# A Physical Count of Supplies on Hand

A Physical Count of Supplies on Hand

Ratio of two densities

Specific gravity

Common symbols

SG
SI unit of measurement Unitless

Derivations from
other quantities

${\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}}}$

South

G

t
r
u
e

=

ρ

s
a
m
p
50
e

ρ

H

2

O

{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}}}

Relative density, or
specific gravity,[1]
[two]
is the ratio of the density (mass of a unit book) of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to h2o at its densest (at 4 °C or 39.2 °F); for gases, the reference is air at room temperature (20 °C or 68 °F). The term “relative density” (often abbreviated
r.d.
or
RD) is often preferred in scientific usage, whereas the term “specific gravity” is deprecated.

If a substance’s relative density is less than 1 then it is less dense than the reference; if greater than one then it is denser than the reference. If the relative density is exactly 1 then the densities are equal; that is, equal volumes of the two substances take the same mass. If the reference material is water, and then a substance with a relative density (or specific gravity) less than 1 will float in water. For instance, an ice cube, with a relative density of about 0.91, will bladder. A substance with a relative density greater than i volition sink.

Temperature and pressure level must be specified for both the sample and the reference. Pressure is virtually e’er one atm (101.325 kPa). Where information technology is non, it is more than usual to specify the density direct. Temperatures for both sample and reference vary from manufacture to manufacture. In British brewing do, the specific gravity, every bit specified above, is multiplied past 1000.[3]
Specific gravity is usually used in industry as a uncomplicated means of obtaining information about the concentration of solutions of various materials such as brines, must weight (syrups, juices, honeys, brewers wort, must, etc.) and acids.

## Bones calculation

Relative density (

${\displaystyle RD}$

R
D

{\displaystyle RD}

) or specific gravity (

${\displaystyle SG}$

S

{\displaystyle SG}

) is a dimensionless quantity, as information technology is the ratio of either densities or weights

${\displaystyle {\mathit {RD}}={\frac {\rho _{\mathrm {substance} }}{\rho _{\mathrm {reference} }}},}$

R
D

=

ρ

due south
u
b
s
t
a
due north
c
due east

ρ

r
e
f
eastward
r
e
north
c
e

,

{\displaystyle {\mathit {RD}}={\frac {\rho _{\mathrm {substance} }}{\rho _{\mathrm {reference} }}},}

where

${\displaystyle RD}$

R
D

{\displaystyle RD}

is relative density,

${\displaystyle \rho _{\mathrm {substance} }}$

ρ

s
u
b
southward
t
a
n
c
east

{\displaystyle \rho _{\mathrm {substance} }}

is the density of the substance being measured, and

${\displaystyle \rho _{\mathrm {reference} }}$

ρ

r
e
f
e
r
e
due north
c
e

{\displaystyle \rho _{\mathrm {reference} }}

is the density of the reference. (Past convention

${\displaystyle \rho }$

ρ

{\displaystyle \rho }

, the Greek alphabetic character rho, denotes density.)

The reference material tin can be indicated using subscripts:

${\displaystyle RD_{\mathrm {substance/reference} }}$

R

D

s
u
b
s
t
a
n
c
e

/

r
e
f
e
r
e
northward
c
e

{\displaystyle RD_{\mathrm {substance/reference} }}

which means “the relative density of
substance
with respect to
reference“. If the reference is not explicitly stated then it is usually assumed to be water at four °C (or, more precisely, 3.98 °C, which is the temperature at which water reaches its maximum density). In SI units, the density of water is (approximately) thou kg/miii
or 1 yard/cmiii, which makes relative density calculations particularly convenient: the density of the object only needs to be divided by 1000 or ane, depending on the units.

The relative density of gases is often measured with respect to dry air at a temperature of twenty °C and a force per unit area of 101.325 kPa absolute, which has a density of 1.205 kg/mthree. Relative density with respect to air tin can be obtained past

${\displaystyle {\mathit {RD}}={\frac {\rho _{\mathrm {gas} }}{\rho _{\mathrm {air} }}}\approx {\frac {M_{\mathrm {gas} }}{M_{\mathrm {air} }}},}$

R
D

=

ρ

grand
a
s

ρ

a
i
r

M

m
a
s

Thousand

a
i
r

,

{\displaystyle {\mathit {RD}}={\frac {\rho _{\mathrm {gas} }}{\rho _{\mathrm {air} }}}\approx {\frac {M_{\mathrm {gas} }}{M_{\mathrm {air} }}},}

where

${\displaystyle M}$

K

{\displaystyle M}

is the molar mass and the approximately equal sign is used considering equality pertains but if 1 mol of the gas and 1 mol of air occupy the same volume at a given temperature and pressure level, i.east., they are both ideal gases. Ideal behaviour is unremarkably only seen at very low pressure. For example, one mol of an ideal gas occupies 22.414 50 at 0 °C and 1 atmosphere whereas carbon dioxide has a molar volume of 22.259 50 under those same conditions.

Those with SG greater than 1 are denser than water and volition, disregarding surface tension furnishings, sink in it. Those with an SG less than ane are less dense than water and volition float on it. In scientific piece of work, the human relationship of mass to volume is usually expressed directly in terms of the density (mass per unit of measurement book) of the substance nether study. It is in industry where specific gravity finds wide awarding, ofttimes for historical reasons.

True specific gravity of a liquid tin can exist expressed mathematically as:

${\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}},}$

South

t
r
u
e

=

ρ

due south
a
m
p
fifty
east

ρ

H

2

O

,

{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{two}O} }}},}

where

${\displaystyle \rho _{\mathrm {sample} }}$

ρ

s
a
m
p
l
e

{\displaystyle \rho _{\mathrm {sample} }}

is the density of the sample and

${\displaystyle \rho _{\mathrm {H_{2}O} }}$

ρ

H

2

O

{\displaystyle \rho _{\mathrm {H_{two}O} }}

is the density of h2o.

The apparent specific gravity is simply the ratio of the weights of equal volumes of sample and h2o in air:

${\displaystyle SG_{\mathrm {apparent} }={\frac {W_{\mathrm {A} ,{\text{sample}}}}{W_{\mathrm {A} ,\mathrm {H_{2}O} }}},}$

South

Grand

a
p
p
a
r
e
n
t

=

W

A

,

sample

W

A

,

H

ii

O

,

{\displaystyle SG_{\mathrm {apparent} }={\frac {W_{\mathrm {A} ,{\text{sample}}}}{W_{\mathrm {A} ,\mathrm {H_{ii}O} }}},}

where

${\displaystyle W_{A,{\text{sample}}}}$

Due west

A
,

sample

{\displaystyle W_{A,{\text{sample}}}}

represents the weight of the sample measured in air and

${\displaystyle {W_{\mathrm {A} ,\mathrm {H_{2}O} }}}$

W

A

,

H

2

O

{\displaystyle {W_{\mathrm {A} ,\mathrm {H_{ii}O} }}}

the weight of an equal book of water measured in air.

It can be shown that truthful specific gravity can be computed from different properties:

${\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}}={\frac {\frac {m_{\mathrm {sample} }}{V}}{\frac {m_{\mathrm {H_{2}O} }}{V}}}={\frac {m_{\mathrm {sample} }}{m_{\mathrm {H_{2}O} }}}{\frac {g}{g}}={\frac {W_{\mathrm {V} ,{\text{sample}}}}{W_{\mathrm {V} ,\mathrm {H_{2}O} }}},}$

Southward

Thou

t
r
u
e

=

ρ

south
a
m
p
l
e

ρ

H

2

O

=

m

s
a
g
p
l
e

V

m

H

ii

O

5

=

thousand

southward
a
m
p
l
e

m

H

2

O

g
g

=

W

V

,

sample

West

5

,

H

2

O

,

{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{ii}O} }}}={\frac {\frac {m_{\mathrm {sample} }}{5}}{\frac {m_{\mathrm {H_{2}O} }}{Five}}}={\frac {m_{\mathrm {sample} }}{m_{\mathrm {H_{ii}O} }}}{\frac {grand}{thousand}}={\frac {W_{\mathrm {V} ,{\text{sample}}}}{W_{\mathrm {5} ,\mathrm {H_{2}O} }}},}

where
g
is the local dispatch due to gravity,
5
is the volume of the sample and of water (the same for both),
ρ
sample
is the density of the sample,
ρ
H2O
is the density of water,
W
V
represents a weight obtained in vacuum,

${\displaystyle {\mathit {m}}_{\mathrm {sample} }}$

m

due south
a
m
p
l
e

is the mass of the sample and

${\displaystyle {\mathit {m}}_{\mathrm {H_{2}O} }}$

H

two

O

{\displaystyle {\mathit {g}}_{\mathrm {H_{2}O} }}

is the mass of an equal volume of water.

The density of water varies with temperature and pressure every bit does the density of the sample. So it is necessary to specify the temperatures and pressures at which the densities or weights were determined. It is nearly ever the case that measurements are made at 1 nominal atmosphere (101.325 kPa ± variations from changing weather patterns). But as specific gravity usually refers to highly incompressible aqueous solutions or other incompressible substances (such as petroleum products), variations in density caused by pressure level are usually neglected at least where apparent specific gravity is being measured. For truthful (in vacuo) specific gravity calculations, air pressure must be considered (encounter below). Temperatures are specified by the note (T
due south/T
r), with
T
southward
representing the temperature at which the sample’due south density was adamant and
T
r
the temperature at which the reference (water) density is specified. For example, SG (20 °C/4 °C) would be understood to mean that the density of the sample was determined at 20 °C and of the h2o at iv °C. Taking into business relationship different sample and reference temperatures, we note that, while
SG
H2O
=

i.000000

(20 °C/20 °C), it is too the example that
SG
H2O
=

0.998203

0.999840

=

0.998363

(20 °C/4 °C). Here, temperature is being specified using the current ITS-90 scale and the densities[4]
used here and in the remainder of this commodity are based on that scale. On the previous IPTS-68 scale, the densities at twenty °C and 4 °C are

0.9982071

and

0.9999720

respectively, resulting in an SG (20 °C/four °C) value for water of

0.9982343
.

As the main utilize of specific gravity measurements in industry is determination of the concentrations of substances in aqueous solutions and as these are found in tables of SG versus concentration, information technology is extremely important that the analyst enter the table with the correct grade of specific gravity. For instance, in the brewing industry, the Plato table lists sucrose concentration by weight against true SG, and was originally (twenty °C/4 °C)[5]
i.e. based on measurements of the density of sucrose solutions fabricated at laboratory temperature (20 °C) only referenced to the density of water at 4 °C which is very close to the temperature at which water has its maximum density,
ρ
HiiO
equal to 999.972 kg/mthree
in SI units (
0.999972 g/cm3

in cgs units or 62.43 lb/cu ft in United states customary units). The ASBC tabular array[6]
in employ today in North America, while information technology is derived from the original Plato tabular array is for apparent specific gravity measurements at (xx °C/20 °C) on the IPTS-68 calibration where the density of water is

. In the carbohydrate, soft drink, beloved, fruit juice and related industries, sucrose concentration by weight is taken from a table prepared by A. Brix, which uses SG (17.5 °C/17.5 °C). As a final example, the British SG units are based on reference and sample temperatures of 60 °F and are thus (15.56 °C/15.56 °C).

Given the specific gravity of a substance, its actual density can be calculated by rearranging the to a higher place formula:

${\displaystyle \rho _{\mathrm {substance} }=SG\times \rho _{\mathrm {H_{2}O} }.}$

ρ

south
u
b
southward
t
a
north
c
e

=
S
M
×

ρ

H

2

O

.

{\displaystyle \rho _{\mathrm {substance} }=SG\times \rho _{\mathrm {H_{ii}O} }.}

Occasionally a reference substance other than h2o is specified (for example, air), in which example specific gravity means density relative to that reference.

## Temperature dependence

See Density for a table of the measured densities of water at diverse temperatures.

The density of substances varies with temperature and pressure so that it is necessary to specify the temperatures and pressures at which the densities or masses were determined. It is about always the case that measurements are made at nominally 1 atmosphere (101.325 kPa ignoring the variations caused by changing atmospheric condition patterns) but as relative density unremarkably refers to highly incompressible aqueous solutions or other incompressible substances (such as petroleum products) variations in density caused by pressure are normally neglected at least where apparent relative density is beingness measured. For truthful (in vacuo) relative density calculations air pressure must be considered (see below). Temperatures are specified by the annotation (Ts
/Tr
) with
Ts

representing the temperature at which the sample’s density was determined and
Tr

the temperature at which the reference (water) density is specified. For case, SG (twenty °C/four °C) would be understood to mean that the density of the sample was adamant at 20 °C and of the h2o at four °C. Taking into account different sample and reference temperatures nosotros note that while SGH2O
= 1.000000 (xx °C/20 °C) it is also the case that RDH2O
=

0.998203
/
0.998840

= 0.998363 (20 °C/4 °C). Hither temperature is being specified using the electric current ITS-90 scale and the densities[7]
used hither and in the residual of this article are based on that scale. On the previous IPTS-68 scale the densities at 20 °C and 4 °C are, respectively, 0.9982071 and 0.9999720 resulting in an RD (20 °C/four °C) value for water of 0.9982343.

The temperatures of the two materials may be explicitly stated in the density symbols; for example:

relative density: 8.xv
20 °C

4 °C
; or specific gravity: 2.432
15

where the superscript indicates the temperature at which the density of the fabric is measured, and the subscript indicates the temperature of the reference substance to which it is compared.

## Uses

Relative density can also assistance to quantify the buoyancy of a substance in a fluid or gas, or determine the density of an unknown substance from the known density of another. Relative density is oft used past geologists and mineralogists to help determine the mineral content of a stone or other sample. Gemologists employ information technology every bit an aid in the identification of gemstones. Water is preferred as the reference considering measurements are then easy to carry out in the field (see beneath for examples of measurement methods).

As the principal employ of relative density measurements in industry is conclusion of the concentrations of substances in aqueous solutions and these are constitute in tables of RD vs concentration it is extremely important that the analyst enter the table with the right form of relative density. For example, in the brewing manufacture, the Plato table, which lists sucrose concentration by mass against truthful RD, were originally (20 °C/iv °C)[8]
that is based on measurements of the density of sucrose solutions made at laboratory temperature (20 °C) but referenced to the density of h2o at 4 °C which is very close to the temperature at which water has its maximum density of
ρ(H

2
O
) equal to 0.999972 g/cm3
(or 62.43 lb·ft−3). The ASBC table[ix]
in use today in North America, while it is derived from the original Plato table is for credible relative density measurements at (xx °C/xx °C) on the IPTS-68 scale where the density of h2o is 0.9982071 g/cm3. In the sugar, soft potable, honey, fruit juice and related industries sucrose concentration by mass is taken from this piece of work[3]
which uses SG (17.5 °C/17.five °C). As a final example, the British RD units are based on reference and sample temperatures of 60 °F and are thus (15.56 °C/fifteen.56 °C).[iii]

## Measurement

Relative density tin be calculated straight by measuring the density of a sample and dividing it by the (known) density of the reference substance. The density of the sample is simply its mass divided past its book. Although mass is easy to measure out, the volume of an irregularly shaped sample can be more than difficult to ascertain. One method is to put the sample in a water-filled graduated cylinder and read off how much h2o it displaces. Alternatively the container tin can be filled to the brim, the sample immersed, and the volume of overflow measured. The surface tension of the water may continue a meaning amount of water from inundation, which is especially problematic for small-scale samples. For this reason information technology is desirable to apply a water container with as pocket-sized a rima oris equally possible.

For each substance, the density,
ρ, is given by

${\displaystyle \rho ={\frac {\text{Mass}}{\text{Volume}}}={\frac {{\text{Deflection}}\times {\frac {\text{Spring Constant}}{\text{Gravity}}}}{{\text{Displacement}}_{\mathrm {WaterLine} }\times {\text{Area}}_{\mathrm {Cylinder} }}}.}$

ρ

=

Mass
Volume

=

Deflection

×

Spring Constant
Gravity

Displacement

W
a
t
due east
r
Fifty
i
n
eastward

×

Area

C
y
l
i
north
d
due east
r

.

{\displaystyle \rho ={\frac {\text{Mass}}{\text{Book}}}={\frac {{\text{Deflection}}\times {\frac {\text{Spring Constant}}{\text{Gravity}}}}{{\text{Displacement}}_{\mathrm {WaterLine} }\times {\text{Area}}_{\mathrm {Cylinder} }}}.}

When these densities are divided, references to the jump constant, gravity and cross-exclusive expanse simply abolish, leaving

${\displaystyle RD={\frac {\rho _{\mathrm {object} }}{\rho _{\mathrm {ref} }}}={\frac {\frac {{\text{Deflection}}_{\mathrm {Obj.} }}{{\text{Displacement}}_{\mathrm {Obj.} }}}{\frac {{\text{Deflection}}_{\mathrm {Ref.} }}{{\text{Displacement}}_{\mathrm {Ref.} }}}}={\frac {\frac {3\ \mathrm {in} }{20\ \mathrm {mm} }}{\frac {5\ \mathrm {in} }{34\ \mathrm {mm} }}}={\frac {3\ \mathrm {in} \times 34\ \mathrm {mm} }{5\ \mathrm {in} \times 20\ \mathrm {mm} }}=1.02.}$

R
D
=

ρ

o
b
j
e
c
t

ρ

r
east
f

=

Deflection

O
b
j
.

Displacement

O
b
j
.

Deflection

R
e
f
.

Displacement

R
eastward
f
.

=

3

i
north

20

g
1000

5

i
n

34

m
m

=

3

i
due north

×

34

m
one thousand

5

i
north

×

xx

m
m

=
1.02.

{\displaystyle RD={\frac {\rho _{\mathrm {object} }}{\rho _{\mathrm {ref} }}}={\frac {\frac {{\text{Deflection}}_{\mathrm {Obj.} }}{{\text{Deportation}}_{\mathrm {Obj.} }}}{\frac {{\text{Deflection}}_{\mathrm {Ref.} }}{{\text{Displacement}}_{\mathrm {Ref.} }}}}={\frac {\frac {3\ \mathrm {in} }{xx\ \mathrm {mm} }}{\frac {v\ \mathrm {in} }{34\ \mathrm {mm} }}}={\frac {three\ \mathrm {in} \times 34\ \mathrm {mm} }{v\ \mathrm {in} \times twenty\ \mathrm {mm} }}=i.02.}

### Hydrostatic weighing

Relative density is more easily and perhaps more than accurately measured without measuring volume. Using a spring scale, the sample is weighed first in air and and so in water. Relative density (with respect to water) can then be calculated using the following formula:

${\displaystyle RD={\frac {W_{\mathrm {air} }}{W_{\mathrm {air} }-W_{\mathrm {water} }}},}$

R
D
=

Westward

a
i
r

W

a
i
r

W

w
a
t
eastward
r

,

{\displaystyle RD={\frac {W_{\mathrm {air} }}{W_{\mathrm {air} }-W_{\mathrm {h2o} }}},}

where

• Due west
air
is the weight of the sample in air (measured in newtons, pounds-forcefulness or some other unit of force)
• W
water
is the weight of the sample in water (measured in the same units).

This technique cannot easily be used to measure relative densities less than one, because the sample will then bladder.
Westward
h2o
becomes a negative quantity, representing the force needed to proceed the sample underwater.

Another practical method uses 3 measurements. The sample is weighed dry out. And so a container filled to the brim with water is weighed, and weighed over again with the sample immersed, after the displaced water has overflowed and been removed. Subtracting the terminal reading from the sum of the start two readings gives the weight of the displaced water. The relative density result is the dry sample weight divided by that of the displaced water. This method allows the employ of scales which cannot handle a suspended sample. A sample less dense than h2o can also be handled, but it has to be held down, and the error introduced past the fixing material must be considered.

### Hydrometer

The relative density of a liquid can be measured using a hydrometer. This consists of a bulb attached to a stalk of constant cantankerous-sectional surface area, as shown in the adjacent diagram.

First the hydrometer is floated in the reference liquid (shown in lite bluish), and the displacement (the level of the liquid on the stalk) is marked (bluish line). The reference could be any liquid, but in practice it is usually water.

The hydrometer is then floated in a liquid of unknown density (shown in green). The alter in displacement, Δx, is noted. In the example depicted, the hydrometer has dropped slightly in the green liquid; hence its density is lower than that of the reference liquid. It is necessary that the hydrometer floats in both liquids.

The application of simple physical principles allows the relative density of the unknown liquid to be calculated from the modify in displacement. (In practice the stalk of the hydrometer is pre-marked with graduations to facilitate this measurement.)

In the explanation that follows,

• ρ
ref
is the known density (mass per unit volume) of the reference liquid (typically water).
• ρ
new
is the unknown density of the new (green) liquid.
• RD
new/ref
is the relative density of the new liquid with respect to the reference.
• V
is the volume of reference liquid displaced, i.due east. the red book in the diagram.
• g
is the mass of the entire hydrometer.
• yard
is the local gravitational constant.
• Δ10
is the change in displacement. In accordance with the way in which hydrometers are ordinarily graduated, Δx
is here taken to be negative if the displacement line rises on the stalk of the hydrometer, and positive if it falls. In the example depicted, Δx
is negative.
• A
is the cross sectional area of the shaft.

Since the floating hydrometer is in static equilibrium, the down gravitational forcefulness acting upon it must exactly balance the upward buoyancy strength. The gravitational force acting on the hydrometer is simply its weight,
mg. From the Archimedes buoyancy principle, the buoyancy force acting on the hydrometer is equal to the weight of liquid displaced. This weight is equal to the mass of liquid displaced multiplied by
chiliad, which in the case of the reference liquid is
ρ
ref
Vg. Setting these equal, we have

${\displaystyle mg=\rho _{\mathrm {ref} }Vg}$

m
thou
=

ρ

r
east
f

V
g

{\displaystyle mg=\rho _{\mathrm {ref} }Vg}

or but

 ${\displaystyle m=\rho _{\mathrm {ref} }V.}$ thousand = ρ r e f 5 . {\displaystyle 1000=\rho _{\mathrm {ref} }V.} (1)

Exactly the same equation applies when the hydrometer is floating in the liquid being measured, except that the new volume is

V

AΔ10

(see annotation above near the sign of Δ10). Thus,

 ${\displaystyle m=\rho _{\mathrm {new} }(V-A\Delta x).}$ m = ρ n due east due west ( 5 − A Δ x ) . {\displaystyle m=\rho _{\mathrm {new} }(V-A\Delta ten).} (2)

Combining (1) and (two) yields

 ${\displaystyle RD_{\mathrm {new/ref} }={\frac {\rho _{\mathrm {new} }}{\rho _{\mathrm {ref} }}}={\frac {V}{V-A\Delta x}}.}$ R D north e w / r due east f = ρ north e w ρ r e f = V 5 − A Δ x . {\displaystyle RD_{\mathrm {new/ref} }={\frac {\rho _{\mathrm {new} }}{\rho _{\mathrm {ref} }}}={\frac {V}{Five-A\Delta x}}.} (3)

But from (1) we take

V
=
g/ρ
ref
. Substituting into (iii) gives

 ${\displaystyle RD_{\mathrm {new/ref} }={\frac {1}{1-{\frac {A\Delta x}{m}}\rho _{\mathrm {ref} }}}.}$ R D north e w / r e f = i 1 − A Δ x yard ρ r e f . {\displaystyle RD_{\mathrm {new/ref} }={\frac {1}{1-{\frac {A\Delta x}{m}}\rho _{\mathrm {ref} }}}.} (4)

This equation allows the relative density to be calculated from the change in displacement, the known density of the reference liquid, and the known backdrop of the hydrometer. If Δx
is small then, every bit a offset-society approximation of the geometric series equation (iv) tin can exist written as:

${\displaystyle RD_{\mathrm {new/ref} }\approx 1+{\frac {A\Delta x}{m}}\rho _{\mathrm {ref} }.}$

R

D

n
e
w

/

r
e
f

1
+

A
Δ

ten

one thousand

ρ

r
due east
f

.

{\displaystyle RD_{\mathrm {new/ref} }\approx 1+{\frac {A\Delta x}{chiliad}}\rho _{\mathrm {ref} }.}

This shows that, for small Δten, changes in displacement are approximately proportional to changes in relative density.

### Pycnometer

An empty drinking glass pycnometer and stopper

A
pycnometer
(from Greek: πυκνός (
puknos
) meaning “dense”), besides called
pyknometer
or
specific gravity bottle, is a device used to determine the density of a liquid. A pycnometer is commonly made of glass, with a shut-fitting basis glass stopper with a capillary tube through it, then that air bubbling may escape from the appliance. This device enables a liquid’due south density to exist measured accurately by reference to an advisable working fluid, such as water or mercury, using an belittling remainder.[
citation needed
]

If the flask is weighed empty, full of water, and total of a liquid whose relative density is desired, the relative density of the liquid tin easily be calculated. The particle density of a powder, to which the usual method of weighing cannot be applied, tin also be determined with a pycnometer. The powder is added to the pycnometer, which is then weighed, giving the weight of the powder sample. The pycnometer is then filled with a liquid of known density, in which the pulverisation is completely insoluble. The weight of the displaced liquid can then exist determined, and hence the relative density of the powder.

A gas pycnometer, the gas-based manifestation of a pycnometer, compares the modify in pressure caused by a measured alter in a closed volume containing a reference (usually a steel sphere of known volume) with the change in force per unit area caused by the sample under the aforementioned conditions. The difference in change of pressure represents the volume of the sample equally compared to the reference sphere, and is usually used for solid particulates that may deliquesce in the liquid medium of the pycnometer blueprint described to a higher place, or for porous materials into which the liquid would not fully penetrate.

When a pycnometer is filled to a specific, but non necessarily accurately known volume,
V
and is placed upon a balance, it will exert a strength

${\displaystyle F_{\mathrm {b} }=g\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}\right),}$

F

b

=
g

(

m

b

ρ

a

thousand

b

ρ

b

)

,

{\displaystyle F_{\mathrm {b} }=g\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}\right),}

where
yard
b
is the mass of the bottle and
g
the gravitational dispatch at the location at which the measurements are beingness made.
ρ
a
is the density of the air at the ambient pressure and
ρ
b
is the density of the material of which the canteen is fabricated (usually drinking glass) so that the second term is the mass of air displaced by the glass of the bottle whose weight, by Archimedes Principle must exist subtracted. The bottle is filled with air but as that air displaces an equal corporeality of air the weight of that air is canceled by the weight of the air displaced. At present we make full the bottle with the reference fluid e.yard. pure water. The force exerted on the pan of the balance becomes:

${\displaystyle F_{\mathrm {w} }=g\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}+V\rho _{\mathrm {w} }-V\rho _{\mathrm {a} }\right).}$

F

westward

=
g

(

m

b

ρ

a

grand

b

ρ

b

+
V

ρ

w

5

ρ

a

)

.

{\displaystyle F_{\mathrm {westward} }=grand\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}+V\rho _{\mathrm {west} }-V\rho _{\mathrm {a} }\right).}

If we subtract the force measured on the empty canteen from this (or tare the residuum before making the water measurement) nosotros obtain.

${\displaystyle F_{\mathrm {w,n} }=gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} }),}$

F

w
,
n

=
g
5
(

ρ

w

ρ

a

)
,

{\displaystyle F_{\mathrm {w,due north} }=gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} }),}

where the subscript
n
indicated that this force is net of the force of the empty bottle. The bottle is at present emptied, thoroughly stale and refilled with the sample. The force, cyberspace of the empty bottle, is now:

${\displaystyle F_{\mathrm {s,n} }=gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} }),}$

F

s
,
n

=
one thousand
V
(

ρ

southward

ρ

a

)
,

{\displaystyle F_{\mathrm {due south,n} }=gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} }),}

where
ρ
s
is the density of the sample. The ratio of the sample and water forces is:

${\displaystyle SG_{\mathrm {A} }={\frac {gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} })}{gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} })}}={\frac {\rho _{\mathrm {s} }-\rho _{\mathrm {a} }}{\rho _{\mathrm {w} }-\rho _{\mathrm {a} }}}.}$

Southward

G

A

=

g
5
(

ρ

s

ρ

a

)

Five
(

ρ

w

ρ

a

)

=

ρ

s

ρ

a

ρ

w

ρ

a

.

{\displaystyle SG_{\mathrm {A} }={\frac {gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} })}{gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} })}}={\frac {\rho _{\mathrm {s} }-\rho _{\mathrm {a} }}{\rho _{\mathrm {westward} }-\rho _{\mathrm {a} }}}.}

This is called the
apparent relative density, denoted by subscript A, because it is what we would obtain if nosotros took the ratio of cyberspace weighings in air from an belittling balance or used a hydrometer (the stem displaces air). Note that the upshot does not depend on the scale of the balance. The only requirement on it is that it read linearly with forcefulness. Nor does
RD
A
depend on the actual book of the pycnometer.

Further manipulation and finally substitution of
RD
V, the true relative density (the subscript V is used because this is often referred to as the relative density

in vacuo
), for
ρ
s/ρ
due west
gives the relationship between apparent and truthful relative density:

${\displaystyle RD_{\mathrm {A} }={{\rho _{\mathrm {s} } \over \rho _{\mathrm {w} }}-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }} \over 1-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}}={RD_{\mathrm {V} }-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }} \over 1-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}}.}$

R

D

A

=

ρ

s

ρ

west

ρ

a

ρ

west

1

ρ

a

ρ

w

=

R

D

V

ρ

a

ρ

due west

1

ρ

a

ρ

w

.

{\displaystyle RD_{\mathrm {A} }={{\rho _{\mathrm {s} } \over \rho _{\mathrm {w} }}-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }} \over 1-{\rho _{\mathrm {a} } \over \rho _{\mathrm {due west} }}}={RD_{\mathrm {V} }-{\rho _{\mathrm {a} } \over \rho _{\mathrm {westward} }} \over 1-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}}.}

In the usual instance nosotros will take measured weights and want the true relative density. This is found from

${\displaystyle RD_{\mathrm {V} }=RD_{\mathrm {A} }-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}(RD_{\mathrm {A} }-1).}$

R

D

5

=
R

D

A

ρ

a

ρ

w

(
R

D

A

i
)
.

{\displaystyle RD_{\mathrm {V} }=RD_{\mathrm {A} }-{\rho _{\mathrm {a} } \over \rho _{\mathrm {west} }}(RD_{\mathrm {A} }-i).}

Since the density of dry air at 101.325 kPa at 20 °C is[x]
0.001205 k/cm3
and that of water is 0.998203 g/cmthree
we see that the divergence between truthful and apparent relative densities for a substance with relative density (twenty °C/20 °C) of nearly i.100 would exist 0.000120. Where the relative density of the sample is close to that of h2o (for example dilute ethanol solutions) the correction is even smaller.

The pycnometer is used in ISO standard: ISO 1183-i:2004, ISO 1014–1985 and ASTM standard: ASTM D854.

Types

• Gay-Lussac, pear shaped, with perforated stopper, adapted, capacity i, 2, v, 10, 25, fifty and 100 mL
• as in a higher place, with ground-in thermometer, adjusted, side tube with cap
• Hubbard, for bitumen and heavy crude oils, cylindrical blazon, ASTM D 70, 24 mL
• equally above, conical type, ASTM D 115 and D 234, 25 mL
• Kick, with vacuum jacket and thermometer, capacity 5, 10, 25 and 50 mL

### Digital density meters

Hydrostatic Pressure-based Instruments: This technology relies upon Pascal’s Principle which states that the pressure difference betwixt two points within a vertical column of fluid is dependent upon the vertical distance between the two points, the density of the fluid and the gravitational force. This technology is often used for tank gaging applications equally a convenient means of liquid level and density measure out.

Vibrating Element Transducers: This type of musical instrument requires a vibrating chemical element to be placed in contact with the fluid of interest. The resonant frequency of the element is measured and is related to the density of the fluid by a characterization that is dependent upon the design of the chemical element. In modern laboratories precise measurements of relative density are made using aquiver U-tube meters. These are capable of measurement to five to half-dozen places beyond the decimal point and are used in the brewing, distilling, pharmaceutical, petroleum and other industries. The instruments measure the actual mass of fluid contained in a fixed book at temperatures between 0 and 80 °C but as they are microprocessor based tin can calculate apparent or truthful relative density and contain tables relating these to the strengths of common acids, sugar solutions, etc.

Ultrasonic Transducer: Ultrasonic waves are passed from a source, through the fluid of interest, and into a detector which measures the acoustic spectroscopy of the waves. Fluid backdrop such every bit density and viscosity can be inferred from the spectrum.

Radiation-based Approximate: Radiation is passed from a source, through the fluid of interest, and into a scintillation detector, or counter. As the fluid density increases, the detected radiations “counts” volition decrease. The source is typically the radioactive isotope caesium-137, with a half-life of well-nigh thirty years. A central advantage for this technology is that the instrument is not required to exist in contact with the fluid—typically the source and detector are mounted on the outside of tanks or piping.[11]

Buoyant Force Transducer: the buoyancy force produced past a bladder in a homogeneous liquid is equal to the weight of the liquid that is displaced by the float. Since buoyancy force is linear with respect to the density of the liquid inside which the float is submerged, the measure out of the buoyancy force yields a measure out of the density of the liquid. Ane commercially available unit claims the instrument is capable of measuring relative density with an accurateness of ± 0.005 RD units. The submersible probe head contains a mathematically characterized spring-float system. When the head is immersed vertically in the liquid, the float moves vertically and the position of the float controls the position of a permanent magnet whose displacement is sensed by a concentric array of Hall-consequence linear displacement sensors. The output signals of the sensors are mixed in a dedicated electronics module that provides a single output voltage whose magnitude is a direct linear measure of the quantity to be measured.[12]

### The relative density in soil mechanics

The relative density

${\displaystyle D_{\mathrm {R} }}$

D

R

{\displaystyle D_{\mathrm {R} }}

a mensurate of the electric current void ratio in relation to the maximum and minimum void rations, and applied effective stress command the mechanical behavior of cohesionless soil. Relative density is defined by

${\displaystyle D_{\mathrm {R} }={\frac {e_{\mathrm {max} }-e}{e_{\mathrm {max} }-e_{\mathrm {min} }}}\times 100\%}$

D

R

=

e

one thousand
a
x

e

e

m
a
10

e

m
i
due north

×

100
%

{\displaystyle D_{\mathrm {R} }={\frac {e_{\mathrm {max} }-eastward}{e_{\mathrm {max} }-e_{\mathrm {min} }}}\times 100\%}

in which

${\displaystyle e_{\mathrm {max} },e_{\mathrm {min} }}$

east

k
a
x

,

e

grand
i
north

{\displaystyle e_{\mathrm {max} },e_{\mathrm {min} }}

, and

${\displaystyle e}$

eastward

{\displaystyle eastward}

are the maximum, minimum and actual void rations.

## Examples

Material Specific gravity
Balsa forest 0.2
Oak forest 0.75
Ethanol 0.78
Olive oil 0.91
H2o ane
Ironwood 1.5
Graphite 1.nine–ii.3
Table salt 2.17
Aluminium 2.7
Cement 3.15
Iron seven.87
Copper eight.96
Mercury thirteen.56
Depleted uranium 19.1
Gold 19.three
Osmium 22.59

(Samples may vary, and these figures are approximate.) Substances with a relative density of one are neutrally buoyant, those with RD greater than 1 are denser than water, and and then (ignoring surface tension furnishings) volition sink in information technology, and those with an RD of less than one are less dense than h2o, and so will float.

Example:

${\displaystyle RD_{\mathrm {H_{2}O} }={\frac {\rho _{\mathrm {Material} }}{\rho _{\mathrm {H_{2}O} }}}=RD,}$

R

D

H

2

O

=

ρ

One thousand
a
t
e
r
i
a
l

ρ

H

2

O

=
R
D
,

{\displaystyle RD_{\mathrm {H_{two}O} }={\frac {\rho _{\mathrm {Material} }}{\rho _{\mathrm {H_{2}O} }}}=RD,}

Helium gas has a density of 0.164 yard/Fifty;[13]
information technology is 0.139 times every bit dumbo as air, which has a density of one.xviii g/L.[13]

• Urine normally has a specific gravity between one.003 and 1.030. The Urine Specific Gravity diagnostic test is used to evaluate renal concentration ability for assessment of the urinary organization.[14]
Low concentration may signal diabetes insipidus, while high concentration may bespeak albuminuria or glycosuria.[fourteen]
• Blood normally has a specific gravity of approximately 1.060.[15]
• Vodka eighty° proof (forty% v/five) has a specific gravity of 0.9498.[16]

## Encounter also

• API gravity
• Baumé scale
• Buoyancy
• Fluid mechanics
• Gravity (beer)
• Hydrometer
• Jolly rest
• Plato scale

## References

1. ^

Dana, Edward Salisbury (1922).
A text-book of mineralogy: with an extended treatise on crystallography…
New York, London(Chapman Hall): John Wiley and Sons. pp. 195–200, 316.

2. ^

Schetz, Joseph A.; Allen Due east. Fuhs (1999-02-05).
Fundamentals of fluid mechanics. Wiley, John & Sons, Incorporated. pp. 111, 142, 144, 147, 109, 155, 157, 160, 175. ISBN0-471-34856-2.

3. ^

a

b

c

Hough, J.S., Briggs, D.E., Stevens, R and Young, T.Westward. Malting and Brewing Science, Vol. 2 Hopped Wort and Beer, Chapman and Hall, London, 1991, p. 881

4. ^

Bettin, H.; Spieweck, F. (1990). “Die Dichte des Wassers als Funktion der Temperatur nach Einführung des Internationalen Temperaturskala von 1990”.
PTB-Mitteilungen 100. pp. 195–196.

5. ^

ASBC Methods of Analysis Preface to Table ane: Extract in Wort and Beer, American Society of Brewing Chemists, St Paul, 2009

6. ^

ASBC Methods of Analysis
op. cit.
Tabular array 1: Extract in Wort and Beer

7. ^

Bettin, H.; Spieweck, F. (1990).
Die Dichte des Wassers als Funktion der Temperatur nach Einführung des Internationalen Temperaturskala von 1990
(in German). PTB=Hand. 100. pp. 195–196.

8. ^

ASBC Methods of Assay Preface to Table 1: Excerpt in Wort and Beer, American Society of Brewing Chemists, St Paul, 2009

9. ^

ASBC Methods of Analysis
op. cit.
Tabular array 1: Extract in Wort and Beer

10. ^

DIN51 757 (04.1994): Testing of mineral oils and related materials; determination of density

11. ^

Density – VEGA Americas, Inc. Ohmartvega.com. Retrieved on 2011-09-30.

12. ^

Procedure Control Digital Electronic Hydrometer. Gardco. Retrieved on 2011-09-30.
13. ^

a

b

“Lecture Demonstrations”.
physics.ucsb.edu.

14. ^

a

b

Lewis, Sharon Mantik; Dirksen, Shannon Ruff; Heitkemper, Margaret M.; Bucher, Linda; Harding, Mariann (five December 2013).
Medical-surgical nursing : cess and management of clinical bug
(ninth ed.). St. Louis, Missouri. ISBN978-0-323-10089-2. OCLC 228373703.

15. ^

Shmukler, Michael (2004). Elert, Glenn (ed.). “Density of blood”.
The Physics Factbook
. Retrieved
2022-01-23
.

16. ^

“Specific Gravity of Liqueurs”.
Good Cocktails.com.

• Fundamentals of Fluid Mechanics
Wiley, B.R. Munson, D.F. Young & T.H. Okishi
• Introduction to Fluid Mechanics
Fourth Edition, Wiley, SI Version, R.W. Play a joke on & A.T. McDonald
• Thermodynamics: An Engineering Approach
Second Edition, McGraw-Hill, International Edition, Y.A. Cengel & 1000.A. Boles
• Munson, B. R.; D. F. Immature; T. H. Okishi (2001).
Fundamentals of Fluid Mechanics
(4th ed.). Wiley. ISBN978-0-471-44250-9.

• Fox, R. W.; McDonald, A. T. (2003).
Introduction to Fluid Mechanics
(4th ed.). Wiley. ISBN0-471-20231-2.

### A Physical Count of Supplies on Hand

Source: https://en.wikipedia.org/wiki/Relative_density

Read:   All of the Following Are Asset Accounts Except

## Use the Following Data to Calculate the Current Ratio

Use the Following Data to Calculate the Current Ratio Utilize the following data to calculate …