A pond initially contains 5,000,000 gallons of freshwater. Water containing an undesirable chemical with a concentration of 0.05 g/gal flows into the pond at a rate of 2,500,000 gal/yr. The mixture flows out at the same rate, so that the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. (a) Construct a mathematical model of this flow process. (b) What would be the amount of chemical present in the pond after 3 years? And after so many years?

Q: Suppose that a tank with a capacity of 90 gallons initially contains 60 gallons of pure water. A…

A: Given that a tank with a capacity of 90 gallons initially contains 60 gallons of pure water. A salt…

Q: Fresh water flows into tank 1; mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3,…

A: Given: Water flows from tank 1. Mixed brine flows from tank 1 to tank 2, tank 2 to tank 3, and out…

Q: In a Couette flow, two large flat plates lie one on top of another, separated by a thin layer of…

A: therefore Estimate of velocity is 201.34 +- 0.7

Q: Derive the material balance for a conservative pulse input tracer in a non- steady state CMFR. The…

A:

Q: 50 kg/min 560 kg 480 kg Tank 1 Tank 2 76 kg/min Two well agitated tanks are connected to each other…

A:

Q: A 750 gallon tank starts off containing 400 gallons of water and 30 pounds of salt. Water with a…

A: Given: A 750 gallon tank starts off containing 400 gallons of water and 30 pounds of salt. Water…

Q: der the proce chamber at a rate of 10 liters per minute. A dye solution having a concentration of…

A: We will formed a differential equation for amount of dye and then solve it to get exact amount after…

Q: A 100-gal tank initially contains 25 gal of 50% salt solution. Fresh water is then poured into the…

A: (a) The problem belongs to the topic differential equation.

Q: A toxic chemical accidentally released into the environment from a metal processing plant degrades…

A:

Q: Derive the material balance for a step input tracer in a steady state CMFR with the following first…

A: System Description:Continuously stirred tank reactor (CMFR)Steady state operationStep input…

Q: A pond contains 2740 L of pure water and an uknown amount of an undesirable chemical. Water…

A: (a) dQdt = inflow rate - outflow rate

Q: The flow system shown in the figure is activated at time t== 0. Let Q.(t) denote the amount of…

A: As this problem is related to differential equation, hope you know how to find inverse of a matrix,…

Q: When a certain polyatomic gas undergoes adiabatic expansion, its pressure p and volume V satisfy the…

A: pv1.2=kdifferentiating both side with respect to t∂p∂tv1.2+1.2v0.2∂v∂tp=0∂p∂tv1.2=-1.2v0.2∂v∂tp

Q: Subject = Discrete Structures In a group of 9 people is it possible for each person to have exactly…

A: It is not possible,  Imagine constructing an acquaintance graph in which each of the 9 people are…

Q: A cylindrical barrel, standing upright on its circular end, contains muddy water. The top of the…

A:

Q: In an (M/M/1): (/FIFO) queueing model, the arrival and service rates are λ = 12/hour and μ =…

A:

Q: Vector A = 6i + 2j - 3k Find the

A: Given: Vector A=6i+2j-3k  To find: Scalar component of A perpendicular to the x-axis.

Q: A 2500-gallon tank initially contains 500 gallons of water with 6 pounds of salt dissolved in it.…

A: Let the amount of salt in tank at a time t is yt.   Given information capacity of tank = 2500 gallon…

Q: Calculate (1/2 (2 (2t - 1)e³t dt.

A: Integrate ∫0122t-1e3tdt

Q: A 100-gal tank initially contains 25 gal of 50% salt solution. Fresh water is then poured into the…

A:

Q: Consider two brine tanks connected as shown in the figure below. Tank 1 contains x(t) pounds of salt…

A:

Q: A tank contains 175 liters of fluid in which 20 grams of salt is dissolved. Brine containing 0.75…

A: Given: A tank contains 175 liters of fluid. Amount of Salt in the fluid = 20 grams Brine containing…

Q: An object, with mass 38 kg and speed 22 m/s relative to an observer, explodes into two pieces, one 3…

A: Given that, An object, with mass 38 kg and speed 22 m/s relative to an observer, explodes into two…

Q: A tank with capacity of 500 gal of water originally contains 300 gal of water with 100 lb of salt in…

A: After t minutes of process the amount of solution in the tank V(t)=300+3t−2t=(300+t) gal.At that…

Q: Two tanks are interconnected as illustrated below: Tank 1 2 C. min min. Tank 2 Suppose that Tank 1…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.