onsequennis then found I., Ic-rting ξ(33)lhe escape velocityof the escape velocity neglects the effect of air resistance, so theincluding the effect of air resistance) is somewhat higher. On the other6.9 mils, or 11.1 km/sThe numerical value of , is approximatelyThe preceding calculation of the escape vetance above sea level before being launched. Both gravitational and frictionalereby reduced; air resistance, in particular, diminishes quite rapidly with increasingeep in mind also that it may well be impractical to impart too large aninstantaneously; space vehicles, for instance, receive their initial accelerationpe velocity can be significantly reduced if the body is transportedconsiderable disforces are thinitial velocityduring a period of a few minutes.PROBLEMSConsider a tank used in certain hydrodynamic experiments. After one experiment thetank contains 200 L of a dye solution with a concentration of 1 g/L. To prepare forthe next experiment, the tank is to be rinsed with fresh water flowing in at a rate of2 L/min, the well-stirred solution flowing out at the same rate. Find the time that willelapse before the concentration of dye inthe tank reaches 1% of its original value.2. A tank initially contains 120 L of pure water. A mixture containing a concentration ofγ g/L of salt enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves thetank at the same rate. Find an expression in terms of y for the amount of salt in the tankat any time t. Also find the limiting amount of salt in the tank as t-oo3. A tank originally contains 100 gal of fresh water. Then water containinglb of salt pergallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave atthe same rate. After 10 min the process is stopped, and fresh water is poured into the tankat a rate of 2 gal/min, with the mixture again leaving at the same rate. Fsalt in the tank at the end of an additional 10 min.mou4. A tank with a capacity of 500 gal originally contains 200 gal of wlbalthin solution. Water containing 1 lb of salt per gallon entering athe mixture is allowed to flow out of the tankof salt in the tank at any time prior to the inFind the concentration (in pounds per gallof overflowing. Compare this concentratithe tank had infinite capacitythhe5. A tank contains 100 gal of water and S

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Asked Jan 23, 2019
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Number 1

onsequenn
is then found I., Ic-rting ξ
(33)
lhe escape velocity
of the escape velocity neglects the effect of air resistance, so the
including the effect of air resistance) is somewhat higher. On the other
6.9 mils, or 11.1 km/s
The numerical value of , is approximately
The preceding calculation of the escape ve
tance above sea level before being launched. Both gravitational and frictional
ereby reduced; air resistance, in particular, diminishes quite rapidly with increasing
eep in mind also that it may well be impractical to impart too large an
instantaneously; space vehicles, for instance, receive their initial acceleration
pe velocity can be significantly reduced if the body is transported
considerable dis
forces are th
initial velocity
during a period of a few minutes.
PROBLEMS
Consider a tank used in certain hydrodynamic experiments. After one experiment the
tank contains 200 L of a dye solution with a concentration of 1 g/L. To prepare for
the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of
2 L/min, the well-stirred solution flowing out at the same rate. Find the time that will
elapse before the concentration of dye inthe tank reaches 1% of its original value.
2. A tank initially contains 120 L of pure water. A mixture containing a concentration of
γ g/L of salt enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the
tank at the same rate. Find an expression in terms of y for the amount of salt in the tank
at any time t. Also find the limiting amount of salt in the tank as t-oo
3. A tank originally contains 100 gal of fresh water. Then water containing
lb of salt per
gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at
the same rate. After 10 min the process is stopped, and fresh water is poured into the tank
at a rate of 2 gal/min, with the mixture again leaving at the same rate. F
salt in the tank at the end of an additional 10 min.
mou
4. A tank with a capacity of 500 gal originally contains 200 gal of w
lb
al
th
in solution. Water containing 1 lb of salt per gallon entering a
the mixture is allowed to flow out of the tank
of salt in the tank at any time prior to the in
Find the concentration (in pounds per gall
of overflowing. Compare this concentrati
the tank had infinite capacity
th
he
5. A tank contains 100 gal of water and S
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onsequenn is then found I., Ic-rting ξ (33) lhe escape velocity of the escape velocity neglects the effect of air resistance, so the including the effect of air resistance) is somewhat higher. On the other 6.9 mils, or 11.1 km/s The numerical value of , is approximately The preceding calculation of the escape ve tance above sea level before being launched. Both gravitational and frictional ereby reduced; air resistance, in particular, diminishes quite rapidly with increasing eep in mind also that it may well be impractical to impart too large an instantaneously; space vehicles, for instance, receive their initial acceleration pe velocity can be significantly reduced if the body is transported considerable dis forces are th initial velocity during a period of a few minutes. PROBLEMS Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 L of a dye solution with a concentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 L/min, the well-stirred solution flowing out at the same rate. Find the time that will elapse before the concentration of dye inthe tank reaches 1% of its original value. 2. A tank initially contains 120 L of pure water. A mixture containing a concentration of γ g/L of salt enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the tank at the same rate. Find an expression in terms of y for the amount of salt in the tank at any time t. Also find the limiting amount of salt in the tank as t-oo 3. A tank originally contains 100 gal of fresh water. Then water containing lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. After 10 min the process is stopped, and fresh water is poured into the tank at a rate of 2 gal/min, with the mixture again leaving at the same rate. F salt in the tank at the end of an additional 10 min. mou 4. A tank with a capacity of 500 gal originally contains 200 gal of w lb al th in solution. Water containing 1 lb of salt per gallon entering a the mixture is allowed to flow out of the tank of salt in the tank at any time prior to the in Find the concentration (in pounds per gall of overflowing. Compare this concentrati the tank had infinite capacity th he 5. A tank contains 100 gal of water and S

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Expert Answer

Step 1

Use below steps to obtain the desired result: -

Let C(t)=the amount of dye(in grams) for any time t.

and let C'=difference between the input rate and output rate that is;

C'=rate Input-rate Output

rate in = 0 because the water is coming in but it does not contaain any dye with it.

and rate output=(C/200)*2  because (C/200) is the dye concentration   and 2 is the rate at which it is leaving the tank.

Now we need to write a differential equation so  that we can model that how the amount of dye change.

Below is the differential equation to model how the amount of dye changes

 

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Step 2

On dividing both sides by C we will get below value: -

 

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Step 3

Now on integrating both sides with respect to ‘t&rs...

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