Respuesta :
Answer:
Cv = 0.026 cm²/min
t = 52.60 min
v% = 41.86 %
tv = 0.1375
t = 8.53 min
v = 53.61 %
Explanation:
given data
height = 2.54 cm
50 % consolidation = 12 min
solution
we get here first Cv value that is express as
Tv = [tex]\frac{Cv\times t}{d^2}[/tex] .................1
here Tv for 50% is 0.196
put here value and we get
0.196 = [tex]\frac{Cv\times 12}{\frac{2.54}{2}^2}[/tex]
solve it we get
Cv = 0.026 cm²/min
and
for tv for 90 % consolidation is 0.848
put value in equation 1
0.848 = [tex]\frac{0.026\times t}{\frac{2.54}{2}^2}[/tex]
solve it we get t
t = 52.60 min
and
v% will be here is
v% = [tex]\frac{0.18}{0.43} \times 100[/tex]
v% = 41.86 %
and
tv = [tex]\frac{\pi }{4}\times \frac{4}{100}^2[/tex]
tv = 0.1375
so now put value in equation 1 we get
0.1375 = [tex]\frac{0.026 \times t}{\frac{2.54}{2}^2}[/tex]
solve it we get
t = 8.53 min
and
now put value of t 14 min in equation 1 will be
tv = [tex]\frac{0.026 \times 14}{\frac{2.54}{2}^2}[/tex]
t = 0.225 min
and v will be after 14 min
0.0225 = [tex]\frac{\pi }{4}\times \frac{v}{100}^2[/tex]
v = 53.61 %
