$(8$ points$)$ The pump shown below is used to increase the pressure of oil in a pipeline. The oil flows into the pump at a rate of $10\mathrm{.}6\frac{L}{s}$ and the pressure is increased by $155$ kPa $.$ The

motor that powers the pump is connected to a $218$ V source.

What is the efficiency of the pump$-$motor system if the motor uses a current of $37\mathrm{.}43$ A $?$

$\%$

If the efficiency of the pump$-$motor system is $79\mathrm{.}9\%,$ what is the current?

A

In this case, if the efficiency of the motor alone is $96\mathrm{.}6\%,$ what is the efficiency of the pump alone?

$\%$

In this case, what is the rate of shaft work transferred from the motor to the pump?

kW

$(6$ points$)$ A large wind turbine is used for electricity generation. The turbine has a blade span diameter of $47$ m and is installed in an area that has steady winds at $3\mathrm{.}9\frac{m}{s}.$ This wind

turbine$-$generator converts $28\mathrm{.}4\%$ of the available energy into electricity. The density of the air is $1\mathrm{.}25\frac{kg}{m^3}.$

$($Hint$.$ Think of the air as flowing through a pipe that has a diamter similar to the wind turbine. Wind turbines take advantage of the air's velocity.$)$

What is the power generated from this windmill?

If the blade span diameter is reduced by $30\%,$ the efficiency of the turbine$-$generator increases to $59\mathrm{.}356\%.$ What is the power generated from this new design.