In the flow through an orifice shown in the diagram, theflow goes through a minimum area downstream of the orifice. This is called the “vena contracta.” The ratio of the flow area atthe 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 = CA_o(2Δp/ρ)^1/2, where A_o is the area of the orifice, Δp 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 pressuredifference of 10 kPa for a 1.5 cm orifice centered in a 2.5-cmdiameterpipe.

Transcribed Image Text:

2.5 cm 1 1.5 cm C Vena contracta