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CE 412L: Fluid Mechanics Laboratory | Experiment No. 1: Determination of Specific Gravity by U-Tube

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EXPERIMENT NO. 1

DETERMINATION OF SPECIFIC GRAVITY BY U-TUBE

Year and Section: 4CE-A Date Started: August 17, 2015

Group Number: 5 Date Finished: August 17, 2015

Group Members: Date Submitted: August 23, 2015

Leyno, Iana Renza L. Montenegro, Louis M.

Lintao, Reychito Jr. P. Montes, Mark Rainier L.

Malenab, Cesar Jr. P. Nakaegawa, Akira Q.

Medina, Mark Laurence A. Pasagui, Christal M.

1. OBJECTIVE/S This activity aims to determine the specific gravity of an unknown liquid using U-tube manonmeter 2. APPARATUS AND SUPPLIES U-tube manometer Beaker Dropper 3. PROCEDURE

1. Pour some amounts of the liquid of unknown specific gravity into the tube until the liquid reaches a level of approximately 3mm.

2. Pour water into both ends to a height of at least 9mm from the level of liquid 3. Pour an additional amount of water into the right leg of the U-tube until there is a

noticeable difference in water level 4. Record the height of the water level and the unknown liquid in the two legs of the

manometer 5. Repeat steps (3) and (4) for additional trials until water is about to overflow

CLEANING PROCEDURE

1. Clean the apparatus before each trial 2. After the experiment, dispose the unknown liquid properly 3. Clean the apparatus supply with soap and water and dry them thoroughly before

returning them 4. DATA AND RESULTS

Trial Height of water (cm)

Height of unknown liquid (cm)

Specific gravity (sg)

cd (left) bc (right) ab (right) de (left)

1 4.2 2.9 4.6 2.9 0.765

2 4.2 2.8 4.8 2.9 0.737

3 4.3 2.7 4.9 2.9 0.800

4 4.5 2.55 5.1 2.9 0.909

5 4.6 2.4 5.2 2.9 0.957

6 4.7 2.35 5.28 2.9 0.988

Average Specific Gravity 0.859

Table 1 - Results


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5. FORMULAS AND COMPUTATIONS

sg = cd bc ab de Where

sg = Specific Gravity cd, bc = Height of Water ab, de = Height of Unknown liquid

average specific gravity = sg no. of trials

5.1 Specific Gravity 5.1.1 TRIAL 1 sg = 4.2 2.9 4.6 2.9 sg =0.765 5.1.2 TRIAL 2 sg = 4.2 2.8 4.8 2.9 sg =0.737 5.1.2 TRIAL 3 sg = 4.3 2.7 4.9 2.9 sg =0.800 5.1.2 TRIAL 4 sg = 4.5 2.55 5.1 2.9 sg =0.909 5.1.2 TRIAL 5 sg = 4.6 2.4 5.2 2.9 sg =0.957 5.1.2 TRIAL 6 sg = 4.7 2.35 5.28 2.9 sg =0.988

5.2 Average Specific Gravity Ave = 0.765+0.737+0.800+0.909+0.957+0.988 6 Ave = 0.859


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6. FIGURES/DIAGRAMS/GRAPHS

Figure 1 Materials

(Beaker, Dropper, U-tube manometer)

Figure 2 Unknown Liquid and Water


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Figure 3 Actual Experiment

7. SOURCES OF ERRORS The experiment is an activity composed of simple instructions to follow. Carefully proceeded with the instructions, we might have been able to achieve a more consistent set of data, thus, obtaining an ideal specific gravity of the unknown liquid. Here are some of the errors that have been noticed during the said experiment:

Human Error liquid formation inside the segment of water Human Error reading of liquid and water Human Error formation of bubbles

Instrumental Error Dropper Instrumental Error U-tube Manometer

There are three human errors being stated here. First is the liquid formation inside the segment of water. Since the U-tube manometer has one end closed, we cant follow the normal procedure, instead, we went by unknown liquid-water-unknown liquid. And because of the water being poured in the middle, there were chances that some drops of unknown liquid went in the waters segment. Next, we have the error while reading the measurement of liquid and water. Since the water and unknown liquid are of the same color, it is hard to check the real reading on the U-tube manometer. Lastly, we have the formation of bubbles. In our group, we take turns using the dropper and some of the members have their hands shaking while using the dropper. Some of the drops they make forms bubbles at the end of the segment of the liquid being poured. Secondly, we have two instrumental errors. The first instruction was to pour 3 mm of unknown liquid and then 9 mm of water. The dropper doesnt have any reading on it and since all the liquid being


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placed in the U-tube manometer goes at the bottom part (The bottom part has no reading.), we just assumed the amount of liquid being poured. And last, we have the U-tube manometer, the instructions being given were not followed because the other end of the apparatus is closed. Thus, having slight errors of the placement of water and unknown liquid. 8. CONCLUSIONS AND REMARKS The term specific gravity, symbolized sp gr, refers to the ratio of the density of a solid or liquid to the density of water at 4 degrees Celsius. The term can also refer to the ratio of the density of a gas to the density of dry air at standard temperature and pressure, although this specification is less often used. Specific gravity is a dimensionless quantity; that is, it is not expressed in units. There are many methods that can be used to determine the specific gravity of liquids. One method uses the hydrometer, an instrument that gives a specific gravity reading directly. Another is the bottle method wherein a flask made to hold the unknown liquid at a specified temperature is weighed and is to be divided by the weight of an equal volume of water to give the specific gravity of liquid. The method used in the experiment is by using a U-tube manometer and getting the height of the liquids. Because the hydrostatic pressure does not vary horizontally, across the connected water, the pressure in the U-tube at the height of the line at the reading of the apparatus is the same on both sides. Starting at the free surface of the oil, we can write: P line = unknown liquid g H unknown liquid. The pressure of the line can also be calculated by the water: P line = water g H water. Equating these two pressures gives: P line = water H water = unknown liquid H unknown liquid which can be re-written as S.G. unknown liquid = unknown liquid/ water which is also equal to, in this experiment, H water (cd-bc)/ H unknown liquid (ab-de).Thus, obtaining 6 different ascending specific gravities from 6 trials. And getting the mean of this data gives us a specific gravity of 0.859 for the unknown liquid. Although we have obtained this specific gravity, there are a few recommendations for the said experiment, especially with the materials and apparatus being used. To have better results, first, we think that the dropper should have a reading in order to attain a more accurate result. Another is the U-tube manometer, having both of the ends of the apparatus open may lower the chances of having the unknown liquid mixed in the segment of water. Third, we also think that changing the color of the liquid or choosing a liquid with color can help the students see the reading better. And last is when a group makes an error, we hope that there is an apparatus that can help in the drying of the U-tube manometer. All these are just recommended ways in order to lessen the amount of error and to help the next batch that will perform the experiment. This experiment is a great way to define the specific gravity using the pressure or pressure head equation. We also learned that using a U-tube manometer enables the pressure of both liquids and gases to be measured with the same instrument. And that the fluid whose pressure is being measured should have a mass density less than that of the manometric fluid (water: sg = 1) and the two fluids should not be able to mix readily. Other problems with regards to this experiment will greatly rely, not just on the instruments, but also on the performance of the students doing the experiment.

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