions 12

## References 13

Introduction
The experiment is meant to study the properties of fluids. Fluids are applied in different areas in industry and everyday life; therefore, it is important to understand their properties. The widely applied fluids, namely vegetable oil and water are used for the experiment.
The fluid properties influence the regimes of fluids application during the industrial processes, types of the devices applied, and the temperature and pressure of the process.
The experiment was conducted in two stages: 1) determining the density; 2) determining viscosity. These are the basic fluids properties, and the experiment was based on relatively simple measurements, namely measurement of the certain volume weight and viscosity by rotational and falling ball device.
Theory
The fluid substances (gases and liquids) significantly differ from solid substances since they move continuously. This means that the layers move over one another, and the velocity gradient is formed. The fluids are assessed with viscosity and density. Viscosity refers to resistance to motion, while density shows the compactness of fluid.
Although gases and liquids are both considered as fluids, they have some substantial discrepancies. In contact with gas, liquids form a boundary layer; liquids are characterized by a certain volume, while gases expand in atmosphere, liquid volume is slightly influenced by temperature and pressure, unlikely gases.
Thus, the different engineering approaches to summarizing the fluid properties were formed: liquids are considered incompressible and their properties are not subject to temperature changes. On the contrary, the gases properties are dependent on temperature and pressure.
Experimental
Density and specific gravity
Density is a measure of compactness that shows mass of the unit of volume. The density units are kg/m3 (CI), and it also can be measured in g/cm3, g/l, lb/ft3, etc. Being a basic physical property, density values of the most common liquids and gases are tabulated.
The experiment of density measurement is based on weighting the known volume of liquid. Thus, the initial data is the volume of liquid. The weight of an empty bottle is measured; then, the bottle is filled with liquid and weighted. The weight difference is the mass of water. Density calculates as:
ρ=mV.
During the experiment, mass and volume are measured in g and ml, therefore the additional mathematical transformations are required for unit conversion:
ρ=m(g)V(ml)∙10-310-6=mgVml∙103[kg/m3].
The triple beam mass balance was used to measure density. The empty bottle was weighted. Then, the bottle was carefully filled with 50 ml of vegetable oil (funnel has to be used to prevent spills and bubbles formation).
The density for water and vegetable oil was calculated by measuring the weight of the constant volume of liquid. Specific gravity is measured with hydrometer (Figure 1)
The figure illustrates the scaled meniscus and reading areas.
Figure 1. Universal and sensitive hydrometer: 1 – narrow stem; 2 – wide stem; 3 – scale; 4 – reading level; 5 – meniscus; 6 – weights.
The tall glass cylinders is placed on the measuring surface, filled with the liquid, and left to allow air to rise to the top. Then, the hydrometer is inserted and settled in the center of the cylinder. After the hydrometer has stabilized, the scale readings are performed (the reading position is depicted as 5 on Figure 1).
Rotational Viscometer
The rotational viscometer was applied for measuring the viscosity of vegetable oil. The device is constructed with two aluminium cylinders, connected with a string to provide the constant angular velocity (Figure 2).
The velocity profile between the cylinder and wall is linear. This provides the constant strain rate at the stable rotation speed of the inner cylinder. If the falling mass moves the cylinder, the applied stress to the fluid is and known. Thus, the strain rate is proportional to the rotation rate and known. When the different weights are applied, the viscosity for each strain rate is measured. The data necessary for calculations are received during the experiment, when the mass is attached to the string, and the time is measured
Figure 2. Rotational viscometer: 1 – test fluid; 2 – stationary cylinder; 3 – rotating cylinder; 4 – weight.
The viscosity is determined by the following expression:
μ=r2mg(R0-Ri)Ri32πLU,
where is dynamic viscosity, r – cylinder pulley radius, m – mass that produces velocity U, Ro – outer cylinder radius; Ri – inner cylinder radius, L – cylinder length, U – fall velocity of the mass m.
The gap between the stationary and rotating cylinders is filled with fluid which viscosity is measured. The rotating cylinder has to be fully immersed in fluid. The different weights are applied to the weight hanger and the velocities of the fall are measured by timing the fall.
Falling Ball Viscometer
The alternate viscosity measurement is performed by a falling ball viscometer, which is a sealed glass device (Figure 3).
Figure 3. Rotational viscometer: 1 – sphere; 2 – callibrated cylinder.
The cylinder is filled with vegetable oil; the density of fluid and diameter of sphere has to be determined. The ball is dropped into the fluid, after the ball passes several centimeter, the time of the ball fall is measured. The measeurements are repeated several times.
Results
Raw results of density measurements

The other data necessary for the viscosity calculation by falling ball method are
mass of ball, mb = 6.9g = 0.0069 kg, ball diameter, d = 2.49 cm = 0.0249 m.
Calculations
The calculations are performed for experimental data processing. During the calculations, the experimental values of density, specific gravity and viscosity are performed.
Density
Density of Water ρwater=(MW-MB)Vb ∙103= 85-3550∙103=1000 kg/m3
Density of vegetable oil ρoil=(MO-MB)Vb ∙103= 82-3550∙103=940 kg/m3
Specific gravity
The average readings on hydrometer floating in oil: 922.8; in water: 996.8.
Specific Gravity is calculated as:
SGT = Density of Fluid at TDensity of water at 60oF(15.6oC)
Specific gravity of water:
SGwater = 996.8999.07=0.998
Specific gravity of oil:
SGwater = 922.7999.07=0.924
Viscosity
The average experimental hydrometer readings are presented in Table 5.

The factors and results of viscosity measurements are presented in Table 6. The sample calculation is:
U=Lτ=11.53=0.6508 m/s.
µ = r2mg(Ro-Ri)Ri32ΠLU = 0.0477520.1∙9.81(0.04725-0.04)0.04i32∙3.14∙1∙0.06508 = 0.0619 kg/ms

Thus, the average viscosity values of oil and vegetable oil are 0.0747 and 0.1181 kg/m∙s, respectively.
The average data of experiments with falling ball are presented in Table 7.

μ==0.0069∙9.81-3.14∙924∙0.02436∙0.00693∙3.14∙0.024∙1.1199=0.008 kg/m∙s
The results obtained by rotational viscometer are close to the theoretical, while the falling ball method provides different results. This is due to systematic errors.
Conclusions
The fluid basic properties have been determined experimentally, namely density, specific gravity and viscosity. The rotation and falling ball viscometer have been applied. Apparently, there are differences in results, and the repeated measurements were performed to ensure the quality. The repeated measurements are performed to minimize random errors. During the lab, the practical skills for measuring the physical properties of fluids have been practiced.
References
Fluid mechanics lab manual (FIT)
Viswanath, D S. Viscosity of Liquids: Theory, Estimation, Experiment, and Data. Dordrecht: Springer, 2007. Internet resource.

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