(1.) density and specific gravity measurements

7/21/2019 (1.) Density and Specific Gravity Measurements

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DENSITY AND SPECIFIC GRAVITY MEASUREMENTS

I.

DEFINITIONS

1.

Density:

Density of a material is the mass per unit volume

V

M =

Where M is the mass (kg or Lb) and V is the volume of the material (m3

or ft3). Therefore, the unit of the density, ρ, is kg/m

3 (in SI system) or

Lb/ft3 (in British unit). Since the volume of a material changes with

temperature while the mass remains constant, the density of a material is

a function of temperature.

2.

Specific Gravity:

Specific gravity of a material is the ratio of the density of the material to

the density of a reference substance at a specific condition. Usually

density of water at 4oC is used as the reference.

FGS

=..

Where ρF is the density of water at 4oC

CHE 215 page of 11 H. Muhamad1



II.

MEASUREMENT OF LIQUID DENSITY

1.

Pycnometer:

A pycnometer is a standard bottle with an accurate volume calibrated at

a specific temperature, e.g. 25 mL calibrated at 20oC. The density of a

liquid can be determined as below:

V

W W 12 =

Where W1 is the weight of the empty pycnometer, W2 is the weight of

the pycnometer filled with liquid and V is the volume of the pycnometer

What would you do if the liquid temperature is not at the calibration

temperature of the pycnometer?




2.

Hydrometer:

A hydrometer consists of a glass float with a weight at the bottom and a

stem on the upper part. The stem has a graduated scale for the specific

gravity reading.

In order to measure the specific gravity of a liquid, simply place the

liquid in a container and let a hydrometer float in the liquid. Once the

hydrometer is stable, take the reading on the scale right at the liquid

level. Make sure that the hydrometer doesn’t touch the wall of the

container so to avoid error in the specific gravity determination.




A hydrometer is:

• easy to use, inexpensive

•

fairly accurate, adaptable to on-line measurement

With a fluid at some reference density, the iron core is symmetrical

across coil 1 and coil 2. As a result, the output voltage is equal to zero.




When the liquid density increases, the iron core moves up with the

hydrometer, resulting in a finite positive voltage output. On the other

hand, when the liquid density decreases, the iron core moves

downwards, resulting in a negative voltage output. The voltage output

can be measured and calibrated to give readings in density or specific

gravity of liquid.

Specific Gravity Scales:

1. Common scale:

C atwater

GS4

..

=

However, usually hydrometer is calibrated at 60oF (15.6

oC). In other

words, the measurement of the specific gravity by the hydrometer is the

ratio of the density of a liquid at 60oF to the density of water at 60

oF.

2.

Degree API (American Petroleum Institute)

5.1315.141

W

L

API Degree

Where ρL and ρW are densities of liquid (usually petroleum) and water

both at 60 oF, respectively.




3.

Degree Baume

For liquid lighter than water:

130140

W

L Baume Degree

Where ρL and ρW are densities of liquid and water both at 60

oF,

respectively.

For liquid heavier than water:

W

L

Baume Degree

145145

Where ρL and ρW are densities of liquid and water both at 60

oF,

respectively.

3.

Differential Pressure Method

liquid in P: pressure sensor

liquid out A: amplifier

C: A/D converter

h

P A C read-out




b) Stressed gauge:

Rx = Ro +ΔR

Va = Ro/(Ro+Ro)·Vs = Vs/2

Vb = Ro/(Ro+Rx)·Vs = Ro/(Ro + Ro + ΔR)·Vs = Ro/( 2Ro + ΔR)·Vs

Vab= Vs/2 - Ro/( 2Ro + ΔR)·Vs = Vs[1/2 – Ro/(2Ro + ΔR)]

Vab= Vs[(2Ro + ΔR-2Ro)/(2(2Ro+ ΔR))]= Vs[(ΔR/Ro)/(2(2+ ΔR/Ro))]

o

oS

R R

R RV Vab

2/1

/

4 Δ

Δ

⋅

Since ΔR << Ro, ΔR/2Ro << 1, the equation for Vab can be simplified

as:

o

S

R

RV Vab

Δ

⋅

4

Vab can be measured under different load conditions on the strain gauge

and calibrated to read the density of liquid in the tank.

II.

MEASUREMENTS OF SOLID DENSITY

1.

For solid insoluble in a liquid:

A pycnometer can be used to measure solid density if the solid is

insoluble in a liquid. The density of the solid can be determined from

the following equation:




L

S W W W W

W W

)34()12(

13

=

Where ρS is the density of solid and ρL is the density of liquid, W1, W2,

W3 and W4 are the weights of the empty pycnometer, the pycnometer

filled up with liquid, the pycnomter plus solid (no liquid), and the

pycnometer plus solid and filled with liquid, respectively. Therefore,

(W3-W1) is the weight of the solid in the pycnometer, (W4-W3) is the

weight of the liquid fraction in the pycnometer.

[(W2-W1)-(W4-W3)]/ρL is the volume of the solid since (W2-W1)/ρL is

the total volume of the pycnometer and (W4-W3)/ρL is the volume

portion occupied by liquid in the pycnometer containing both solid and

liquid.

2.

Gas pycnometer:

For solids that are soluble in water and other organic solvents, a gas

pycnometer can be used to measure the solid density.




Tank

1 Tank

2

T, V T, V

Gas valve

The two tanks are of the same size with the volume V at the same

temperature, T.

a)

When the valve is closed, tank 2 contains some compressed air at

pressure P2 and tank 1 contains some solid and at a pressure P1,

which is lower than P2.

According to the ideal gas law:

P1V1 = n1 RT

P2V2 = n2 RT

b)

The valve is then opened:

P3V3 = (n1 + n2) RT

Where V3 = V1 + V2




Therefore,

P3 (V1 + V2) = n1 RT + n2 RT = P1 V1 + P2 V2

V2 (P2 – P3) = V1 (P3 – P1)

The volume of the gas in tank 1 is:

13

3221

P P

P PV V

=

Assuming the volume of the connecting pipe between the two tanks is

very small compared to the volume of the tanks, V2 = V that is known.

The volume of the solid fraction in tank 1 is (V-V1). Thus, the density of

the solid can be readily determined as:

1V V

M S

=

Where M is the mass of solid in tank1.


(1.) density and specific gravity measurements

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