You are examining a venturi system to see if, by flowing water through it, you can achieve relative vacuum like the venturi valves in gas pump handles (i.e., the ones that go click when your tank is full). Assuming the density of water is 1 g/cm^3 and the viscosity is 0.01 g/(cm s), would the system in the figure work? Report your answer as the gauge pressure (in N/m^2) midway down the length of the constriction (i.e., the pressure in the middle of the constriction minus atmospheric pressure) with a negative pressure indicating a partial vacuum. Note that, because of assumptions and the limitations of this quiz format, you may get some pretty unrealistic numbers! For the variables in the diagram, the inlet pressure is 113920 N/m^2 and the outlet is at atmoshperic pressure (101000 N/m^2). The lengths of the pipes are L,p = 6.9 cm and the constriction is 6.75 cm long. The pipe diameters are d,p = 0.79 cm and d,c = 0.08 cm. For simplicity, you can assume laminar flow/smooth walls, there are no effects from the expansions/contractions, and the pipe/constriction are circular cross-sections.

Lp Lp Lc Pin dp dc dp Lp Lp Lc Pin dp dc dp