Respuesta :
Answer:
(a). The coefficient of permeability is [tex]8.6\times10^{-3}\ cm/s[/tex].
(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
[tex]Q=\dfrac{V}{t}[/tex]
Put the value into the formula
[tex]Q=\dfrac{405}{90}[/tex]
[tex]Q=4.5\ cm^3/s[/tex]
(a). We need to calculate the coefficient of permeability
Using formula of coefficient of permeability
[tex]Q=kiA[/tex]
[tex]k=\dfrac{Q}{iA}[/tex]
[tex]k=\dfrac{Ql}{Ah}[/tex]
Where, Q=discharge
l = length
A = cross section area
h=constant head causing flow
Put the value into the formula
[tex]k=\dfrac{4.5\times175\times10^{-1}}{\dfrac{\pi(175\times10^{-1})^2}{4}\times38}[/tex]
[tex]k=8.6\times10^{-3}\ cm/s[/tex]
The coefficient of permeability is [tex]8.6\times10^{-3}\ cm/s[/tex].
(c). We need to calculate the discharge velocity during the test
Using formula of discharge velocity
[tex]v=ki[/tex]
[tex]v=\dfrac{kh}{l}[/tex]
Put the value into the formula
[tex]v=\dfrac{8.6\times10^{-3}\times38}{17.5}[/tex]
[tex]v=0.0187\ cm/s[/tex]
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
[tex]V_{s}=\dfrac{M_{s}}{V_{s}}[/tex]
Put the value into the formula
[tex]V_{s}=\dfrac{4950\times10^{-3}}{2710}[/tex]
[tex]V_{s}=1826.56\ cm^3[/tex]
We need to calculate the volume of the soil specimen
Using formula of volume
[tex]V=A\times L[/tex]
Put the value into the formula
[tex]V=\dfrac{\pi(17.5)^2}{4}\times17.5[/tex]
[tex]V=4209.24\ cm^3[/tex]
We need to calculate the volume of the voids
[tex]V_{v}=V-V_{s}[/tex]
Put the value into the formula
[tex]V_{v}=4209.24-1826.56[/tex]
[tex]V_{v}=2382.68\ cm^3[/tex]
We need to calculate the seepage velocity
Using formula of velocity
[tex]Av=A_{v}v_{s}[/tex]
[tex]v_{s}=\dfrac{Av}{A_{v}}[/tex]
[tex]v_{s}=\dfrac{V}{V_{v}}\times v[/tex]
Put the value into the formula
[tex]v_{s}=\dfrac{4209.24}{2382.68}\times0.0187[/tex]
[tex]v_{s}=0.0330\ cm/s[/tex]
The seepage velocity is 0.0330 cm/s.
Hence, (a). The coefficient of permeability is [tex]8.6\times10^{-3}\ cm/s[/tex].
(b). The seepage velocity is 0.0330 cm/s.
(c). The discharge velocity during the test is 0.0187 cm/s.
