Question

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.

Answer 1

(a). The coefficient of permeability is
`8.6*10^(-3)\ cm/s`.

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

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

Step-by-step 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=(V)/(t)`

Put the value into the formula

`Q=(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=(Q)/(iA)`

`k=(Ql)/(Ah)`

Where, Q=discharge

l = length

A = cross section area

h=constant head causing flow

Put the value into the formula

`k=(4.5*175*10^(-1))/((\pi(175*10^(-1))^2)/(4)*38)`

`k=8.6*10^(-3)\ cm/s`

The coefficient of permeability is
`8.6*10^(-3)\ cm/s`.

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

Using formula of discharge velocity

`v=ki`

`v=(kh)/(l)`

Put the value into the formula

`v=(8.6*10^(-3)*38)/(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)=(M_(s))/(V_(s))`

Put the value into the formula

`V_(s)=(4950*10^(-3))/(2710)`

`V_(s)=1826.56\ cm^3`

We need to calculate the volume of the soil specimen

Using formula of volume

`V=A* L`

Put the value into the formula

`V=(\pi(17.5)^2)/(4)*17.5`

`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)=(Av)/(A_(v))`

`v_(s)=(V)/(V_(v))* v`

Put the value into the formula

`v_(s)=(4209.24)/(2382.68)*0.0187`

`v_(s)=0.0330\ cm/s`

The seepage velocity is 0.0330 cm/s.

Hence, (a). The coefficient of permeability is
`8.6*10^(-3)\ cm/s`.

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

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