A centrifugal pump operates with an inlet diameter of $0\mathrm{.}2$ m and an outlet diameter of $0\mathrm{.}1$ m$.$ If the pump delivers water at a rate of $0\mathrm{.}1$ m$^3/$s$,$ calculate the discharge velocity at the outlet and the head developed by the pump.A steel shaft with a diameter of $0\mathrm{.}05$ m and a length of $2$ m is subjected to a torsional moment of $500$ Nm$.$ Calculate the shear stress in the shaft, the angle of twist in radians, and the polar moment of inertia.A steam turbine receives steam at $4$ MPa and $400$C$.$ It expands to a pressure of $0\mathrm{.}4$ MPa with a dryness fraction of $0\mathrm{.}9.$ Calculate the work done by the turbine per kilogram of steam, the change in enthalpy, and the exit temperature assuming air behaves as an ideal gas with a specific heat ratio of $1\mathrm{.}3.$A heat exchanger transfers heat from hot water entering at $90$C and leaving at $70$C to cold water entering at $20$C and leaving at $40$C$.$ The hot water flow rate is $0\mathrm{.}5$ kg$/$s$,$ and the cold water flow rate is $1$ kg$/$s$.$ Calculate the rate of heat transfer in the exchanger and the effectiveness of the heat exchanger.A gear train consists of two gears with $18$ and $36$ teeth, respectively. If the smaller gear rotates at $1500$ rpm$,$ calculate the speed of the larger gear and the torque transmitted if the power input is $6$ kW$.$ Explain about libraries in python.