Chapter 6, Problem 6.105P

Example Consider the simplified model of an automobile shown in Figure, let the parameter have the values m = 1500 kg, Ic = 2000 kg m2, k₁ = 36000 kg/m, k₁ = 40000 kg/m, a = 1.3 m and b = 1.7 m, calculate the natural modes of the system and write the expression for the response. ט 0 Solution T Equilibrium position 6(1)

6.3 Contamination of vegetable oil Vegetable oil is used in a food processing factory to prepare instant breadcrumbs. A stirred tank is used to hold the oil. During operation of the breadcrumb process, oil is pumped from the tank at a rate of 4.8 1 h-¹. At 8 PM during the night shift, the tank is mistakenly connected to a drum of cod liver oil, which is then pumped into the tank. The volume of vegetable oil in the tank at 8 PM is 60 1. (a) If the flow rate of cod liver oil into the tank is 7.5 1h-1 and the tank has a maximum capacity of 100 1, will the tank overflow before the factory manager arrives at 9 AM? Assume that the density of both oils is the same. (b) If cod liver oil is pumped into the tank at a rate of 4.8 1 h 1 instead of 7.5 1 h−1, what is the composition of oil in the tank at midnight?

6.1 Dilution of sewage In a sewage treatment plant, a large concrete tank initially contains 440,000 litres of liquid and 10,000 kg of fine suspended solids. To flush this material out of the tank, water is pumped into the vessel at a rate of 40,000 1 h −1. Liquid containing solids leaves at the same rate. Estimate the concentration of suspended solids in the tank at the end of 5 h. State your assumptions.

6.13 Heating glycerol solution An adiabatic stirred tank is used to heat 100 kg of a 45% glycerol solution in water. An electrical coil delivers 2.5 kW of power to the tank; 88% of the energy delivered by the coil goes into heating the vessel contents. The glycerol solution is initially at 15°C. (a) Write a differential equation for the energy balance. (b) Integrate the equation to obtain an expression for temperature as a function of time. (c) Assuming glycerol and water form an ideal solution, how long will the solution take to reach 90°C?

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Homework#7

I tried to draw a mohr's circle but I don't think i'm doing it correctlly can you help me figure this out please?

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Homework#7