Orifice

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Overview

An opening, in a vessel, through which the liquid flows out is known as orifice. This hole or opening is called an orifice, so long as the level of the liquid on the upstream side is above the top of the orifice.

The typical purpose of an orifice is the measurement of discharge. An orifice may be provided in the vertical side of a vessel or in the base. But the former one is more common.

Types Of Orifices

Orifices can be of different types depending upon their size, shape, and nature of discharge. But the following are important from the subject point of view. A. According to size:

Small orifice
Large orifice

B. According to shape:

Circular orifice
Rectangular orifice
Triangular orifice

C. According to shape of edge:

Sharp-edged
Bell-mouthed

D. According to nature of discharge:

Fully submerged orifice
Partially submerged orifice

Jet Of Water

The continuous stream of a liquid, that comes out or flows out of an orifice, as known as the Jet of Water.

Vena-contracta

Consider an orifice is fitted with a tank. The liquid particles, in order to flow out through the orifice, move towards the orifice from all directions. A few of the particles first move downward, then take a turn to enter into the orifice and then finally flow through it.

23547/image001.jpg — *Image Courtesy* http://diracdelta.co.uk/science/source/v/e/vena%20contracta/source.html

It may be noted, that the liquid particles loose some energy, while taking the turn to enter into the orifice. It can be observed that the jet, after leaving the orifice, gets contracted. The maximum contraction takes place at a section slightly on the downstream side of the orifice, where the jet is more or less horizontal. Such a section is known as Vena-Contracta.

Hydraulic Coefficients

The following four coefficients are known as hydraulic coefficients or orifice coefficients.

Coefficient of contraction
Coefficient of velocity
Coefficient of discharge
Coefficient of resistance

Coefficient Of Contraction

The ratio of the area of the jet, at vena-contracta, to the area of the orifice is known as coefficient of contraction. Mathematically coefficient of contraction,

$C_{c} = \frac{Area\;of\;jet\;at\;vena\;contracta}{Area\;of\;the\;orifice}$

The value of Coefficient of contraction varies slightly with the available head of the liquid, size and shape of the orifice. The average value of $\inline C_{c}$ is 0.64.

Coefficient Of Velocity

The ratio of actual velocity of the jet, at vena-contracta, to the theoretical velocity is known as coefficient of velocity.

The theoretical velocity of jet at vena-contracta is given by the relation, $\inline v = \sqrt {2gh}$ , where h is the head of water at vena-contracta.

Mathematically coefficient of velocity,

$C_{v} = \frac{Actual\;velocity\;of\;the\;jet\;at\;vena\;contracta}{Theoretical\;velocity\;of\;the\;jet}$

The difference between the velocities is due to friction of the orifice. The value of Coefficient of velocity varies slightly with the different shapes of the edges of the orifice. This value is very small for sharp-edged orifices. For a sharp edged orifice, the value of $\inline C_{v}$ increases with the head of water.

Coefficient Of Discharge

The ratio of a actual discharge through an orifice to the theoretical discharge is known as coefficient of discharge. Mathematically coefficient of discharge,

$C_{d} = \frac{Actual\;discharge}{Theoretical\;discharge}$

$= \frac{Actual\;velocity \times Actual\;area}{Theoretical\;velocity \times Theoretical\;area}$

$= C_{v} \times C_{c}$

Thus the value of coefficient of discharge varies with the values of $\inline C_{v}$ and $\inline C_{c}$ . An average of coefficient of discharge varies from 0.60 to 0.64.

Coefficient Of Resistance

The ratio of loss of head in the orifice to the head of water available at the exit of the orifice is known as coefficient of resistance.

$C_{r} = \frac{Loss\;of\;head\;in\;the\;orifice}{Head\;of\;water}$

The loss of head in the orifice takes place, because the walls of the orifice offer some resistance to the liquid as it comes out. The coefficient of resistance is generally neglected, while solving numerical problems.