+(a) A tank contains 100 liters of saltwater with 5 kg of dissolved salt. Freshwaterenters the tank at a rate of 4 liters per minute, and the well-mixed solution leavesthe tank at the same rate. Let y(t) represent the amount of salt (in kg) in the tankat time t (in minutes). Set up and solve a differential equation to find y(t).[Hint: The inflow rate of fresh water equals to the outflow rate of the well-mixedsolution, so the total volume of the saltwater in the tank (100 liters) remainsconstant over time. At any time (t), the salt content (concentration) in the tank isy(t) (kg/liter)]100(b) How much time does it take for the salt content to decrease by 50%.[Note: Write down the numerical expression, no need to use calculator]

Part (a) Differential Equation for y(t) Initial ConditionsVolume of tank V=100 liters…

Answered: + (a) A tank contains 100 liters of…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

A tank initially contains 200 gallons of water in which 50 lbs of salt are dissolved. A salt solution containing 0.5 lb of salt per gallon is poured into the tank at a rate of 1 gal/min. The mixture in the tank is stirred and drained off at the rate of 2 gal/min. a) Find the amount of salt in the tank until the tank is empty. b) Find the concentration of salt in the tank until the tank is empty. Where: x (t) = amount of substance dissolve in the solution at any time t ri = container SHOW FBD flow rate of the solution coming in the C₁ = concentration of the solution coming into the container dx dt ro = flow rate of the solution coming out from the container Co = concentration of the solution coming out from the container || r¡Ci - roCo
USING FOL Differential Equation APPLICATION SOLVE THE FOLLOWING PROBELM AND SHOW COMPLETE SOLUTION AND FINAL ANSWER.In a tank of 100 liters of brine containing 50 kg total dissolved salt. Pure water is allowedto run into the tank at the rate of 3 liters a minute. Brine runs out of the tank at the rateof 2 liters a minute. The instantaneous concentration in the tank is kept uniform bystirring. How much salt is in the tank at the end of 1hour?
The question refers to a well-mixed aeration pond or aeration lagoon that can be modeled according to the diagram below. The pond is simply a body of water that holds the wastewater for some detention time before the waste degrades or leaves in the effluent stream. There is no recycle line. You should derive a mass balance on X to solve these problems, make sure to include all terms in the mass balance. You may assume no X flows in with the influent. A rectangular, well-mixed aeration lagoon that has the same conceptual model above is 60 m long, 5 m wide, and 2 m deep. It receives 400 m3/d of wastewater with a BOD5 of 336 mg BOD5/L for treatment. The biodegradation rate constants for the wastewater are yield coefficient = 0.8 mg VSS/mg BODs, endogenous decay constant = 0.08 d—1 , maximum specific microbial growth rate = 1.10 d—1 , and the half velocity constant = 76.0 mg BOD5/L. Note: BOD refers to substrate concentration and it also refers to how much O2 is required to consume the…
The question refers to a well-mixed aeration pond or aeration lagoon that can be modeled according to the diagram below. The pond is simply a body of water that holds the wastewater for some detention time before the waste degrades or leaves in the effluent stream. There is no recycle line. You should derive a mass balance on X to solve these problems, make sure to include all terms in the mass balance. You may assume no X flows in with the influent. The perfectly mixed aeration pond with no recycle (return line) above serves as the biological reactor for a small community. The pond receives 30 m3/d of influent with a BOD5 of 350 mg/L that must be reduced to 20 mg/L before discharge. It has been found that the kinetic constants for the system are Ks=100mg/L BOD5, kd=0.10 d—1 , μm = 1.6 d—1 , and Y is 0.60 mg VSS/mg BOD5. Note: In this system each day, the bacteria have to grow at the same rate as they leave in the effluent, in order for the bacteria population to stay at a steady…
Read the question carefully and give me right solution according to the question.
A tank contains 100 gallons of water and 50 oz of salt. Water containing a salt concentration of 1 4 (1 + 1 2 sin t) oz/gal flows into the tank at a rate of 2 gal/min, and the mixture in the tank flows out at the same rate. (a) Find the amount of salt in the tank at any time. (b) Plot the solution for a time period long enough so that you see the ultimate behavior of the graph. (c) The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation?
A storage tank contains a liquid at depth y where y=0 when the tank is half full. Liquid is withdrawn at a constant flow rate Q to meets demands. The Contents are resupplied at a sinusoidal rate 30sin (t). Equation can be written as: d(Ay) = 3Q sin?(1) – Q (1)p (change in` (inflow) – (outflow) volume since the surface area A is constant sin²ce) – O A dy d(t) Use Euler's method to solve for the depth y from t = 0 to 10 d with a step size of 0.5 d. The parameter values are A = 1200 m? and Q = 500 m/d. Assume that the initial condition is y = 0.
Three tanks containing brine are shown below. Construct a model for the number of pounds of salt x₁(t), x₂(t), x²(t) at time t in tanks A, B, and C respectively. Then write it in matrix form. You do not need to solve. pure water 4 gal/min A 100 gal mixture 2 gal/min mixture 6 gal/min B 100 gal mixture 1 gal/min mixture 5 gal/min 100 gal mixture 4 gal/min
Show simple complete solution with formula
Air hair Sea Tresh water water Mercury Figure 1 Figure 1 shows a U-tube manometer that connects two pipelines that runs in parallel each other. One pipeline has fresh water flowing through it while the other transports seawater. i) Calculate the difference in pressure between the two pipelines. Give your answer in the typical unit for pressure. ii) From your answer in (i), state which pipeline has more pressure? Use pseawater = 1035 kg/m³, pHg= 13600 kg/m², híg= 10 cm, hw = 60 cm and hsea = 40 cm. Also, you may neglect the density of air since its effects are minimal in comparison to seawater or fresh water. Make all necessary assumptions and state them clearly.
Illustrate the diagram
Hydrology: Unconfined flow to a well Can you give me an example with a solution and answer using this formula. Thank you

SEE MORE QUESTIONS

Recommended textbooks for you

Structural Analysis

Civil Engineering

ISBN:

9781337630931

Author:

KASSIMALI, Aslam.

Publisher:

Cengage,

Structural Analysis (10th Edition)

Civil Engineering

ISBN:

9780134610672

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Principles of Foundation Engineering (MindTap Cou…

Civil Engineering

ISBN:

9781337705028

Author:

Braja M. Das, Nagaratnam Sivakugan

Publisher:

Cengage Learning

Structural Analysis

Civil Engineering

ISBN:

9781337630931

Author:

KASSIMALI, Aslam.

Publisher:

Cengage,

Structural Analysis (10th Edition)

Civil Engineering

ISBN:

9780134610672

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Principles of Foundation Engineering (MindTap Cou…

Civil Engineering

ISBN:

9781337705028

Author:

Braja M. Das, Nagaratnam Sivakugan

Publisher:

Cengage Learning

Fundamentals of Structural Analysis

Civil Engineering

ISBN:

9780073398006

Author:

Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning

Publisher:

McGraw-Hill Education

Sustainable Energy

Civil Engineering

ISBN:

9781337551663

Author:

DUNLAP, Richard A.

Publisher:

Cengage,

Traffic and Highway Engineering

Civil Engineering

ISBN:

9781305156241

Author:

Garber, Nicholas J.

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS