Problem $4(25$ points$)$ Normal domestic water pressure is $1$ MPa $.$ While hanging shelves, a homeowner mistakenly drilled a $2$ mm hole in a water pipe inside a wall, what is the water leak rate? Express your answer in terms of $k\frac{g}{s}$ and gallons per minute $(gpm)\mathrm{.}1k\frac{g}{s}=15\mathrm{.}85gpm.$ Assume:

a$)$ The water pressure is $1$ MPa $.$

b$)$ The water density is $1000k\frac{g}{m^3}.$

c$)$ The velocity of the water in the pipe is small owing to its much larger diameter.

d$)$ The atmospheric pressure is $100$ kPa $.$

e$)$ The hole acts as an ideal nozzle with no losses.