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April 17, 2014

April 17, 2014

Posted by **Joseph** on Tuesday, February 22, 2011 at 2:38am.

Thanks,

Joseph

jadinoff @ gmail . com

- calc -
**MathMate**, Tuesday, February 22, 2011 at 8:52amYou can set up a first order differential equation to determine the time at which the required concentration remains.

The volume, V of the pit should be known.

The initial amount of juice, j, should be known.

The input concentration c1 of juice is zero.

The input rate r1=r=Q/t (in m³/s) should be known.

Assuming perfect agitation, the output concentration is c2=j/V.

The output rate, r2 equals input rate r1=r.

The equation would be

dj/dt = r1*c1-r2*c2

substituting values,

dj/dt = r*0 - r*(j/V)

dj/dt = -(Q/(Vt))j

Separate variables, to get

dj/j = -(Q/V)*dt/t

Integrate (do not forget the integration constant) and solve for j in terms of t.

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