Development Team. Paper No: 5 Water Resources and Management Module 6 : Processing of Hydrometer Data. Environmental Sciences

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1 Paper No: 5 Module 6 : Processing of Hydrometer Data Principal Investigator & Co- Principal Investigator Paper Coordinator Content Writer Content Reviewer Development Team Prof. R.K. Kohli Prof. V.K. Garg & Prof. Ashok Dhawan Central University of Punjab, Bathinda Dr Hardeep Rai Sharma Kurukshetra University, Kurukshetra Dr Deeksha Katyal, USEM, Guru Gobind Singh Indraprastha Univ., New Delhi Prof V. Subramaniam (Retd) SES, JNU, New Delhi Anchor Institute Central University of Punjab 1

2 Description of Module Subject Name Paper Name Module Name/Title Module Id EVS/WRM-V/6 Pre-requisites Objectives To understand the principle and working of hydrometer To understand the ranges and scales of hydrometer Keywords Specific gravity, Density, Correction and calibration 2

3 Introduction Hydrometer is an economical and simple tool that is used to measure the density of liquids. Specific gravity of a liquid is the ratio of its mass to the ratio of the mass of equal volume of pure water. As we know that the density of liquid is temperature dependent therefore, hydrometers are calibrated accordingly for various references and temperatures. The typical hydrometer is made up of glass and consists of a cylindrical stem with bulb at its lower end. This bulb is weighted with mercury or lead to make it float straight. Inside the stem lies a scale on which readings are taken (John and Wright, 2008). There are minute errors in the positioning of the scale and the density measurements and can be improved by addition of rectification to the hydrometer readings. Figure1: Schematic drawing of hydrometer The liquid, whose specific gravity is to be measured, is poured in to the cylindrical container and the hydrometer is placed gently into the liquid in a way that it floats freely. The point at which the surface of liquid touches the stem of a hydrometer is read and that point corresponds to the specific gravity of that liquid. Hydrometer works on the Archimedes principle which states that any object which is comparatively lighter than any liquid is immersed in that liquid then the liquid displaced by the body is equal to its 3

4 mass as well as its volume (Stott and Dunstan, 1938). This principle is also called as buoyancy and can be stated as Any object which is wholly or partially immersed in a liquid is buoyant up by a force equal to the mass of the liquid that is displaced by that object. Ranges of Hydrometer: Range of hydrometer depends upon the density of liquid for example, while measuring low density liquids such as kerosene, alcohol and gasoline hydrometer sinks deeper as compared to the high density liquids such as brine, milk and acids. Hydrometer having mark near the top of the stem is used for the measurement of low density liquids and the one having mark near the bottom is used for high density liquids. Scales of hydrometer: Hydrometer has variety of scales depending upon its intended use. Some of the examples are as follows: API gravity: This scale is used by the petroleum industries worldwide. Baume scale: This scale is previously used in the industrial chemistry and pharmacology. Brix scale: This scale is mainly used in the food processing industries such as fruit juice, wine making and sugar industries. Oechsle scale: This scale is used to measure the density of grape must. Plato scale: This scale primarily used in brewing industry. Twaddell scale: This scale was previously used in the bleaching and dyeing industries. There are certain specialized hydrometers such as Lactometer: It is used to measure the density of milk. Since milk consists of several substances with varying density therefore specific gravity of milk is not the convincing sign of its composition. In addition to specific gravity, various other tests (fat content) should be performed to assess the overall composition of milk. The lactometer is divided into hundred fractions. Milk is dispensed into the instrument and allowed to stand till cream is formed. Based on the depth of cream formed in degrees, conclusion is drawn on the quality of milk. If lactometer floats on the milk, we can say milk sample is pure and if not then milk is adulterated. 4

5 Saccharometer: This type of hydrometer is used to measure the quantity of sugar in a liquid. Saccharometer was invented by Thomas Thomson, it is mainly used in the wine making and brewing industries but can also be other industries such as ice cream making etc. Saccharometer consists of a big bulb with slender stem rising from the top and has calibrated marking on it. It works on the principle of buoyancy and sugar content can be determined by reading the value where the surface of liquid crosses the scale. If bulb floats higher on the liquid then the liquid consist of high amount of sugar and if bulb floats lighter then the liquid is less dense i.e. has less sugar content. Alcoholometer: It is used to measure the elevated levels of alcohol in spirits and also known as proof and Tralles hydrometer. Alcoholometers have scales distinct with volume percents of "potential alcohol", based on a pre-calculated specific gravity. An elevated potential alcohol reading on this scale is indicative of high specific gravity which is implicit to be caused by the introduction of dissolved sugars. A reading is taken before and after fermentation and fairly accurate alcohol content is calculated by subtracting the post fermentation reading from the pre-fermentation reading. Urinometer: It is the clinical hydrometer used for urine analysis. The specific gravity of urine is representative of ratio of solutes to water. With the use of Urinometer, quick determination of overall hydration of patients is possible. Use in soil analysis: Hydrometers are used in the soil analysis for the purpose of gradation of fine grained soil, silt and clay. Hydrometer analysis is performed if the grain size is too small for sieve analysis. Principles of hydrometer analysis: The analysis of data generated by hydrometer is based on the application of Stroke s law which governs the terminal velocity at which the spherical particles settle through the column of liquid. According to the strokes law the particles which have comparable density and are in firm, spherical in shape do not interact with each other during sedimentation, remains separated from each other and possess large size so that their settlement is not directed by Brownian motion. (Wen et al., 2002). The analysis process of hydrometer involves the mixing of sediment or any solute into the water to make suspension. According to the principle given by Stroke, particle tends to settle out of the water 5

6 column. The density of that suspension is governed by the concentration and specific gravity of the sediment present in it. When this suspension is allowed to stand still, particles will settle out of the suspension and density of that suspension begins to fall down. Hydrometer determines the density of suspension at a particular depth. There are two very fundamental formulas through which we can calculate the hydrometer analysis: 1. Diameter of particle at a particular time and depth D = 30η Gs 1 L t Where, D = equivalent sedimentation diameter of particle (millimeters), η = viscosity of water (grams seconds per square centimeter), Gs = specific gravity of sediment, L = effective depth measured from water surface to center of gravity of hydrometer bulb (centimeters), and t = time measured from start of sedimentation (seconds). 2. Percentage of original sample mass still left is suspension % Finer= Where, Gs V (Rh B) Gs 1 M 10 Gs = Specific gravity of sediment, V = total water-sediment volume (1000 ml), M = dry sample mass (grams), Rh = corrected hydrometer reading of slurry mixture (grams per liter), and B = hydrometer reading of reference mixture of dispersing agent and distilled water (grams per liter). 6

7 Corrections in hydrometer readings: Zero correction: the zero reading in the hydrometer (in the control cylinder) is below the water meniscus, it is (+), if above it is ( ), if at the meniscus it is zero. Meniscus Correction (Fm): Difference between upper level of meniscus and water level of control cylinder. Temperature correction (Ft): The temperature of the test should be 20 C but the actual temperature may vary. The temperature correction is approximated as : Ft = T (for T between 15 C to 28 C) Procedure: 1. Add 125 ml. of 4% of sodium metaphosphate (NaPO3) to set up control jar and fill it up with distilled water to make volume 1000 ml (alternatively this solution can be made by mixing dry chemical to the distilled water to make volume 1000 ml.) Put the hydrometer into the control jar to record the zero and meniscus correction, after that place the thermometer to record the temperature. 2. Sieve the soil by using no. 200 sieve and weigh precisely 50 gm of sieved soil. Mix the soil with 125 ml. of 4% of sodium metaphosphate solution. Allow this soil mixture to stand for about 12 hrs. 3. At the end of the soaking period, shift the mixture to a dispersion (or malt mixer) cup and put in tap water until the cup is about two-thirds full. Mix for 1 minute. After mixing, cautiously shift all the contents of the dispersion cup to the sedimentation cylinder. Rinse any soil in the dispersion cup by using a plastic squeeze bottle or adding stabilized water and pour this into the sedimentation cylinder. Now add distilled water to fill the cylinder to the 1000 ml mark. 7

8 4. Cap the sedimentation cylinder with a No. 12 rubber stopper and carefully agitate for about 1 min. Agitation is defined as turning the cylinder upside down and back 60 turns for a period of 1 min. An upside down and back movement is 2 turns. 5. Put the sedimentation cylinder beside the control cylinder and start the stopwatch immediately. This is cumulative time t = 0. Insert the hydrometer into the sedimentation cylinder. 6. Take hydrometer readings at cumulative times t = 0.25 min., 0.5min., 1 min. and 2 min. Always read the upper level of meniscus. Remove and place the hydrometer in the control jar. 7. Continue taking hydrometer and temperature readings at approximate elapsed times of 8, 15, 30 and 60 min. and then 2, 4, 8, 24 and 48 hr. For each reading, insert the hydrometer into the sedimentation cylinder about 30 sec before reading is due. After the reading is taken, remove the hydrometer and put it back into the control cylinder. Calculation: Calculate corrected hydrometer reading for percent finer, RCP = R + Ft + Fz Calculate percent finer = (A * RCP * 100) / Ws where, Ws = dry weight of soil used for hydrometer analysis A = correction for specific gravity (as hydrometer is calibrated for Gs = 2.65 ) Therefore, 8

9 A = 1.65 * Gs / ((Gs 1 ) * 2.65 ) Calculate corrected hydrometer reading for determination of effective length, RCL = R + Fm Determine L (effective length) corresponding to RCL given in Table 1. Determine A from Table 2 Determine D (mm) = A L (cm.) / t (min.) Table 1. Variation of L with Hydrometer Reading Hydrom eter Reading L (cm) Hydrom eter Reading L (cm) Hydrom eter Reading L (cm) Hydrom eter Reading L (cm)

10 Table-2 Variation of A with Gs Temperature ( C) Gs Temperature ( C) Gs Combined Analysis 10

11 1. Calculate the percent passing the No. 200 sieve. (This should be equal to the percent finer for the soil retained on No. 200 sieve from the Sieve Analysis) 2. The modified percent finer = percent finer for hydrometer method x percent passing No. 200 sieve from Step The total modified percent finer for samples retained on No. 200 sieve and above would be the same as calculated in sieve analysis; for samples passing No. 200 sieve, the same as calculated in Step 2. Note: Plot the percent finer versus grain size for both Hydrometer Method and Combined Method. Use arithmetic scale and vertical axis for percent finer and log scale and horizontal axis for grain size. This curve is called grain size distribution curve. Calibration of hydrometer: The measurements by hydrometers and the precision of calculated data depend on the standard setting under which they are used; rectification for the temperature and the surface tension should be undertaken taken. In the similar manner the working temperature, kind of liquid and its surface tension, and the correct method of reading are the chief conditions that must also be taken into account during their calibration to obtain high accuracy (Lorefice and Malengo 2006) As a rule, hydrometers graduated in density units or having different scale units are both calibrated against density readings at the reference temperature t of 20 o C and for a range of surface tension on the basis of information they bear on it. Usually hydrometers are calibrated at three or four graduation marks of the scale and for each of them the correction C is calculated as C= ρx ρr Where, ρx is the density of liquid on which hydrometer freely float at the scale reading ρr. The estimation of ρx is particularly linked with the used calibration method. 11

12 Methods of Calibration: A. The direct comparison method: This technique is the simplest mode to check hydrometers by means of diverse standards liquids with known density. It is better if the standard physical properties such as density and surface tension are close to those of the liquids where the hydrometer under test is intended to float freely. The density of standards could be measured experimentally at the testing temperature, e.g. (i) by the relation between density by hydrostatic weighing of a sinker of known mass and volume, (ii) against a more accurate and temperature obtained reference hydrometer or by suitable density meters and (iii) finally, estimated by charts and tables in handbooks listing detailed information about the densities of solutions as a function of their composition (typically, in terms of per cent solute in the solution). The environmental temperature and the liquid temperature should be kept constant during the observations; otherwise if the temperature of the liquid changes, it can not only cause differences in density but also cast doubts about the actual temperature. However, the main drawback of the direct comparison method is due to the need to have several reference liquids with appropriate density in order to cover the whole liquid density range. B. The ring method: This is based on the principle of the constant-volume hydrometers; the hydrometer under test floats in a single liquid of known density and it is immersed to the tested scale reading ρr by loading the top of its stem with weights (Gupta and Nath, 1984). These weights are metallic rings of suitable material and size, chosen so that when one is slipped on the hydrometer under test the latter sinks down to the specified graduation. The mass of the rings required to float the hydrometer to graduation, depends upon the scale range, the volume of the bulb and the value of the density corresponding to the lowest graduation of the hydrometer under test. The number and the weight of the rings and the feature of the buoyant liquid have limited the application of this method. C. Hydrostatic weighting: The procedure to calibrate hydrometers based on hydrostatic weighing was introduced by Cuckow, Hydrometers of any range can be calibrated at 12

13 different designed graduation marks, measuring the buoyancy force when the hydrometer is placed in air and immersed in a reference liquid. At first, the hydrometer to be calibrated is weighed in air and then it is sunk into a reference liquid, whose density is known at the reference temperature, with the stem connected to an upper balance through a metal wire. The depth of immersion of the hydrometer is adjusted by a mechanical device so that the middle of the graduation under calibration is aligned with the horizontal surface of the reference liquid. In those situations where the range of the hydrometer to be calibrated is lower than the density of the reference liquid, additional weights are added to the hydrometer to cause it to sink. References: 1. Cuckow, F. W. A new method of high accuracy for the calibration of reference standard hydrometers, J.S.C.I, Gupta, S.V. and Nath, M. A method for calibrating low density hydrometer using a standard hydrometer calibrated for higher densities Bull. OIML vol. 54, pp. 7 10, John, D. and Wright V.E. NIST Calibration Service for Hydrometers, special publication, Lorefice, S. and Malengo, A. Calibration of hydrometers, Measurement science and technology, vol. 17, pp , Stott, V. and Dunstan, A.E. Hydrometers, in the Science of Petroleum, (London, Oxford University Press), vol. 3, pp , Wen, B., Aydin, A. and Duzgoren-Aydin, S. A comparative study of particle size analyses by sieve-hydrometer and laser diffraction methods, Geotech. Test. J., vol. 25(4), pp ,