One device to measure fluid flowrates is the venturi meter. Functionally, the venturi meter consists of a restriction in a pipe. Pressure is measured upstream and at the point of maximum constriction (the throat), and the pressure difference can be related to the flow rate. Let the cross-sectional area of the pipe be A and a at points 1 and 2, respectively. A manometer is connected between points 1 and 2 to measure the pressure difference. Write an expression for flow rate, v, in terms of A,a,g,h,, and m, where m is the density of the manometer fluid. Assume incompressible fluid, turbulent flow, and negligible friction. Hint: Solve this problem in two pieces. First write an expression for v in terms of P using an appropriate form of the energy balance, and then use a manometer equation to write an expression for P that can be substituted in