Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tankA into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside eachtank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If,initially, tank A contains pure water and tank B contains 20 kg of salt.A6 L/min0.2 kg/Lx(t)100 L4 L/minx(0) = 0 kg3 L/minBy(t)100 Ly(0) = 20 kg2 L/min1 L/minFigure Q1 - Mixing problem for interconnected tanksDetermine the mass of salt in each tank at time t > 0:Analytically (hand calculations)

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Answered: Two large tanks, each holding 100 L of…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of 6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If, initially, tank A contains pure water and tank B contains 20 kg of salt. A 6 L/min 0.2 kg/L x(t) 100 L 4 L/min x(0) = 0 kg 3 L/min 1 L/min B y(t) 100 L y(0) = 20 kg 2 L/min Figure Q1 - Mixing problem for interconnected tanks Determine the mass of salt in each tank at time t≥ 0: Analytically (hand calculations) Using MATLAB Numerical Functions (ode45) Creating Simulink Model Plot all solutions on the same graph for the first 15 min. The graph must be fully formatted by code.
1. At time t = 0 a tank contains Qo Ib of salt dissolved in 100 gal of water. Assume that water containing 1/4 Ib of salt/gal is entering the tank at a rate of r gal/min, and that the well-stirred mixture is draining from the tank at the same rate. Set up the initial value problem that describes this flow process. Find the amount of salt Q(t) in the tank at any time, and also find the limiting amount QL that is present after a very long time. If r = 3 and Qo 2Q, find the time T after which the salt level is within 2% of Q. Also find the flow rate that is required if the value of T is not to exceed 45 min. %3D %3D
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4. The circular tank of water is being filled from a pipe shown in figure below. The velocity of flowof water from the pipe is 10 ft/s. What will be the rate of rise ( in ft/s) of the water surface in the tank?
As part of a processing of biofuels, water is pumped into a circular tank with a diameter Dt, as shown in Figure Q3. The flowrate into the tank is Q₁ and the flowrate out is Q2. When the vessel is heated, water evaporates. The average velocity at which the vapour rises across the entire tank is vevap. You may assume that water has a density of Pw, and vapour has a density of pv. Acceleration due to gravity is g. a) Find an expression for the rate of change of the mass of water in the tank. b) At time t = 0, the height of water in the tank is ho. Find an expression for the height as a function of time, h(t). c) An alarm is triggered when the pressure at the bottom of the tank exceeds Palarm. Find an expression for the time at which the alarm goes off. Q₁ } } Vevap D₁ Figure Q3: Water being pumped through a heated evaporation tank.
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Transcribed Image Text:As part of a processing of biofuels, water is pumped into a circular tank with a diameter Dt. as shown in Figure Q3. The flowrate into the tank is Q₁ and the flowrate out is Q₂. When the vessel is heated, water evaporates. The average velocity at which the vapour rises across the entire tank is vevap- You may assume that water has a density of Pw, and vapour has a density of Pv. Acceleration due to gravity is g. 2₁ Vevap Q₂ => D₂ Figure Q3: Water being pumped through a heated evaporation tank. Find anexpressio for the rate of chnage of the mass of water in the tank At time t= 0 the height of water in the tank is h0. Find an expression for the height as a function of time h(t) An alarm is triggered when the pressure at the bottom of the tank exceeds P alarm. Find an expression for the time at which the alarm goes off
A siphon is a device in which liquid is transferred from one place to another without requiring any pump power. A tank is filled with water, and a valve at the top is open to the atmosphere. A siphon is used to drain water as shown in the figure below where X = 4.6 m and Y = 0.9 m. The siphon has the outside diameter (OD) of 50 mm and the wall thickness of 1.5 mm. Any loss can be ignored. Water Y X +B 50-mm OD x 1.5-mm wall 25-mm diameter (a) What is the volume flow rate of water at the nozzle exit? (b) Evaluate the pressure at points A and B. (c) What is the distance X required to obtain a volume flow rate of 7.1 x 10-3 m³/s? (d) It is required that the siphon transport water at the volume flow rate of 5.6 x 10-3 m³/s. What is the maximum allowable distance Y when the gauge pressure at B is -18 kPa.
Your company is designing a new pump that will continuously infuse saline into a patient's circulatory system at a controlled rate. The pump must output no more than 1 J of energy during piston movement, or otherwise could generate sufficient force to damage the patient's blood vessels. Utilizing the diagram below for the cylindrical pump assembly, calculate the maximum stroke distance (x) of the piston in meters and an expression of the final temperature of the saline as the solution leaves the pump and enters the patient's body (assume that the starting temperature is 37C).
Q4: A pressurized tank is providing water for a fountain at a steady flow rate, shown in the following figure. The pipe has a constant diameter. If the tank is pressurized to 50 kPa. Determine: 1) The height h, to which the water rises (hint: apply the Bernoulli's equation between points 0 and 2, where velocity is both zero); 2) The water velocity in the pipe (hint: apply the Bernoulli's equation between points 0 and 3 after h is found); 3) The static pressure of water in the horizontal part of the pipe. 2 All Water 50 kN/ 0 Figure 4. Q4
PROBLEM 2 Consider a firefighter who is standing on a ladder and spraying water with a hose into Chief Inspector Jacques Clouseau's (Figure 3a) third-story apartment. A diagram of the hose/nozzle used by the firefighter is shown in Figure 3b. Assume the nozzle has little effect on the flow in the hose and water in the hose/nozzle is incompressible. The temperature of the water in the hose is 15 °C. (a) Chief Inspector Jacques Clouseau investigating the cause of the fire in his apartment. water hose diameter=10cm outlet diameter=5cm Figure 3 个个个 outlet velocity=6ms¹ (b) Fire hose/nozzle used to extinguish the fire in Inspector Clouseau's apartment.
can you please solve question 1

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