x*****y
发帖数: 118 | 1 Two identical bottles, Bottle A filled with 100% salt solution, bottle B
filled with water. Now we have a continuous stable flow from bottle A to
bottle B. And the solution in bottle B is flowing to the waste at the same
flow rate. A stirring bar in the bottle B is mixing the solutions. Question:
what's the salt concentration in bottle B after all the solution in bottle
A runs out? | N***m
发帖数: 4460 | 2 what does 100% salt solution look like?
Question:
bottle
【在 x*****y 的大作中提到】
: Two identical bottles, Bottle A filled with 100% salt solution, bottle B
: filled with water. Now we have a continuous stable flow from bottle A to
: bottle B. And the solution in bottle B is flowing to the waste at the same
: flow rate. A stirring bar in the bottle B is mixing the solutions. Question:
: what's the salt concentration in bottle B after all the solution in bottle
: A runs out?
| Q***5
发帖数: 994 | 3 Let f(t) be the concentration at time t,
f(t+ dt) = (f(t) + v dt)/(1+ v dt), where v is the volume/second of liquid
flowing from A to B, volume is in percentage of the total volume of A (or B)
, so at the end (time T), \int_0^T v dt = 1.
Now,
(f(t+dt)-f(t)) = v (1-f(t)) dt
so df(t)/(1-f(t)) = v dt to get
f(t) = 1-exp(-\int_0^t v dt);
f(T) = 1-exp(-1)
Question:
bottle
【在 x*****y 的大作中提到】
: Two identical bottles, Bottle A filled with 100% salt solution, bottle B
: filled with water. Now we have a continuous stable flow from bottle A to
: bottle B. And the solution in bottle B is flowing to the waste at the same
: flow rate. A stirring bar in the bottle B is mixing the solutions. Question:
: what's the salt concentration in bottle B after all the solution in bottle
: A runs out?
| l***o
发帖数: 7937 | 4 C(V)=C(0)*exp(-V/V0), where C(0)=100%
C(V0)=100%*exp(-1)=36.8%
B)
【在 Q***5 的大作中提到】
: Let f(t) be the concentration at time t,
: f(t+ dt) = (f(t) + v dt)/(1+ v dt), where v is the volume/second of liquid
: flowing from A to B, volume is in percentage of the total volume of A (or B)
: , so at the end (time T), \int_0^T v dt = 1.
: Now,
: (f(t+dt)-f(t)) = v (1-f(t)) dt
: so df(t)/(1-f(t)) = v dt to get
: f(t) = 1-exp(-\int_0^t v dt);
: f(T) = 1-exp(-1)
:
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