Geotechnical Engineering

DHARM

54 GEOTECHNICAL ENGINEERING

Calibration
The method of calibration can be easily understood from Fig. 3.12.
Let h be the higher of the bulb and H be the height of any reading Rh from the top of the
bulb or neck. The jar with a soil suspension is shown in Fig. 3.12 (b); the surface is xx and the
level at which the specific gravity of the suspension is being measured is designated yy, the
depth being He, the effective depth.
As shown in Fig. 3.12 (c), on immersion of the hydrometer into the suspension in the jar,
the levels xx and yy will rise to x′x′ and y′y′ respectively.

1.040

1.030

1.020

1.010

1.000

–5 0.995

0

5

10

15

20

25

30

35

40

Rh Sp. gr.

H

h

x

yy

x

He

x¢

y¢

x¢

y¢ V /2A

h

h/2

V/Ah

H

Rh

(a) Hydrometer (b) Sedimentation jar before

immersion of hydrometer

(c) Sedimentation jar after

immersion of hydrometer

Fig. 3.12 Calibration of hydrometer with respect to sedimenation jar

If Vh is the volume of the hydrometer and A is the area of cross-section of the jar containing

the suspension, the rise in the level xx is given by Vh/A. The rise in the level yy will be approxi-

mately vh/2A since the effective depth is reckoned to the middle level of the hydrometer bulb.

The level y′y′ correspond to this mid-level, but the soil particles at this level are in the same

concentration as they were at yy, as the level yy has merely risen to y′y′ consequent to the

immersion of the hydrometer in the suspension.

Therefore, on correlating (b) and (c),

He = H

h V

A

V

A

F ++hh

HG

I

KJ

−

22

or He = H +

1

2

h

V

A

F − h

HG

I

KJ

...(Eq. 3.32)

Thus, the effective depth He at which the specific gravity is measured depends upon H
and, hence, upon the observed hydrometer reading, Rh′. However, h, Vh, and A are independ-
ent of Rh′, and may be easily obtained with a fair degree of accuracy. A calibration graph
between Rh′ and He can be prepared as shown in Fig. 3.13 for use with a particular hydrometer
and a particular suspension jar.