In wastewater treatment processes a filtration device may be used to remove water from the sludge formed by a precipitation reaction. The initial concentration of sludge softening reaction is 2 percent (20000 mg/L) and the volume of sludge is 100 m3. After filtration the sludge solids concentration is 35 percent. Assume that the sludge does not change density during filtration, and that liquid removed from the sludge contains no sludge. Using the mass balance method, determine the volume of sludge after filtration.

A2-m rigid tank initially contains saturated water vapor at 100 kpa. the tank is connected to a supply line through a valve. steam is flowing in the supply line at 600 kpa and 300 c. the valve is opened, and steam is allowed to enter the tank until the pressure in the tank reaches the line pressure, at which point the valve is closed. a thermometer placed in the tank indicates that the temperature at the final state is 200°c. determine (a) the mass of steam that has entered the tank (b) the amount of heat transfer.

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?

Starting wih an energy balance on a rectangular volume element, derive the one- dimensional transient heat conduction equation for a plane wall with constant thermal conductivity and no heat generation.