FLOW THROUGH ORIFICES 1. INTRODUCTION
The analysis of the quantity of water which can be discharged through an orifice is arrived at in a simple, straightforward manner by the application of Bernoulli's equation. However, experimental tests typically produce a result which is only some 6! of the solution indicated by the simple analysis. The study of water flow through an orifice is therefore a classic topic to illustrate the need for a semi"empirical approach which is so often required in #echanics of $luids. 2. DESCRIPTION 2.1 General Description
The %ussons &nlet Head Tan (6)*+ can be used for the investigation of the flow of water through a horiontal or a vertical orifice. This tan is detailed in (art ) of the manual. -ater is supplied to the tan via a hose connection to the base inlet, and is then distributed within the tan by a vertical v ertical perforated sparge pipe. This arrangement avoids excessive turbulence and enables a steady level surface to be maintained. Two threaded holes are cut into the tan in which to mount the orifice being studied, one in the tan base for 'vertical' discharge, and the other in the tan side for 'horiontal' discharge. n orifice can be screwed into either of the threaded holes and the unused aperture sealed with the blaning plug provided. The union adaptor piece supplied with the &nlet Head Tan is not required for the orifice experiments and should be removed before insertion of the orifice under test. scale is mounted on the side of the tan to enable the height of of the water above either orifice position to be determined. The ero of the scale coincides with the centre of the side outlet ou tlet position, but note that the face of the bottom outlet position is +/mm below the centre line of the side outlet. -hen an orifice is fitted fitted in the horiontal discharge position a Tra0ectory (rofile Hoo 1auge (6)*2 can be used to determine the 0et profile. The details of the gauge are given in (art ) of the manual. 3etails of the orifices are given below and are illustrated in figure ). 2.2 P22! Ele"entar# Ori$ices
set of three circular orifices are supplied in a plastic case. 4ach orifice is mounted in a )5 B( threaded orifice holder, secured between an '7' ring and a circlip. The orifice details are8 a9 +mm diameter orifice, square edged *:6)mm thic b9 mm diameter orifice, square edged ):;;mm thic c9 /mm diameter orifice, square edged ):;;mm thic.
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$igure ) !. THEOR% !.1 Intro&'ction
There are two methods of analying the discharge of a vessel through an orifice. The first of these applies when the orifice is small in comparison with the head above the orifice@ this is nown as small orifice analysis. &n this case variations in velocity with height within the 0et of water can be ignored and the velocity is assumed to be constant. The alternative analysis for large orifices taes into account the variation of velocity with height within the 0et of water issuing from the orifice. +.).) Aist of ymbols
a
cross sectional area of orifice
m2
ac
cross sectional area at vena contracta
m2
A
cross sectional area of orifice tank
m2
C c
coefficient of contraction
C d
coefficient of discharge
C v
coefficient of velocity
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length of side of square
m
F
force
N
g
acceleration due to gravity 9·807
m/s2
h
difference in height
m
head
meters
d
H
k
constant
l
length of side of equilateral triangle
m
area ratio
M
mass flow rate
m
kg/s
n
constant
P
pressure
ars
volume flow rate
m! /sec
t
time
secs
V
velocity
m/s
W
mass
gm
x
hori"ontal distance
m
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y
vertical distance
m
Z
height
m
!.2 Flo( T)ro'*) + S"all Ori$ice
%onsider a small orifice in either the base or side of a vessel with the head of water above the orifice ept constant.
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Figure 2 Discharge Through an Orifice
pplying Bernoulli's theorem between the surface of the water 1 and the orifice 0 yields
However P 1 = P o = atmospheric pressure
hence substituting these into Bernoulli's equation gives
&n other words, the theoretical velocity of the water passing through the orifice is given by
and hence the quantity of water being discharged through the orifice is given by
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However in practice the discharge is always less than this theoretical amount due to the viscosity of the fluid, to surface tension and due to resistance of the air. The disparity between the theoretical discharge velocity and the actual discharge velocity is allowed for by introducing a factor C v nown as the Coe$$icient o$ ,elocit# so that
&f the discharge from a sharp edged orifice is examined closely it will be observed that the minimum diameter of the 0et of water discharging from the orifice is smaller than the orifice diameter. The plane at which this occurs is nown as the ,ena Contracta , which is the plane where stream lines first become parallel. pplying the discharge equation at the vena contracta,
which can be written as
where or more simply as
where Typical values of C d range from *:6 to *:6, i.e. the actual flow through a sharp edged orifice is approximately 6*! of the theoretical value. The value of the %oefficient of 3ischarge may be determined by measuring the quantity of water discharged over a period of time whilst the head is maintained at a constant level.
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Flo( T)ro'*) Ori$ices List O$ E-peri"ents
4xperiment ) " $low through a %ircular 7rifice Settin* Up T)e Ori$ice E-peri"ent
Ca9 &f the Hoo 1auge and cale (6)*2 are to be used to measure the tra0ectory of horiontal 0ets then place the two positioning rails on the wortop of the Hydraulics Bench engaging them onto the locating pegs. 4nsure that the engraved rail is placed closest to the front of the Hydraulics Bench with the engraved side uppermost. Cb9 (osition the %onstant Head &nlet Tan (6)*+ onto the wortop of the Hydraulics Bench Cover the Hoo 1auge positioning rails, if fitted9 at the left hand side engaging two of the feet of the &nlet Tan onto the locating pegs. &f the orifices are to be fitted into the base of the inlet tan then the left hand support feet of the inlet tan should engage with the locating pegs so that the orifice can discharge downwards into the weir chan nel. &f the orifice is to be fitted into the side of the inlet tan then it should be moved to the left so that the right hand support feet engage with the locating pegs.
Cc9 Demove the hexagonal C+2mm across flats9 bush and adaptor from the side of the inlet tan. $it the required orifice into either the screwed hole in the ba se or in the side and plug the unused hole using the blaning plug provided.
Cd9 &f using either the triangular or square orifices in the side of the inlet tan, use the orientation tool to twist the orifice into the required position. Eote F These ; orifices are not tested in this experiment.
Ce9 %onnect the hydraulics bench flexible delivery tube to the connection provided on the rear of the inlet tan base. &nsert the flexible overflow tae off pipe, which is connected to the boss on the front of the inlet tan, into the overflow pipe of the volumetric measuring tan.
Cf9 Demove or refit the overflow extension tube Cscrewed9 in the inlet head tan to obtain a nominal head of ;*mm or **mm above the side orifice.
Operation
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Ca9 Settin* t)e Oer$lo( witch on the pump and control the flow rate by either ad0usting the hydraulics bench delivery v alve or by ad0usting the pump speed. The flow should be ad0usted carefully to produce a small but constant overflow and then fine ad0usted to give ;* or **mm head as required. Cb9 Flo( /eas're"ent The discharge from the orifice may be measured using the standard weir or much more accurately by using the volumetric measuring tan and taing the time required to collect a quantity of water. The quantity should be chosen so that the time to collect the quantity is at least );* seconds to obtain a sufficiently accurate result. Because of the action of the overflow it is not possible to u se the rotameter for this experiment.
Cc9 /eas're"ent o$ Hea& The scale attached to the side of the inlet tan has its ero level with the centre line of the side outlet boss. The face of the bottom outlet is +/mm below the centre line of the side outlet. -hen the bottom outlet is used, a fixed increment should be added to the scale reading of ;6mm C+/ " );9 for all orifices. E0PERI/ENT 1 FLOW THROUGH + CIRCUL+R ORIFICE +i" To investigate the discharge characteristics of circular orifices sub0ected to a constant head. E-peri"ental Proce&'re
). $it the +mm diameter orifice into the side of the inlet head tan. Demove the overflow extension pipe. tart the pump and set up an inlet head of ;cm. #easure the flow rate using the volumetric measuring tan. ;. Deplace the overflow extension pipe and set up an inlet head of *cm. #easure the flow rate. +. Demove the orifice and refit it into the base of the inlet tan and refit the blaning plug into the side of the tan. Depeat the readings with the inlet head tan levels of ; and *cm, which are now equivalent to a head above the orifice of ;2:6 and ;:6cm. >. Depeat the procedure using the mm and /mm orifices. Res'lts an& +nal#sis
). Decord the results on a copy of the result sheet for discharge characteristics. ;. $or each result calculate the flowrate.
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+. (lot a graph of square root of the head against the flow rate for each orifice diameter, the results should lie on a straight line passing through the origin to confirm that
#easure the slope of each graph and calculate the coefficient of discharge for each orifice from
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