In the flow through an orifice shown in the diagram the flow goes through a minimum area downstream of the orifice. This is called the “vena contracta.” The ratio of the flow area at the vena contracta to the area of the orifice is 0.64.

a. Derive an equation for the discharge through the orifice in the form Q = CAo(2∆p/ρ)^1/2, where A_o is the area of the orifice, ∆p is the pressure difference between the upstream flow and the vena contracta, and ρ is the fluid density. C is a dimensionless coefficient.

b. Evaluate the discharge for water at 1000 kg/m³ and a pressure difference of 10 kPa for a 1.5 cm orifice centered in a 2.5 cm diameter pipe

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