Small signals. In lecture 1 we mentioned several methods for determining the size of a signal.Intuition suggests that even though they are not the same, the measures shouldn't be toodifferent. After all, a small signal is a small signal, right? In this problem we explore thisissue. Consider a family of signals described by u(t)=\left\{\begin{array}{ll}

Problem 1. A lagoon with a volume of 1,200 m3 has been receiving a steady flow of a stream at a rate of 100 m3/day. A pollutant in the incoming stream has a concentration of 10 mg/Land the pollutant degrades at a rate of 0.20 day-1. Assuming completely mixed conditions,and that there is an outlet from the lagoon as well.What would be the concentration of pollutant in the effluent leaving the lagoon at steady state conditions?If the input waste concentration then suddenly increased to 100 mg/L, what would the concentration in the effluent be 7 days later.

7. Use the Fujimoto method to determine the BOD reaction rate constant: BOD, = 0;BOD1 = 65; BOD2 = 109; BOD3 = 138; BOD4 = 158; BOD5 = 178; BOD6 = 190;BOD, = 200; BOD3 = 205; BOD, = 210; BOD10 = 212 mg/L.

A tannery with a wastewater flow of 0.011 m³/s and a BOD5 of 590 mg/L discharges into the Cattaraugus Creek (Nemerow, 1974). The creek has a10-year, 7-day low flow of 1.7 m/s. Upstream of the tannery, the BOD5of the creek is 0.6 mg/L. The BOD rate constants k are 0.115 d¯' for the tannery and 3.7 d¯' for the creek. The temperature of both the creek and the tannery wastewater is 20°C. Calculate the initial ultimate BOD after mixing.

The dilution factor (P) for an unseeded mixture of waste and water is 0.030. The DO of the mixture is initially 9.0 mg/L, and after 5 days, it has dropped to 3.0 mg/L. The reaction rate constant (k) has been found to be 0.22 day-1. What would be theremaining BOD (in mg/L) after 5 days?

1. (Problem 6-13) Determine the lime and soda ash dose, in mg/L as CaCO3, to soften the following water to a final hardness of 80 mg/L as CaCO3. The ion concentrations reported below are all mg/L as CACO;: Са =2 120; Mg 2 30, НСО3: 70, СО2 10.

5) (20 points) A water tower containing 4,000 m³ of water has been taken out of service for installation of a chlorine monitor. The concentration of chlorine in the water tower was 2.0 mg/L when the tower was taken out of service. If the chlorine decays with a rate constant of 1.0 d'', what is the chlorine concentration when the tank is put back in service 8 hours later? What mass of chlorine (in kg) much be added to the tank to raise the level back to 2.0 mg/L? For this problem assume the tank is well-mixed.

Problem 1 The dry adiabatic lapse rate (discussed in class) is 10°C km². That means for every km of elevation, the 'natural' cooling because of the ideal gas law is 10°C. The atmospheric pressure decreases with elevation at roughly 0.11 atm km'. The MW of dry air is 28.97 g/mole. Let's say a pocket of air at ground level (with a P=1 atm, T=40°C) rises 1 km in elevation in a dry environment. What is it's density at ground level, and what is its density after it rises to 1km in elevation (hint, its P and T changes according to the rates above) (in g/L)?а. b. If the "actual" temperature of the atmosphere at 1 km elevation is only 9°C cooler (soT=31°C), what is the density of the air 'outside the pocket' that rose (in g/L)? So is the pocket of air that rose to 1 km in elevation less dense or more dense than the air"outside of it'? Does the pocket of air keep rising or does it fall? (denser air pockets falls,lighter air pockets rises) Is the atmosphere stable or unstable? What sort of air pollution plume' would occur (if you could see it).

Problem 2. Consider the air over a city to be represented by a box 100 km on two sides that reaches up to an altitude of 1.0 km. Clean air is blowing into the box along one of its sides with a speed of 4 m/s (and thus air is blowing out of the 'box' on the opposite side as well).Suppose an air pollutant with a degradation reaction rate k = 0.2 hr-1 is emitted into the box at a total rate of 10.0 kg/s. Find the steady-state concentration if the air is assumed to be completely mixed. If the windspeed suddenly drops to 1 m/s, estimate the concentration of the pollutant two hours later.Additionally, using MS EXCEL, Plot the concentration for every 15 minute increment of time over 8 hours. Make your excel plot look neat (axis labeled, units shown, data points clear,etc), and show clearly the table of your calculations used to make the plot.

4. Each month the Speedy Dry Cleaning Company buys 1 barrel (0.160 m³) of dry cleaning fluid. Ninety percent of the fluid is lost to the atmosphere and 10% remains as residue to be disposed of. The density of the dry cleaning fluid is 1.5940 g/mL Draw a mass balance diagram and estimate the monthly mass emission rate to the atmosphere in kg/mo.

A solid waste processing plant has two classifiers that produce a refuse-derived fuel (RFD) from a mixture of organic (A) and inorganic (B) refuse. A portion of the plant schematic and the known flow rates are shown in the Figure below. a. What is the flow of A and B from Classifier I to Classifier II [QA2 and QB2] b. What is the composition of the Classifier II exit stream (QA3 and QB3)? c. What is the purity of the RFD and the recovery of component A?