The ultimate BOD of a river just below a sewage outfall is 50.0 mg/L, and the DO is at the saturation value of 10.0 mg/L. The deoxygenation rate coefficient kd is 0.30/day, and the reaeration rate coefficient kr is 0.90/day. The river is flowing at the speed of 48.0 miles per day. The only source of BOD on this river is this single outfall. (a) Find the critical distance downstream at which DO is a minimum. (b) Find the minimum DO. (c) If a wastewater treatment plant is to be built, what fraction of the BOD would have to be removed from the sewage to assure a minimum DO of 5.0 mg/L everywhere downstream

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg.m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?