Consider a closed circular vortex filament of strength γ and radius a. assume that the center of the circular filament is located at the origin and the filament lies in thex-y plane. using the biot-savart law, obtain an expression for the velocity induced at(0,0,z). note that this corresponds to a general point on the z-axis. what is the velocityinduced at the origin (center of the vortex filament)?

When subject to a steady load (within elastic range) over a long period of time, what is the major difference in material behavoir between steel and plastic?

A5 kg block of fe is dropped into a very large vat of water. the fe and water initial temperatures are 95 and 25 c, respectively. the fe final temperature is 25 c and the water can be treated as a thermal reservoir,. treated as a thermal reservoir take the water to be the system and determine the entropy generation. report vour answer in kj/k.

1in2 processor chip can be modelled as an isothermal plane wall of silicon, isothermal on both sides. the power input to the bottom of the plane wall, or the processing power of the chip, often called the thermal design power (tdp), is 100w. assume the periphery is adiabatic. the silicon is 400 microns thick. the temperature at the junction, or in this case on the bottom of the isothermal plane wall, is 85°c. what is the top surface temperature, assuming that the only mode of heat transfer is conduction