In a cylindrical pipe with length L and radius Rr water is flowing at a constant velocity u. The total momentum of the water flowing through the cylinder, denoted P. is given by P := p x u x V, where p = 0.997kg/'m3 is the density of water and lizard-32L is the volume of the cylinder. However. a general pipe need not be a cylinder since the radius R can change as you go along the length. That is if :1: indicates hour.r far along the pipe you are. R 2 RM). Due to a principal called conservation of massr the velocity of the water must change if the radius changes. 'Il- -ID llHx O X l_ (smaller arrows indicate smaller velocity). In particular. the velocity at is a function of R: u = 35(3). {a} {6 points} For a general pipe of length L, use the method of slices to give an integral formula for the total momentum of the water flowing through the pipe. (b) [4 points) Suppose now that L = 0.5 and 1 1 Use your formula that you derived in {a} to find the total momentum ofthe water flowing through the pipe