## Flow through Orifices

**Introduction: **Orifice Discharge into Free Air 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

Q =discharge, ft^{3}/s (m^{3}/s)

C=coefficient of discharge

a=area of orifice, ft^{2}(m^{2})

g=acceleration due to gravity, ft/s^{2}(m/s^{2})

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

The coefficient of discharge C is the product of the coefficient 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 V_{2}=? 2gh

The coefficient of contraction C_{c} is the ratio of the smallest area of the jet, the vena contract, 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 no submerged orifices

**Approximate flow through an orifice:** There are several reasons you might want to install a restrictive device or orifice in a piping system.

- To create a false head for a centrifugal pump, allowing you to run the pump close to its BEP.
- To increase the line pressure.
- To decrease the flow through a line.
- To increase the fluid velocity in a line.

The equation for flow through an orifice is a simple one to understand. Only the units are somewhat awkward.

Q = AV

Q = the flow in cubic feet per second (ft^{3}/sec).

A = the area of the orifice in square feet (ft^{2}).

V = the velocity of the liquid in feet per second (ft/sec).

Experience shows that the actual flow is quite different than calculated because of the different shapes of the various orifices. Look at the following diagrams and you will see some of these popular shapes. Each has been assigned a "K" value.

We will enter that "K" value into our equation and the new equation becomes:

Q = AVK

To make the equation easier to handle we can express the velocity "V" as: