Throat Inlet 1 2 (a) (10 pts) Show that Pressure tappings 2(Pm-P)gAh Q=CA P(A² / a² −1) - Exit

A volumetric flow rate Q of isopentane of density ρI flows through a pipe of crosssectional area A, and then passes through the Venturi “meter” shown in the following figure,
whose “throat” cross-sectional area is a. A manometer containing mercury (ρM) is connected
between an upstream point (station 1) and the throat (station 2), and registers a difference in
mercury levels of Δh.
(a)  Show that the equation on the figure is correct

(b)  If the diameters of the pipe and the throat of the Venturi are 6 in. and 3 in.,
respectively, what flow rate (gpm) of iso-pentane (ρi = 38.75 lbm/ft3 ) would register a Δh
of 20 in. on a mercury (s = 13.57) manometer? What is the corresponding pressure drop
in psi? Assume a discharge coefficient of CD = 0.98. 

the answers should be 1053 gpm and 9.35 psi