$(40$ points$)$ Consider the turbine installed at the bottom of a dam, as shown in the figure. The density of water is $1000k\frac{g}{m^3}.$ The acceleration due to gravity is $9\mathrm{.}81\frac{m}{s^2}.$ The pipe has a constant diameter of $1$ m $.$ The water moves through the pipe and turbine at $5\frac{m}{s}.$

Use hydrostatics to calculate the gage pressure at point B$.$

Use Bernoulli's equation to calculate the pressure a point C$.$ Point $C$ is the inlet to the pipe. Use a streamline connecting point $B($where the water is still$)$ and point $C($where the water is moving at $5\frac{m}{s}).$

Use the energy equation for the pipe and turbine to calculate the usable power extracted by the turbine if the water moves through the pipe at $5\frac{m}{s}.$ Assume that the efficiency of the turbine is $70\%$ and assume $4700$ W of power is lost due to friction in the pipe $($head loss$).$

Water