Hydraulics The velocity of a molecule of liquid flowing through a pipe depends on the distance of the molecule from the center of the pipe. The velocity, in inches per second, of a molecule is given by the function v(r) = k(R² - r²), where r is the distance of the molecule from the center of the pipe in inches, R is the radius of the pipe in inches, and k is a constant. Suppose for a particular liquid and a particular pipe that k = 0.65 and R = 0.5.

a. Graph v(r).

b. Determine the limiting velocity of molecules closer and closer to the wall of the pipe.