A20-m-long and 8-cm-diameter hot-water pipe of a district heating system is buried in the soil 80cm below the ground surface. the outer surface temperature of the pipe is 60°c. taking the surface temperature of the earth to be 5°c and the thermal conductivity of the soil at that location to be 0.9w/m°c, determine the rate of heat loss from the pipe.

An engine, weighing 3000 n, is supported on a pedestal mount. it has been observed that the engine induces vibration into the surrounding area through its pedestal at the maximum operating speed. determine the stiffness of the dynamic vibration absorber spring in (n/m) that will reduce the vibration when mounted on the pedestal. the magnitude of the exciting force is 250 n, and the amplitude of motion of the auxiliary mass is to be limited to 2 mm note: in this question type-in right numbers, no decimals, no fractions, no unit. approximate to right number if needed