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FALL 2015

MIDDLE EAST TECHNICAL UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING

ME 305 FLUID MECHANICS I GROUP 01

EXPERIMENT 1 MEASUREMENT OF FLUID PROPERTIES

PREPARATION: In this course, you will conduct the experiments at the Fluid Mechanics

Laboratory, by yourself, with little 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. You must use a pen (not a pencil) when recording your

data. Although you are going to perform the experiment as a group, each student will submit a

separate report using the data recorded during the experiment. The report of the experiment is

attached to this manual. You will complete the report and submit it at the end of the lab period.

You will complete the report in 1 hour following the experiment and submit it before leaving the lab.

There cannot be a “group study” in writing the reports – everyone will prepare his/her report individually

using the data recorded during the experiment.

1.1 MEASUREMENT OF THE DENSITY OF A LIQUID

1.1.1 Objective

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 density of a liquid. When

it floats in a liquid, its weight (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 immersed part of the hydrometer. In Figure 1.1, a hydrometer is shown

submerged in two different liquids. Reference liquid has a known density of ref (Figure 1.1a).

Weight of the hydrometer is balanced by the buoyancy force applied by the reference liquid,

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Figure 1.1 A hydrometer in reference liquid of known density and in a test liquid of unknown density

refW g (1.1)

where W is the weight of the hydrometer, g is the gravitational acceleration (9.81 m/s2) and is

the volume of the submerged part of the hydrometer in reference liquid. The free surface level

corresponds to 1 h on the hydrometer scale.

When the hydrometer is floated in the test liquid (Figure 1.1b) the free surface level

corresponds to 2 h on the hydrometer scale. The equation for the vertical equilibrium becomes

( )test gW Ah (1.2)

where test is the unknown density of the test liquid, A is the cross-sectional area of the stem and

2 1 h h h . For the case shown in Figure 1.1, test liquid has a higher density than the reference

liquid and h is positive. h would be a negative value for liquids lighter than the reference liquid.

Combining Equations (1.1) and (1.2) and solving for test yields

test ref Ah

(1.3)

h1 level

(a) Reference liquid of known density

gstem

bulbtiny

metal spheres

(b) Test liquid of unknown density

h2 level

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1.1.3 Experimental Procedure

You will be using

a hydrometer

a Vernier calliper

a graduated cylinder filled with reference liquid

a container filled with test fluid of unknown density

These can be seen in Figure 1.2. Reference liquid is alcohol with density

3804 kg / mref . The hydrometer scale starts from zero at the top of the stem and ends at 120

mm at the bottom.

(a) (b) (c)

(d)

Figure 1.2 (a) Graduated cylinder with alcohol in it, (b) Hydrometer, (c) Bucket with test liquid in it, (d) Vernier calliper

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The Vernier calliper that you will be using has Vernier scale increment of 0.05 mm.

Figure 1.3 shows how to use it.

Figure 1.3 How to use a Vernier calliper

Step by step procedure is as follows:

(i) Using the Vernier calliper measure the diameter of hydrometer’s stem and record it

in the report sheet as D.

(ii) Without the hydrometer in it, read the alcohol level inside the graduated cylinder and

record it as initial in the report sheet.

(iii) Put the hydrometer inside the alcohol and read the new alcohol level in the graduated

cylinder. Record it as final in the report sheet. Also read the free surface level on the hydrometer

scale and record it as 1h in the report sheet.

(iv) Take the hydrometer out of the alcohol, clean it and put it inside the dark test liquid.

Read the free surface level on the hydrometer scale and record it as 2h in the record sheet.

(v) Calculate in Equation (1.3) by using final initial .

(vi) Calculate h in Equation (1.3) by using 2 1h h h .

(vii) Calculate A of Equation (1.3) by using 2 / 4A D .

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(viii) Calculate the density of the test liquid by using Equation (1.3).

1.1.4 Uncertainty Calculation

In Figure 1.4 a ruler is used to measure the length of an object. The length is between 38

mm and 39 mm, closer to 38 mm. It is possible to report this measurement as

38 mm 0.5 mmL L

where 38 mmL is the part of the measurement we’re certain about and 0.5 mmL is the

uncertainty, which is taken as half of the smallest scale of the ruler. This reporting means that

the actual value is between 37.5 mm and 38.5 mm. A more careful eye can claim that the

measurement must be reported as 38.5 mm 0.5 mm , which is also acceptable and has the same

uncertainty of 0.5 mm.

Figure 1.4 Measuring the length of an object with a ruler

Consider that the width of the object is also measured as

5 mm 0.5 mmW W

If the task is to calculate the area of this object we can use

2 38 mm 5 mm 190 mmA LW

But what about the uncertainty of A? How does L and W contribute to A? Using a

first order Taylor series analysis it is possible to show that uncertainties propagate as follows:

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A A

A L WL W

(1.4)

which gives the following result

25 mm 0.5 mm + 38 mm 0.5 mm 22 mmA W L L W

Therefore the proper way to report the area calculation is

2 2190 mm 22 mmA A

which means the actual area is between 168 mm2 and 212 mm2.

Let’s apply the idea to the calculation of test . Equation (1.3) can be written as follows:

2

4

test ref Dh

(1.5)

To calculate test , Equation (1.5) uses the measured quantities of , D and h.

Uncertainties of these measurements can be linked to the smallest scales on the measuring

devices as follows:

5 31 ml 0.5 10 m

2

40.05 mm 0.25 10 m

2D

31 mm 0.5 10 m

2h

Following the idea behind Equation (1.4), uncertainty of test can be calculated using

test test testtest D h

D h

(1.6)

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where

2

22

4

4

testref

Dh

Dh

22

2

4

testref

Dh

D Dh

2

22

4

4

testref

D

h Dh

Here, we assumed that ref is exact (free of uncertainty).

In the report sheet, calculate test using Equation (1.6) and determine the measurement

that contributed the most to it.

1.2 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 1.5, 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).

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Figure 1.5 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

t

BAt (1.7)

where A and B are calibration constants having the values of 0.226x10-6 m2/s2 and 195x10-6 m2,

respectively, 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 1.6. In this viscometer, there are 4

different liquid reservoirs, each attached to a separate outflow tube (each end is sealed with a

different cork) as shown. You will use reservoir 2 in this experiment. There are two flasks

provided to you to help fill the reservoir with the appropriate amount of liquid.

minimum level of the liquid in the

reservoir

universal outlet tubecork

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Figure 1.6 The Saybolt Viscometer in the Fluid Mechanics Laboratory

(i) Check (by visual inspection) if reservoir 2 is filled with the liquid. Make sure the

cork below the tube of reservoir 2 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).

(ii) Place the empty flask (the one with the 60 cm3 level marked) under the tube of

reservoir 2. 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

(1.7).

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 1.7, 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

the two flasks

cork on the outlet tube of reservoir 2

other reservoirs

the two flasks

reservoir 2

60 cm3 level mark on the flask

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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 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.

Figure 1.7 Dead-weight tester

1.3.3 Experimental Procedure

The dead weight tester and the weights in the Fluid Mechanics Laboratory are shown in

Figure 1.8. 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, 1p , on the Bourdon gage. This is the pressure

corresponding to the weight of the piston.

(iv) Record the applied pressure, 2p , by the dead weight tester ( 2p = 1 kg/cm2 without

any extra weights on the piston; i.e. this is the pressure that the piston weight exerts)

weight

piston

screw

Bourdon gage

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Figure 1.8 Dead-weight tester and the weights in the Fluids Mechanics Laboratory

(v) Release the screw (and reduce oil pressure) 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 1p (y-axis) versus 2p (x-axis) curve for the calibration of the Bourdon

gage.

(viii) Find the calibration constant of the Bourdon gage (the slope of the graph).

screw

Bourdon gage to be calibrated

piston to be loaded with

weights weight

NAME OF THE STUDENT: LABORATORY GROUP:

ID NUMBER: DATE:

NAME OF THE LAB. SUPERVISOR: COURSE SECTION:

ME 305 FLUID MECHANICS I

EXPERIMENT 1: MEASUREMENT OF FLUID PROPERTIES

EXPERIMENT REPORT

1.1 MEASUREMENT OF THE DENSITY OF A LIQUID

1.1.1 Data

ref (kg/m3) 804

D (mm)

1 (ml)

2 (ml)

1h (mm)

2h (mm)

1.1.2 Calculation and Result

h

A

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Calculate test below:

1.2 MEASUREMENT OF VISCOSITY

1.2.1 Data

S.U.S.

1.2.2 Calculation and Result

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1.3 CALIBRATION OF A BOURDON GAGE BY USING A DEAD WEIGHT TESTER

1.3.1 Data

1p (kg/cm2)

[Bourdon gage reading] 1p (kg/cm2)

[Dead weight]

1

2

3

4

5

1.3.2 Plot of 1p versus 2p Curve

1.3.3 Calculation of Calibration Constant of Bourdon Gage

(kg/cm2)

(kg/cm2)