Manning’s equation: Hydrologists sometimes use Manning’s equation to calculate the velocity v, in feet per second, of water flowing through a pipe. The velocity depends on the hydraulic radius R in...

Manning’s equation: Hydrologists sometimes use Manning’s equation to calculate the velocity v, in feet per second, of water flowing through a pipe. The velocity depends on the hydraulic radius R in feet, which is one-quarter of the diameter of the pipe when the pipe is flowing full; the slope S of the pipe, which gives the vertical drop in feet for each horizontal foot; and the roughness coefficient n, which depends on the material of which the pipe is made. The relationship is given by

For a certain brass pipe, the roughness coefficient has been measured to be n = 0.012. The pipe has a diameter of 3 feet and a slope of 0.2 foot per foot. (That is, the pipe drops 0.2 foot for each horizontal foot.) If the pipe is flowing full, find the hydraulic radius of the pipe, and find the velocity of the water flowing through the pipe.