Water flows through a Venturi meter, as shown in the figure. The pressures of the water at locations a and b in the pipe support columns of water that differ in height by L $=14$ in$.$ The atmospheric pressure is $14\mathrm{.}7$ lbf$/$in$2,$ the specific volume of water is $0\mathrm{.}01604$ ft$3/$lb$,$ and the acceleration of gravity is g $=32\mathrm{.}0$ ft$/$s$2.$