Answer:
(a). The coefficient of permeability is
.
(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}](https://tex.z-dn.net/?f=Q%3D%5Cdfrac%7BV%7D%7Bt%7D)
Put the value into the formula
![Q=\dfrac{405}{90}](https://tex.z-dn.net/?f=Q%3D%5Cdfrac%7B405%7D%7B90%7D)
![Q=4.5\ cm^3/s](https://tex.z-dn.net/?f=Q%3D4.5%5C%20cm%5E3%2Fs)
(a). We need to calculate the coefficient of permeability
Using formula of coefficient of permeability
![Q=kiA](https://tex.z-dn.net/?f=Q%3DkiA)
![k=\dfrac{Q}{iA}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7BQ%7D%7BiA%7D)
![k=\dfrac{Ql}{Ah}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7BQl%7D%7BAh%7D)
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}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B4.5%5Ctimes175%5Ctimes10%5E%7B-1%7D%7D%7B%5Cdfrac%7B%5Cpi%28175%5Ctimes10%5E%7B-1%7D%29%5E2%7D%7B4%7D%5Ctimes38%7D)
![k=8.6\times10^{-3}\ cm/s](https://tex.z-dn.net/?f=k%3D8.6%5Ctimes10%5E%7B-3%7D%5C%20cm%2Fs)
The coefficient of permeability is
.
(c). We need to calculate the discharge velocity during the test
Using formula of discharge velocity
![v=ki](https://tex.z-dn.net/?f=v%3Dki)
![v=\dfrac{kh}{l}](https://tex.z-dn.net/?f=v%3D%5Cdfrac%7Bkh%7D%7Bl%7D)
Put the value into the formula
![v=\dfrac{8.6\times10^{-3}\times38}{17.5}](https://tex.z-dn.net/?f=v%3D%5Cdfrac%7B8.6%5Ctimes10%5E%7B-3%7D%5Ctimes38%7D%7B17.5%7D)
![v=0.0187\ cm/s](https://tex.z-dn.net/?f=v%3D0.0187%5C%20cm%2Fs)
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}}](https://tex.z-dn.net/?f=V_%7Bs%7D%3D%5Cdfrac%7BM_%7Bs%7D%7D%7BV_%7Bs%7D%7D)
Put the value into the formula
![V_{s}=\dfrac{4950\times10^{-3}}{2710}](https://tex.z-dn.net/?f=V_%7Bs%7D%3D%5Cdfrac%7B4950%5Ctimes10%5E%7B-3%7D%7D%7B2710%7D)
![V_{s}=1826.56\ cm^3](https://tex.z-dn.net/?f=V_%7Bs%7D%3D1826.56%5C%20cm%5E3)
We need to calculate the volume of the soil specimen
Using formula of volume
![V=A\times L](https://tex.z-dn.net/?f=V%3DA%5Ctimes%20L)
Put the value into the formula
![V=\dfrac{\pi(17.5)^2}{4}\times17.5](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B%5Cpi%2817.5%29%5E2%7D%7B4%7D%5Ctimes17.5)
![V=4209.24\ cm^3](https://tex.z-dn.net/?f=V%3D4209.24%5C%20cm%5E3)
We need to calculate the volume of the voids
![V_{v}=V-V_{s}](https://tex.z-dn.net/?f=V_%7Bv%7D%3DV-V_%7Bs%7D)
Put the value into the formula
![V_{v}=4209.24-1826.56](https://tex.z-dn.net/?f=V_%7Bv%7D%3D4209.24-1826.56)
![V_{v}=2382.68\ cm^3](https://tex.z-dn.net/?f=V_%7Bv%7D%3D2382.68%5C%20cm%5E3)
We need to calculate the seepage velocity
Using formula of velocity
![Av=A_{v}v_{s}](https://tex.z-dn.net/?f=Av%3DA_%7Bv%7Dv_%7Bs%7D)
![v_{s}=\dfrac{Av}{A_{v}}](https://tex.z-dn.net/?f=v_%7Bs%7D%3D%5Cdfrac%7BAv%7D%7BA_%7Bv%7D%7D)
![v_{s}=\dfrac{V}{V_{v}}\times v](https://tex.z-dn.net/?f=v_%7Bs%7D%3D%5Cdfrac%7BV%7D%7BV_%7Bv%7D%7D%5Ctimes%20v)
Put the value into the formula
![v_{s}=\dfrac{4209.24}{2382.68}\times0.0187](https://tex.z-dn.net/?f=v_%7Bs%7D%3D%5Cdfrac%7B4209.24%7D%7B2382.68%7D%5Ctimes0.0187)
![v_{s}=0.0330\ cm/s](https://tex.z-dn.net/?f=v_%7Bs%7D%3D0.0330%5C%20cm%2Fs)
The seepage velocity is 0.0330 cm/s.
Hence, (a). The coefficient of permeability is
.
(b). The seepage velocity is 0.0330 cm/s.
(c). The discharge velocity during the test is 0.0187 cm/s.