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ladessa [460]
3 years ago
12

A permeability test was run on a compacted sample of dirty sandy gravel. The sample was 175 mm long and the diameter of the mold

175 mm. In 90 s the discharge under a constant head of 38 em was 405 cm3 The sample had a dry mass of 4950 g and its Ps was 2710 kg!m3 Calculate (a) the coefficient of permeability, (b) the seepage velocity, and (c) the discharge velocity during the test.
Physics
1 answer:
LUCKY_DIMON [66]3 years ago
8 0

Answer:

(a). The coefficient of permeability is 8.6\times10^{-3}\ cm/s.

(b). The seepage velocity is 0.0330 cm/s.

(c). The discharge velocity during the test is 0.0187 cm/s.

Explanation:

Given that,

Length = 175 mm

Diameter = 175 mm

Time = 90 sec

Volume= 405 cm³

We need to calculate the discharge

Using formula of discharge

Q=\dfrac{V}{t}

Put the value into the formula

Q=\dfrac{405}{90}

Q=4.5\ cm^3/s

(a). We need to calculate the coefficient of permeability

Using formula of coefficient of permeability

Q=kiA

k=\dfrac{Q}{iA}

k=\dfrac{Ql}{Ah}

Where, Q=discharge

l = length

A = cross section area

h=constant head causing flow

Put the value into the formula

k=\dfrac{4.5\times175\times10^{-1}}{\dfrac{\pi(175\times10^{-1})^2}{4}\times38}

k=8.6\times10^{-3}\ cm/s

The coefficient of permeability is 8.6\times10^{-3}\ cm/s.

(c). We need to calculate the discharge velocity during the test

Using formula of discharge velocity

v=ki

v=\dfrac{kh}{l}

Put the value into the formula

v=\dfrac{8.6\times10^{-3}\times38}{17.5}

v=0.0187\ cm/s

The discharge velocity during the test is 0.0187 cm/s.

(b). We need to calculate the volume of solid in the ample

Using formula of volume

V_{s}=\dfrac{M_{s}}{V_{s}}

Put the value into the formula

V_{s}=\dfrac{4950\times10^{-3}}{2710}

V_{s}=1826.56\ cm^3

We need to calculate the volume of the soil specimen

Using formula of volume

V=A\times L

Put the value into the formula

V=\dfrac{\pi(17.5)^2}{4}\times17.5

V=4209.24\ cm^3

We need to calculate the volume of the voids

V_{v}=V-V_{s}

Put the value into the formula

V_{v}=4209.24-1826.56

V_{v}=2382.68\ cm^3

We need to calculate the seepage velocity

Using formula of velocity

Av=A_{v}v_{s}

v_{s}=\dfrac{Av}{A_{v}}

v_{s}=\dfrac{V}{V_{v}}\times v

Put the value into the formula

v_{s}=\dfrac{4209.24}{2382.68}\times0.0187

v_{s}=0.0330\ cm/s

The seepage velocity is 0.0330 cm/s.

Hence, (a). The coefficient of permeability is 8.6\times10^{-3}\ cm/s.

(b). The seepage velocity is 0.0330 cm/s.

(c). The discharge velocity during the test is 0.0187 cm/s.

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