Question

7 Salt water containing 1.92 lb/gal of salt flows at a fixed rate of 2 gal/min into a 100 gal tank, initially filled with fresh water. The density of the incoming solution is 71.8 lb/ft3. The solution, kept uniform by stirring, flows out at a fixed rate of 19.2 lb/min. How many pounds of salt will there be in the tank at the end of 1 h and 40 min? What is the upper limit for the number of pounds of salt in the tank if the process continues indefinitely? How much time will elapse while the quantity of salt in the tank changes from 100 to 150 lb?

Answer 1

The quantity of salt is "957 lb". A further explanation is given below.

Step-by-step explanation:

(1)

As we know,

1 hour 40 Min

= 60 min + 40 min

= 100 min

Salt water is going in at the rate of 2 gal/min

Salt water went into the tank in 100 min will be:

=
`2 \ gal/min* 100 \ min = 200 \ gal`

We have 1.92 lb of salt per gal.

In 200 gal, salt went in 1 hour 40 min will be:

=
`1.92 \ salt/gal* 200 \ gal`

=
`384 \ lb`

Now,

ft3 = 7.5 gal

The density of solution will be:

=
`(71.8 \ lb)/(7.5 \ gal)`

=
`9.57 \ lb/gal`

The solution went out in 100 min 1920 lb as well as going out at 19.2 lb per min.

=
`(1920 \ lb)/(9.57 \ lb/gal)`

=
`200 \ gal` (salt went out)

The salt remained in the tank at the end of 1 hour 40 min i.e.,

=
`384 - 200`

=
`184 \ lb`

(2)

As well as the upper limit for the no. of pounds for continues stirring indefinitely per 100 gal will be:

=
`957 \ lb`