Orifice Discharge into Free Air

An orifice plate is a thin plate with a hole in it, which is usually placed in a pipe. When a fluid (whether liquid or gaseous) passes through the orifice, its pressure builds up slightly upstream of the orifice but as the fluid is forced to converge to pass through the hole, the velocity increases and the fluid pressure decreases. The equation to determine the flow rate for a Rectangular Submerged Orifice is: Where: = Flow Rate through the orifice (cfs). = The cross sectional area of the open rectangular orifice in square feet (height x width). = Height (elevation) difference between the upstream and downstream still water surfaces. Multifarious hydrodynamic cavitating flow patterns have been detected in the flow of de-ionized water through a 40.5 μ m wide and 100.8 μ m deep rectangular slot micro-orifice established inside a 202.6 μ m wide and 20 000 μ m long microchannel. This article provides calculation methods for correlating design, flow rate and pressure loss as a fluid passes through a nozzle or orifice. Nozzles and orifices are often used to deliberately reduce pressure, restrict flow or to measure flow rate.

An orifice is an opening with a closed perimeter through which water flows. Orifices may have any shape, although they are usually round, square, or rectangular.
Discharge through a sharp-edged orifice may be calculated from:

Q = Ca?2gh

Laminar flow through slots is investigated using a flow-visualization technique and the numerical solution of the Navier-Stokes equations for steady flow. In the flow situation studied here, the fluid enters an upper channel blocked at the rear end and leaves through a lower channel blocked at the front end.

where
Q= discharge, ft³/s (m³/s)

C =coefficient of discharge

a =area of orifice, ft² (m²)

g =acceleration due to gravity, ft/s² (m/s²)

h =head on horizontal center line of orifice, ft (m)

The coefficient of discharge C is the product of the coef- ficient of velocity C_v and the coefficient of contraction C_c. The coefficient of velocity is the ratio obtained by dividing the actual velocity at the vena contracta (contraction of the jet discharged) by the theoretical velocity. The theoretical velocity may be calculated by writing Bernoulli’s equation for points 1 and 2.Thus

V₂= ?2gh

The coefficient of contraction C_c is the ratio of the smallest area of the jet, the vena contracta, to the area of the orifice.

Submerged Orifices

Flow through a submerged orifice may be computed by applying Bernoulli’s equation to points 1 and 2 in figure below

Values of C for submerged orifices do not differ greatly from those for nonsubmerged orifices.

This article provides calculation methods for correlating design, flow rate and pressure loss as a fluid passes through a nozzle or orifice. Nozzles and orifices are often used to deliberately reduce pressure, restrict flow or to measure flow rate.

Subscripts

Flow Through A Narrow Slot

In the case of a simple concentric restriction orifice the fluid is accelerated as it passes through the orifice, reaching the maximum velocity a short distance downstream of the orifice itself (the Vena Contracta). The increase in velocity comes at the expense of fluid pressure resulting in low pressures in the Vena Contracta. In extreme cases this may lead to cavitation when the local pressure is less than the vapour pressure of a liquid.

Downstream of the Vena Contracta in the recovery zone, the fluid decelerates converting excess kinetic energy into pressure as it slows. When the fluid has decelerated and returned to the normal bulk flow pattern the final downstream pressure has been reached.

The discharge coefficientcharacterises the relationship between flow rate and pressure loss based on the geometry of a nozzle or orifice. You can find typical values in our article on discharge coefficients for nozzles and orifices.

The relationships for flow rate, pressure loss and head loss through orifices and nozzles are presented in the subsequent section. These relationships all utilise the parameter, the ratio of orifice to pipe diameter which is defined as:

Where the point downstream of the orifice is sufficiently far away that the fluid has returned to normal full pipe velocity profile.

Horizontal Orifices and Nozzles

For orifices and nozzles installed in horizontal pipework where it can be assumed that there is no elevation change, head loss and flow rate may be calculated as follows:

Flow Through Slot Orifice

Vertical Orifices and Nozzles

For orifices and nozzles installed in vertical piping, with elevation change, the following head loss and flow rate equations may be used:

Expansion Coefficient

The expansion coefficient takes account of the difference between the discharge coeffcicient for compressible and incompressible flows. It is defined as:

The expansion factoris typically determined empirically and can be calculated using one of the formulas below.

For incompressible fluids:

American Gas Association method as described in AGA 3.1:

International Standards Organistion method as described in ISO 5167-2: