Water flows into a tank at the variable rate Rin-(b) Find the maximum value of V.maximum value of V =451+tgal/min and out at the constant rate Rout(a) Set up a differential equation for V(t) and solve it with the initial condition V(0) = 80.V (t) =gal-5 gal/min. Let V(t) be the volume of water in the tank at time t.

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Answered: Water flows into a tank at the variable…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Tank A initially contains 500 Litres of a brine solution with a concentration of 0.5 kg perlitre and tank B contains 500 Litres of water. Solution is pumped from tank A to tank B ata rate of 4 Litres /min and from tank B to tank A at a rate of 8 Litres /min. The tanks are keptwell stirred. Let the number of kilograms of salt in tank A be A1 after t minutes and B1in tank B.(a) Write down equations showing, respectively, the concentrations C1 and C2 inthe tanks after t minutes.(b) Write down two differential equations to show how A1 and B1 vary with time.(c) What is the relation between A1 and B1?(d) Eliminate B1 between the two equations in (b) and solve the resulting equationfor A1.(e) What is the concentration in tank A after 10 minutes?
A 160 pound object is suspended from a spring The spring stretches an extra 80 inches with the weight attached. The spring-and-mass system is then submerged in a viscous fluid that exerts 18 pounds of force when the mass has velocity 2 fisec. What is the differential equation for this spring-and-mass system? (Use u as the dependent varlable) This system is? For what value of y would the system be critically damped? (if the given system is already critically damped, enter the given value for y)
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The motion of an object dropped from a certain height relative to sea level in the atmosphere will be studied. OBTAIN DIFFERENTIAL equations (models) that give the object's position, velocity and acceleration at a certain moment by USING THE PRINCIPLE OF THE CONSERVATION OF ENERGY AND MAKE SOLUTIONS. Assumptions: Frictionless environment, No heat exchange between the object and its environment, No chemical interaction, No phase change, No wind and rain. Special Information: G = mg, V = dy / dt
At t=0, a 600 liter tank initially contains 50 grams of salt dissolved in 300 liters of water. Then, water that contains 2 grams of salt per liter is poured into the tank at a rate of 5 liters per minute. The solution in the tank is constantly stirred so the salt concentration is uniform at any given time t. Water leaves the tank at a rate of 2 liters per minute. Determine when the tank will overflow and create a differential equation to determine how much salt will be in the tank after 1 hour.

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