A sedimentation analysis by the hydrometer method (152 H) was conducted with 50 g (= Ms)of oven dried soil. The volume of soil suspension is V = 10^3 cm^3. The hydrometer reading Ra = 19.50 after a lapse of 60 minutes after the commencement of the test. Given: Cm (meniscus) = 0.52, L (effective) =

Question

A sedimentation analysis by the hydrometer method (152 H) was conducted with 50 [latex]g \left(=M_{s} ight)[/latex]of oven dried soil. The volume of soil suspension is [latex]V=10^{3} cm ^{3}[/latex]. The hydrometer reading [latex]R_{a}=19.50[/latex] after a lapse of 60 minutes after the commencement of the test.

Given: [latex]C_{m} ext { (meniscus) }=0.52, L ext { (effective) }=14.0 cm , C_{o}( ext { zero correction })=+2.50, G_{s}=2.70[/latex] and [latex]\mu=0.01[/latex]1 poise.

Calculate the smallest particle size, which would have settled a depth of 14.0 cm and the percentage finer than this size. Temperature of test = 25° C.

Accepted Answer

From Eq. (3.24)

[latex]D=\sqrt{\frac{30 \mu}{\left(G_{s}-1 ight) \gamma_{w}}} \sqrt{\frac{L}{t}}=K \sqrt{\frac{L}{t}}[/latex] (3.24)

where [latex]\mu=0.01 imes 10^{-3}( gm - sec ) / cm ^{2}[/latex].

Substituting

[latex]D=\sqrt{\frac{30 imes 0.01 imes 10^{-3}}{(2.7-1)}} imes \sqrt{\frac{14}{60}}=0.0064[/latex] mm.

From Eq. (3.31)

[latex]C_{s g}=\frac{1.65 G_{s}}{2.65\left(G_{s}-1 ight)}[/latex] (3.31)

[latex]R_{c}=R_{a}-C_{o}+C_{t}[/latex]

From Table 3.6 for [latex]T=25{ }^{\circ} C , C_{T}=+1.3[/latex]. Therefore,

[latex]R_{c}=19.5-2.5+1.3=18.3[/latex]

From Eqs (3.32) and (3.31), we have

[latex]P^{\prime}=\frac{C_{s g} R_{c}}{M_{s}} imes 100[/latex] (3.32)

[latex]P^{\prime} \%=\frac{C_{s g} R_{c}}{M_{s}} imes 100, \quad C_{s g}=\frac{1.65 G_{s}}{2.65\left(G_{s}-1 ight)}[/latex]

[latex]C_{s g}=\frac{1.65 imes 2.7}{2.65(2.7-1)}=0.99, \quad P^{\prime} \%=\frac{0.99 imes 18.3}{50} imes 100=36.23 \%[/latex]

Table 3.6 Temperature correction factors [latex]C_{T}[/latex]
Temp °C	[latex]C_{T}[/latex]	Temp °C	[latex]C_{T}[/latex]
15	-1.10	23	+0.70
16	-0.90	24	+1.00
17	-0.70	25	+1.30
18	-0.50	26	+1.65
19	-0.30	27	+2.00
20	0.00	28	+2.50
21	+0.20	29	+3.05
22	+0.40	30	+3.80

Question 3.10: A sedimentation analysis by the hydrometer method (152 H) wa...

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