calc

posted by .

I would greatly appreciate your help with a math equation needed for a science experiment I'm researching. The case is the following: there is a pit full of juice and a stream of water is flowing through the pit (so that the amount of water which enters also exits). The goal is for there to be only 3 units of juice in the pit (regardless of the amount of water). As the stream flows through we assume that the stream water mixes evenly with the juice in the pit so that what exits is a proportion of stream water and juice. The question I'm stuck on is, how much stream water needs to pass through the pit in order for there to remain only 3 units of juice water. Since the proportions constantly change, it seems like a calc question to me, although I may be wrong. Could you do me a favor and email me the equation that I could use for any given amount of juice?
Thanks,
Joseph
jadinoff @ gmail . com

  • calc -

    You 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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics

    tad drops a cherry pit out the car window 1 m above the ground while traveling down the road at 18 m/s. a.how far, horizontally, from the initial dropping point will the pit hit the ground?
  2. College Physics

    Illinois Jones is being pulled from a snake pit with a rope that breaks if the tension in it exceeds 755 . If Illinois Jones has a mass of 70.0 and the snake pit is 3.90 deep, what is the minimum time that is required to pull our intrepid …
  3. Physics

    Illinois Jones is being pulled from a snake pit with a rope that breaks if the tension in it exceeds 755. If Illinois Jones has a mass of 70.0 and the snake pit is 3.90 deep, what is the minimum time that is required to pull our intrepid …
  4. College Physics

    Illinois Jones is being pulled from a snake pit with a rope that breaks if the tension in it exceeds 755 N. If Illinois Jones has a mass of 70.0 kg and the snake pit is 3.90m deep, what is the minimum time that is required to pull …
  5. science

    a large fiberglass tank was placed in a pit, before pipes could be attached and the tank filled with gasoline, the workers were asked to move the tank to another location. which of the following suggestions would be the best way to …
  6. Physics

    Drew drops a cherry pit out the car window 1.0 m above the ground while traveling down the road at 18 m/s. (a) How far, horizontally, from the initial dropping point will the pit hit the ground?
  7. physics

    A high jumper, falling at 3.8 m/s, lands on a foam pit and comes to rest compressing the pit 0.38 m. If the pit is able to exert an average force of 1100 N on the high jumper in breaking the fall, what is the jumper's mass?
  8. Math

    Staring from the pit, Helen made three laps around a circular track at 40 seconds per lap. She than made a 30-second pit stop and two and a half laps before running off the track and getting stuck in the mud for the remainder of the …
  9. LIVINGSTONIA UNIVERSITY

    A STONE IS DROPPED DOWN A PIT AND HITS THE BOTTOM 4.5 SECONDS LATER.CALCULATE THE DEPTH OF THE PIT.
  10. Science

    A bear is running behind you, and there is a 19m pit in which you jumped in order to be saved. If your jump was 0.6 m high and you took 2 seconds time to fall into that pit. What's the colour of the Bear?

More Similar Questions