ORIFICE

 INTRODUCTION

An orifice is a small opening of any cross-section (such as circular, triangular, rectangular etc.) on the side or at the bottom of a tank through which a fluid is flowing.

• It is used to measure rate of flow of fluid 
• Thickness of orifice in direction of flow is very small in comparison to its other dimensions. i.e Orifice has a sharp edge so that there is an contact with fluid and consequently minimum friction resistance at its sides.
• If sharp edge is not provided the flow will depend on thickness of orifice and roughness of its boundary too.
• The rate of flow of fluid through orifice depend on shape, size and form of orifice.

CLASSIFICATION OF ORIFICE

A) On the basis of cross sectional area

1. Circular orifice 
2. Triangular orifice
3. Rectangular orifice
4. Square orifice

B) According to size

1.  Small orifice - If head of liquid (H) >5 Times depth of orifice
2. Large orifice - H< 5d

C) According to shape of edge

1. Sharp edge orifice 
2. Bell mounted

D) According to nature of discharge

1. Fully submerged orifice 
2. Partially submerged orifice

FLOW THROUGH AN ORIFICE

   Consider a tank fitted with a circular orifice one of its sides as shown in fig.1 . Let H be the head of liquid above centre of orifice. The liquid flowing through orifice forms a jet of liquid whose area of cross section is less than orifice. The area of jet of fluid goes on decreasing and a section c-c section area is minimum . This c-c section is known as Vena contacta. C-C section approximately at a distance of half of diameter of orifice. 

At c-c the streamline are straight and parallel to each other and perpendicular to the plane of orifice . Beyond c-c the jet diverges and is attracted in the downward direction by gravity

 

        Now consider two points 1& 2 at vena contracta

Let the flow is steady and at a constant head H . Applying Bernoullis equation between 1 & 2 .

V1 is very small in comparison to V2 as area of tank is large as compared to area of jet.

HYDRAULIC CO-EFFICIENTS

1) Co-efficient of velocity Cv

2) Co-efficient of contraction Cc

3) Co-efficient of discharge Cd

Coefficient of velocity Cv

It is defined as ratio between actual velocity of a jet of liquid at vena-contracta and the theoritical velocity of a jet.

    Cv= Actual velocity of jet at vena-vena contracta 

                        theoritical velocity

Cv varies from 0.95 to 0.99

Coefficient of contraction (Cc)

It is defined as the ratio of area of the jet at vena contracta to the area of orifice.

Cc= Area of jet at vena contracta 

                  Area of orifice

    Cc varies from 0.61 to 0.69

Coefficient of discharge (Cd)

It is defined as ratio of actual discharge from an orifice to theoritical discharge from an orifice .

    Cd =        Actual discharge            =        Actual velocity x Actual area

                Theoritical discharge               Theoritical velo. x theoritical area

FLOW THROUGH PIPE

Pipe- It is a closed conduit generally of circular cross-section, used to carry fluid. Here we will consider flow of fluid through p under pressure only.

    Loss of energy in pipe.

when fluid flow through a pipe, the fluid experiences some resistance due to which some of the energy fo fluid is lost. This loss of energy is classified as 

Major losses

Due to friction

calculated by

i) Darcy- weisbach formula

ii) Chezy's formula

Minor losses

 This is due to

a) Sudden expansion in pipe

b) Sudden contraction 

c) Bend in pipe

d) Pipe fitting

e) An obstruction in pipe

Major losses:- The loss of head (or energy) in pipe to friction is known as Major losses.

        

Fiction between pipe wall and fluid layer (due to viscosity ) these losses are calculated by Darcy Weisbach Equation 

Hf-  Loss of head due to friction 

f-  Coefficient of friction . Function of Reynold's No.

f = 16/Re    for Re < 2000  

L = length of pipe.

V = mean velocitly

d = diameter of pipe.

Chezy's formula - for losses due to friction.

V = mean velocity

M = Hydraulic mean depth = Area of flow / wetted perimeter

M = A/P         for circular pipe

M = d/4 

C = Chezy's contant  =

i = loss of head per unit length = Hf/L

Hf = head loss due to friction 

L = length of pipe

Minor losses:- The loss of head or energy due to change of velocity of fluid in magnitude or direction is known as minor loss.

        In case of long pipe the above losses are small compared to losses due to friction.

a) Loss of head due to sudden expansion (or  enlargement) 

Consider a liquid flowing through a pipe which has sudden expansion.

Head loss will

b) Loss of head due to sudden contraction .

Consider a pipe which has a sudden contraction in area.