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Measurement of fluid properties Essay

In this course, you will conduct the experiments at the Fluid Mechanics Laboratory, by yourselves, without any help or instruction from the teaching assistants. You must read the lab sheet thoroughly and understand what you are expected to do (and why) for each experiment, before coming to the lab. At the end of each experiment, you will have to do certain calculations, present and plot (when asked) your results on the provided report sheets attached to the end of the lab sheet.

The experiment and the report-writing will all take place in the lab within the time allocated to your group (total: 1 hour). You will not have any time to study the lab sheet during the lab hour, if you have not done so before. Therefore, you must come to the lab fully prepared. Although you perform the experiments as a group, each person will submit a separate report (not a single group report) at the end of the lab hour. There will be no “group study” in writing the reports – everyone will prepare his/her report individually using the data he/she recorded during the experiments.

For Experiment 1, you must bring a calculator to the laboratory. You must also have your watch or a timer (you will record time in one of the experiments).

The density of a liquid is to be measured using a hydrometer.

1.1.2 Theory
A hydrometer uses the principle of buoyancy to determine the specific gravity of a liquid. Here, the weight of the hydrometer (set by the metal spheres in
its bulb) is balanced by the buoyancy force exerted by the liquid in which it is immersed. The buoyancy force is the weight of the liquid displaced by the solid. Figure 1.1 presents the working principle of a hydrometer. In this sketch, a hydrometer is shown submerged in two different liquids. The stem of the hydrometer has a cross-sectional area of A. If the liquid is distilled water (Figure 1.1a), then its specific gravity will be 1.0. At equilibrium,

W = ρw g V

* revised by M. Erdal, October 2011

Figure 1.1 A hydrometer in distilled water and in another liquid where W is the weight of the hydrometer, ρW is the density of the distilled water, g is the gravitational acceleration ( 9.81 m/s2 ) and V is the volume of the submerged part of the hydrometer in distilled water . The position of the distilled water surface is marked on the stem of the hydrometer to indicate the reference specific gravity. When the hydrometer is now floated in another liquid with a specific gravity of s, as shown in Figure 1.1b, the equation for the vertical equilibrium becomes where ρ indicates the density of the second liquid. Note that h would be measured as a negative value for liquids lighter than water, i.e. when the position of the liquid level on hydrometer is above the reference level (s = 1.0). Combining Equations (1.1) and (1.2) and solving for s yields

The liquid position on the stem may then be marked off to read the liquid specific gravity, s (Figure 1.1b).

1.1.3 Experimental Procedure
The hydrometer to be used in the measurement is shown in Figure 1.2. On the hydrometer scale (Figure 1.2 (a)), the level 1000 refers to the water level,
s = 1.0. The remaining levels above are scaled relative to s = 1.0, e.g. the level 700 corresponds to s = 0.7 and so on. In the lab test set-up, you will

Read the specific gravity, s, of the liquid from the stem of the hydrometer, at the position where the liquid interface intersects the stem of the hydrometer. Record s onto the data table in the report sheet.

(iii)

Find the value of the density of water, ρw, at the recorded temperature by using the water thermodynamic table provided to you in the lab. Record this density onto the data table in the report sheet.

(iv)

Evaluate the density of the liquid, ρ, as

ρ = s ρw

(1.4)

and show the calculation in the report sheet.

MEASUREMENT OF VISCOSITY

1.2.1 Objective
The viscosity of a liquid is to be measured using a Saybolt Universal Viscometer.

1.2.2 Theory
Several different types of viscometers are used for viscosity measurements. These are (i) efflux, (ii) rotating and (iii) falling sphere type viscometers.

Saybolt viscometer, the sketch of which is shown in Figure 1.3, is one of the efflux type viscometers and accepted as a standard instrument in U.S.A. Various others used in Europe are Engler (Germany), Reduced (England) and, Barbey (France).

Saybolt viscometer consists of a narrow reservoir connected to a small discharge tube. The reservoir is filled with the liquid whose viscosity is to be determined. Under the action of gravity, the liquid of unknown viscosity flows through the discharge tube into a standard receiving flask with a capacity of 60 cm3. When the flask is filled with the liquid up to its neck, the full capacity of the flask is reached (60 cm3 of liquid).

Figure 1.3 Saybolt Standard Viscometer

After the cork at the bottom of the viscometer is removed, the time in seconds, which is known as the Saybolt Universal Seconds (S.U.S.), for the liquid to fill the 60 cm3 standard flask is measured. This may then be converted to kinematic viscosity, by using the formula where A and B are calibration constants having the values of 0.226×10-6 m2/s2 and 195×10-6 m2, respectively, ν is the kinematic viscosity in m2/s and t is the time in s. The determination of viscosity is based on the premise that liquids with higher viscosities would take longer to fill the flask since their resistance to deformation (and hence, flow) would be higher. Note that
the determined property is kinematic viscosity, rather than dynamic viscosity, as the density of the liquid is an influential factor for flow due to gravity.

1.2.3 Experimental Procedure
The Saybolt viscometer in the lab is shown in Figure 1.4. In this viscometer, there are 4 different liquid reservoirs, each attached to a separate outflow tube (each end is sealed with a different

Check (by visual inspection) if reservoir 2 is filled with the liquid. Make
sure the cork below the reservoir 2 tube is in place. If reservoir 2 is not filled with the liquid, one or both flasks will have the liquid in them. Fill reservoir 2 by pouring the liquid from the flask(s). Place the empty flask (the one with the 60 cm3 level marked) under the reservoir 2 tube.

(ii)

Remove the cork at the bottom of the tube to start the flow. (iii)

Record the time for the liquid to fill the flask up to the 60 cm3 level and write this value in your report.

(iv) Convert the Saybolt Universal Seconds to the kinematic viscosity using Equation (1.5). 1.3

CALIBRATION OF A BOURDON GAGE BY USING A DEAD WEIGHT
TESTER

1.3.1 Objective
A Bourdon gage is to be calibrated using a dead weight tester.

1.3.2 Theory
A dead weight tester, the schematic of which is shown in Figure 1.9, is a device by which the exact values of fluid pressure may be produced through the use of standard weights acting vertically on a frictionless piston of known area. A Bourdon gage, which is attached to the other end of the tester, can be calibrated by reading the values indicated by its pointer, and comparing with the corresponding pressure values due to the presence of the weights on the piston.

The tightening of the screw will increase the pressure of the oil under the piston. The oil exerts pressure on the piston and the Bourdon 5 gage. As the piston starts to rise, the pressure applied by the weights becomes equal to the oil pressure inside the piston. The readings on the Bourdon gage should be recorded at this equilibrium. By changing the number of weights on the piston and recording the corresponding gage readings, a calibration curve for the Bourdon gage can be obtained.

weights
Bourdon
gage
piston

screw

Figure 1.9 Dead-weight tester

1.4.3 Experimental Procedure
The dead weight tester and the weights in the Fluid Mechanics Laboratory are shown in Figure 1.10. The Bourdon gage to be calibrated is attached to the tester. The weights are to be loaded on the piston on the left. The magnitude of each weight is written on it. (i)

Release the pressure under the left piston by turning the piston counterclockwise.

(ii)

Without placing any weights, tighten the screw (turn clockwise) until the left piston rises. During tightening, spin the upper end of the left piston slowly clockwise to reduce the friction between the piston and the cylinder. By tightening the screw, you are pressurizing the oil under the piston so that this pressure can overcome the weight of the piston.

(iii)

Record the pressure reading, p1, on the Bourdon gage. This is the pressure corresponding to the weight of the piston.

piston to be
loaded with
weights

Bourdon gage to
be calibrated
weights

screw

Figure 1.10. Dead-weight tester and the weights at the Fluids Mechanics Laboratory

6

(iv)

Record the applied pressure, p2, by the dead weight tester (p2 = 1 kg/cm2 without any extra weights on the piston; i.e. this is the pressure that the piston weight exerts)

(v)

Release the screw by turning it counterclockwise.

(vi)

Repeat steps (ii) to (v) by adding different weights on the piston. Note that you will record a total of 5 data points. Obtain pressure values that cover the range of the Bourdon gage, as evenly as possible.

(vii)

Plot the p1(y-axis) versus p2(x-axis) curve for the calibration of the Bourdon gage.

(viii)

Find the calibration constant of the Bourdon gage (the slope of the graph) and comment on the result briefly.

7

NAME OF THE STUDENT:

LABORATORY GROUP:

LIST NUMBER:

DATE:

NAME OF THE LAB. SUPERVISOR:

COURSE SECTION:

ME 305 FLUID MECHANICS I
EXPERIMENT 1 REPORT
MEASUREMENT OF FLUID PROPERTIES

1.1

MEASUREMENT OF THE DENSITY OF A LIQUID

1.1.1 Data
Temperature (°C)
Specific gravity, s
Density of water, ρw,@15°C (kg/m3)

1.1.2 Calculation and Result

1.2

MEASUREMENT OF VISCOSITY

1.2.1 Data

S.U.S.

1.2.2 Calculation and Result

ME 305 – Experiment 1 Report

Page 1 of 2

1.3

CALIBRATION OF A BOURDON GAGE BY USING A DEAD WEIGHT
TESTER

1.3.1 Data
p1 (kg/cm2)
[Bourdon gage reading]

p2 (kg/cm2)
[Dead weight]

1.3.2 Plot of p1 versus p2 Curve
p2 (kg/cm2)

p1 (kg/cm2)
1.3.3 Calculation of Calibration Constant of Bourdon Gage and Comments

ME 305 – Experiment 1 Report

Page 2 of 2


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