The first method of mechanical analysis is sieve analysis. It is pretty straight forward and involves straining a soil sample through a series of sieves. Generally the sieves are stacked as seen in the above diagram with a US Standard Sieve No. 4 at the top (This sieve size has a 4.75 mm opening) and a Sieve No. 200 at the bottom (with a 0.075 mm opening). The stack usually consists of 5 to 7 sieves and has a pan at the bottom. As you can see, the opening in the sieve gets smaller as you go down. Therefore larger particles will be captured while smaller particles will pass through. This allows us to measure how much soil of each size was in the original soil sample.
A few important steps:
- the soil sample needs to be oven-dried and all clumps broke.
- the weight of the empty sieves needs to be obtained.
Once this is done, the soil sample is placed into the top sieve, the lid is placed on the stack and the stack is placed in a mechanical shaker. The stack will then be shaken vigorously for approximately 5 minutes to ensure proper distribution of the particles.
The next step is to calculate what is called the percent passing or the percent finer. This is simply the percentage of the entire soil sample that passed through a particular sieve. For example, the percent passing the No. 200 sieve would be the mass of the soil in the bottom pan (since that is the soil that passed through the No. 200 sieve) divided by the total mass of the original soil sample. So in general we can write:
- %P is the percent passing
- i represents the ith sieve
- n represents the number of sieves
- m is the mass
Once the percent passing is determined for each sieve, a plot is made of sieve or particle size versus percent passing as seen below. The percent passing is on the ordinate and the sieve or particle size is on the abscissa. Also notice the abscissa is reverse logarithmic.
In future posts we will look more carefully at what information this distribution curve can provide, but for now we are highlighting the process. If you have any questions, please let me know in the comments.
Another frequently used measure of water quality along with electrical conductivity and turbidity is the pH. pH is a measure of the hydrogen ion activity in a solution. Solutions with high hydrogen (H+) or hydronium ion (H3O+) activity are called acids and solutions with low hydrogen ion activity are called bases. Another way of looking at it is by looking at the reciprocal quantity of hydroxyl ions (OH-). The more hydroxyl ions, the more basic a solution is and so on. pH is a mathematical way of quantifying these concentrations and placing them on a relative scale. It is defined as:
In a parallel fashion the quantity pOH is defined as:
Conversely, to determine the activity or concentrations given the pH or pOH, we have:
The relationship between pH and pOH at standard temperature conditions (25 degrees Celsius) is:
pH + pOH = 14
From here, we can see that the relative scale used is from a pH of 0 to a pH of 14 with 0 being very acidic, 14 being very basic, and 7 being neutral.
There are 2 basic types of techniques for measuring pH. The first type is called colorimetric measurement. The use of litmus paper is a colorimetric technique. The second type is called electrometric and is done using an electrical instrument. The instrument is calibrated with 3 standard solutions at known pHs of 4, 7, and 10. Then the instrument can be used to measure unknown solutions. The typical range for drinking water is ideally around 6 – 8.5.
The specific gravity of soil is an important weight-volume property that is helpful in classifying soils and in finding other weight-volume properties like void ratio, porosity, and unit weight. In this lab we first weighed an empty 1000 mL graduated cylinder. Then we filled it to 500 mL with distilled water and weighed it again. This allowed us to find the density or unit weight of the water. Secondly we filled another graduated cylinder with a mixture of soil and water. This mixture was heated on a stove to remove air from the mixture. Then it was filled to the 500 mL mark with additional distilled water and weighed. Finally an oven-safe container was weighed empty and then the soil/water mixture was poured into the container and dried in the oven for a 24-hour period. This enabled us to find the weight of the dry soil solids. Once this procedure was completed and the data collected, the specific gravity could be obtained via the following computations.
The specific gravity is defined as the ratio of the unit weight of the soil solids to the unit weight of water.
The unit weight of the soil solids is given by:
Where Ws is the weight of the soil solids and Vs is the volume of the soil solids. Likewise the unit weight of water is given by:
Consequently we can substitute these expressions into the first equation and obtain:
To obtain the weight of the soil we subtracted the weight of a dish container from the weight of the dish container with the oven-dried soil.
The volume of water we used was known at 500 mL.
The weight of the water corresponding to this volume was simply obtained by subtracting the weight of the flask or graduated cylinder from the weight of the flask with the volume of water.
Determining the volume of the soil was more difficult. We used the mixture that consists of the flask, soil, and water. Here the volume of the soil will be the total volume minus the volume of the water. (The volume of air is negligible)
In order to evaluate this we make the assumption that the unit weight of the water is constant.
We know all the values in this last expression except Ww2. This is the weight of the water in the water-soil-flask mixture. It can be found by:
This is all the information we needed. Simply substitute the solution from this last equation into the equation for the second volume of water, the solution from that into the equation for volume of soil, and all the known and determined values into the substituted equation for specific gravity to obtain the specific gravity. Here are the values and calculations we obtained in our experiment.
This was a reasonable finding since the specific gravity of soils typically falls in the range of 2.6 to 2.9.
Another method of analyzing water quality is through the measurement of turbidity and its correlation with total solids. Turbidity is a relative measure of the clarity of a water sample by measuring the scatter of light as it passes through a sample. A sample with high turbidity will appear unclear while a sample with low turbidity will appear more clear because light passes through it with less scatter and absorption. It is relative in that it is measured against a standardized sample of stabilized formazin or gelex. The preferred units used in turbidity measurements are nephelometric turbidity units or NTUs. It is usually measured with a nephelometric turbidimeter or spectrophotometer. A key point here is that the turbidity can be measured in just a few minutes including calibration.
Total solids can be categorized into 4 categories: suspended solids, dissolved solids, settable solids, and volatile solids. They include all the solid materials that are contained in the water matrix. They can be measured as a concentration of the sample volume using gravimetric measurement techniques. This requires that we use an Imhoff cone to measure settlable solids, a filter to measure suspended solids, and the filtrate to measure dissolved solids. Usually suspended solids is the primary concern. These constituents are what typically affect the clarity of the water. However since it is time consuming and not necessarily practical to collect a sample, put it in an evaporating dish, evaporate the water in an oven over the course of 24 hours or more, and weight the solids remaining, we attempt to find a correlation between suspended solids and turbidity. Turbidity cannot by itself be used to quantify the concentration of suspended solids in a body of water. However by analyzing a few samples we can find and plot the correlation between concentration of suspended solids and turbidity. This gives us a relationship (valid only for a particular location and time) so that we can determine the amount of suspended solids in a body of water by simply measuring the turbidity.
The primary reasons that suspended solids are a concern is first, simple aesthetics and second, the harboring of pathogens or pathogen supporting envirnoments. The EPA has set primary drinking water quality standards at less than 1 NTU. Prior to 2002, less than 5 NTU was acceptable.
Our second electical circuits lab was an exercise in verifying Ohm’s Law. To start, let’s look at what Ohm’s Law is and the theory behind it.
All materials have a general property of resisting the flow of electricity through themselves. This material property is quantitatively called the resistivity. (Interesting enough, resistivity is the reciprocal of conductivity.) The more difficult it is for electricity to flow through a material, the higher the resistivity value. Resistivity is purely a material property and does not depend on any particular configuration or geometry of the material. It can however be affected by temperature changes. The resistance, on the other hand, is a function of this material property, but also of the material shape. This relationship is given by:
Where R is the resistance, ρ is the resistivity, L is the length of the portion of material, and A is the uniform cross-sectional area.
The circuit element that we utilize as a model for resistance is called the resistor. The German physicist Georg Ohm investigated the relationship between the voltage across a resistor and the current through a resistor. Through this study he developed the following relationship known today as Ohm’s Law:
In order to verify this relationship for ourselves, we experimentally varied one element of the voltage, current, and resistance, kept one constant, and took readings and recorded values for the third. Then we determined the error between these recorded values and the expected values given by Ohm’s Law. Below are the tables of calculated values, measured values, and percent error for 3 different configurations.
The equipment we utilized and had set up in the first configuration consisted of a power supply (DC), a potentiometer, and the digital multimeter. The apparatus was configured as follows:
Here is the procedure for the first configuration.
- Ensure the power supply is in the off position.
- For part A we kept the voltage constant at 10 volts. Therefore, the first step is to connect the power supply to the digital multimeter with 2 leads, set the multimeter to read DC voltage, turn the power supply on, and adjust the voltage on the power supply until the multimeter reads 10 volts.
- Turn the power supply back off.
- Next connect the lead (we used red) from the positive terminal of the power supply to positive or red terminal of the potentiometer.
- Using a lead (we used black), connect the negative or black terminal of the potentiometer to the lower left black terminal of the digital multimeter.
- Using a lead (we used two leads in series for length and end plugs) Connect the lower right red terminal (for reading current) of the digital multimeter to the negative or black terminal of the power supply. At this point the circuit is complete.
- Set the digital multimeter to read milliamperes of current.
- Turn the power supply on.
- Adjust the switches on the potentiometer to obtain the required value for the current displayed on the multimeter. (See the data tables for more. The values were 10,9,8,7… and so on.)
- Add up and record the resistance supplied by the potentiometer that generated the corresponding current value.
- Compare this resistance value to the resistance value predicted by Ohm’s Law. Computer the percent error for each measurement.
- Repeat steps 9 through 11 for each required current value.
Here is a graph of our results for the first configuration. It shows the calculated values using Ohm’s Law, the measured values, and a predictive trendline with equation using the calculated values.
This first configuration gives you the idea. I have the procedure and graphs for the other implementations if anyone is interested. I have omitted them here for brevity.
Our first environmental engineering lab was concerning one method of water quality assessment called electrical conductivity. The theory behind this technique is based on the fact that pure water is not a good conductor of electricity. As the amount of inorganic, ionic elements or compounds in the water increases, the conductivity also increases. Conductivity also increases with temperature, therefore most results are standardized at 25 degrees Celsius. With this understanding we can make comparative analysis of conductivity values to assess the purity of the water. Conductivity in this context is usually in units of microsiemens per centimeter. In the lab we utilized a handheld electrical conductivity meter like the one above. Below is a table we were given of the typical value range found in different types of water.
The reason for the high conductivity in seawater is the high salt content and thus a high number of sodium and chloride ions in this aqueous solution. If you are interested in additional information, I found a good EPA website concerning water quality monitoring and electrical conductivity.
My first soil mechanics lab was an exercise in analyzing the moisture content of a soil mixture. Soil is an aggregate consisting of what are called “phases”. The 3 phases are solids (tiny rocks and minerals), water, and air. The water and air make up what is called the void space. In evaluating moisture content (w), we are only interested in the water and solids portion. In fact, the moisture content is defined as the ratio of the weight of the water content (Ww) to the weight of the solid content (Ws). The weight of the air is considered negligible.
The procedure we followed to obtain values for these calculations was to use 3 small metal tins or canisters. First we used a digital scale to measure the weight of each canister. This weight we called W1. Next we partially filled each canister with a small sample of soil. Next we measured the canister and the soil. This weight we called W2. Finally we placed the canisters in a soil drying oven to dry out the soil and remove the water from the samples. After 24 hours we returned to the lab and used the digital scale to measure the dried soil samples in the canisters. This weight we called W3. To find the weight of the water (Ww) we used:
To find the weight of the solids (Ws) we used:
Here is a tabulation of the results we obtained: