Sharp-Edge Orifice Flow Equation

A sharp-edge orifice is a thin plate with a precisely drilled hole that restricts fluid flow, creating a pressure drop. The fundamental orifice flow equation relates flow rate to the orifice geometry and pressure differential:

Q = Cd x A x sqrt(2 x dP / rho)

• Q: Volumetric flow rate
• Cd: Discharge coefficient (typically 0.6 - 0.65 for sharp-edge)
• A: Orifice area = pi x d^2 / 4
• dP: Pressure drop across the orifice
• rho: Fluid density

Discharge Coefficient (Cd)

The discharge coefficient accounts for the fact that actual flow is less than theoretical due to the formation of the vena contracta - the point where the jet contracts to its minimum diameter after passing through the orifice.

For sharp-edge orifices, typical Cd values are:

• 0.60: Conservative value, thin sharp edge
• 0.62: Typical for well-made sharp-edge orifice
• 0.65: Slightly rounded edge or thick plate

Cd depends on Reynolds number, edge sharpness, orifice thickness, and upstream flow conditions.

Vena Contracta

When fluid passes through a sharp-edge orifice, it cannot make an instantaneous 90-degree turn at the orifice edge. Instead, the streamlines continue to converge downstream, reaching a minimum cross-sectional area called the vena contracta.

For a sharp-edge orifice, the vena contracta occurs approximately 0.5 to 1 diameter downstream and has an area roughly 0.6-0.65 times the orifice area.

Velocity Through Orifice

The theoretical velocity through the orifice (ignoring losses) is given by Torricelli's equation:

V = sqrt(2 x dP / rho)

The actual velocity at the vena contracta is approximately equal to this theoretical velocity multiplied by a velocity coefficient (typically 0.98-0.99).