Department of Civil and Environmental Engineering
UNIVERSITY COLLEGE LONDON
Course E241 YEAR 1 FLUID MECHANICS
Title of coursework ORIFICE COEFFICIENT
Type Individual laboratory report
Member of staff Dr R. SIMONS
Date of lab classes Nov – Dec 2005
Submission date By 5.00pm on first day of Winter Term
Submission procedure in coursework box outside Departmental Office
The assessment will be based on the standard of presentation,
the accuracy of calculations/graphs etc. and the completeness,
relevance and conciseness of the discussion and conclusions.
Assessment If the presentation is of an unacceptably low standard, the report
criteria will be returned unmarked.
Overall grades A,B,C,D,E are passes. Grade F is a failure, and
the report can be revised and resubmitted if desired; if then
satisfactory, a grade E will be awarded.
Penalty for late submission 25% loss of marks per week
Date and method of return 4th week of Spring Term
after marking - via personal tutor
Details of the work required and the contents of the submission are included in the
During your work you should take pay full attention to the general information about
coursework preparation, production and submission given in the Departmental
DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING
E241 - 1ST YEAR FLUID MECHANICS
EXPERIMENT G - "FLOW THROUGH AN ORIFICE"
To determine the coefficients of contraction, velocity and discharge for a sharp-edged orifice in the base of
a tank. Hence, to determine a practical relationship between discharge rate through the orifice and head of
water in the tank. [Reports should be prepared individually and submitted before the deadline notified to
you at the start of session.]
Water enters the cylindrical tank through a perforated diffuser placed below the water surface. The flow
passes down the tank and leaves through a sharp-edged orifice, 25 mm diameter, set flush into the base.
The emerging jet is directed through the bench top into the calibrated collection tank. The volumetric flow
rate is measured by recording the time taken to collect a known volume of water in the tank.
The head of water is monitored in a tube connected to the base of the tank and mounted against a vertical
scale. A second vertical monitor tube is connected to a Pitot tube which can be moved into the water jet to
measure the total energy head. The Pitot tube may be traversed horizontally on a vernier slide graduated in
0.02 mm divisions.
The diameter of the jet is measured by traversing a fine horizontal wire (0.35 mm dia.) mounted on the
vernier slide, from one edge of the jet to the other - noting the distance on the vernier scale.
For STEADY, FRICTIONLESS flow of an INCOMPRESSIBLE fluid along a STREAMLINE,
Bernoulli's equation states :
p/ρg + u /2g + z = constant,
and, for the streamline 1 - 2 shown in the diagram above :
p1 /ρg + u1 /2g + z1 = p2/ρg + u2 /2g + z2 Equation 1
As the orifice diameter is small compared to that of the tank, then by continuity, u1 << u2 and u1 may be
considered negligibly small. Further, p2 = pa (atmospheric pressure), and from hydrostatics, p1 = ρg ( z2 +
ho - z1 ) + pa . Substituting these values into eqn. 1:
gives u2 /2g = ho
and u2 = ( 2gho ) Equation 2
Note that the choice of streamline is arbitrary. Therefore the theory predicts that the jet velocity is the same
for all streamlines i.e the velocity is constant across the jet.
Due to frictional effects, the actual velocity uA2 at section 2 is slightly less than ( 2gho ) and it may be
determined from the Pitot tube reading hc as :
uA2 = ( 2ghc ) Equation 3
The energy loss is represented by ( ho - hc ), and the coefficient of velocity Cv is defined as
Cv = uA2 /u2 = ( hc /ho ) Equation 4
On leaving the orifice the jet contracts because the direction of fluid motion cannot be changed
instantaneously at the orifice edge. The section of the jet where the streamlines first become parallel is
called `the vena contracta' and quantities labelled with suffix 2 relate to this section. The coefficient of
contraction Cc is defined by the ratio of cross sectional areas of the vena contracta a2 and the orifice ao
Cc = a2 /ao Equation 5
If the jet discharged at the ideal velocity u2 over the whole orifice area, the discharge Qo would be given by
: Qo = ao u2 . But the actual discharge Q must be equal to a2 uA2 , and a coefficient of discharge can be
defined as :
Cd = Q/Qo = a2 uA2 /ao u2 = Q/ ( ao ( 2gho ) ) Equation 6
Each coefficient is less than unity, and it can be seen from equations 4, 5 and 6 above that:
Cd = C v Cc .
1. Slide the wire and Pitot tube mounted on the vernier slide clear of the orifice jet zone. Turn the
inlet valve just above the cylindrical orifice tank fully open. (The outlet valve on the 6 inch supply
main has been pre-set to avoid overflow in the cylindrical orifice tank). Wait for the flow depth ho
to stabilize by carefully monitoring the manometer tube.
2. After the depth has stabilized, record the depth ho . Close the outlet valve on the calibrated
collection tank under the bench. Record the time taken to collect 100 litres of water. Great care
should be taken to start and stop the timer at the exact instant the water level in the monitoring
tube passes the relevant volume marks on the adjacent scale. Aim for 1 percent accuracy in the
flow rate determination. Repeat measurement and take average of the two values.
3. Carefully move the wire mounted on the vernier slide until it just touches the edge of the orifice
jet. Read and record the vernier scale. Withdraw the wire and repeat 5 times (in all). Push the
wire through the jet and similarly record 5 contact positions on its opposite side. Subtract the
average of the vernier scale readings and the wire diameter (0.35 mm) from the result to obtain the
diameter of the vena contracta.
4. Slide the Pitot tube to the centre of the jet and record the head hc in the manometer tube after the
head has fully stabilized. Traverse the Pitot tube across the jet at say 2 mm intervals recording hc
at each position. Try and get a reading as close to the jet edge as possible to pick up any possible
reduction in edge velocity due to friction effects. Prior to withdrawing the Pitot tube from the jet
replace the spring clamp on the connecting hose to prevent the manometer tube draining out
between ho changes.
5. Repeat 2, 3 and 4 above for 5 different levels of water in the tank, (adjusted by altering the inlet
flow rate), always allowing the water level to stabilise before starting to take readings. Note
smallest value of ho should have corresponding water level coincident with top of diffuser.
6. Plot a graph of Q against ho , and use the gradient of the line with equation 6 to determine an
average value of Cd .
Calculate Cd directly for each ho value using the relationship:
Cd = Q/Qo = Q/ ( ao ( 2gho ) ).
Calculate Cc , Cv for each head of water ( ho ) tested and hence the corresponding Cd values using
the relationship Cd = Cc Cv
Plot velocity profiles across the jet for the 5 values of ho .
Compare the values of Cd found in the 3 different ways. Comment on the comparison, thinking in
particular about the velocity profile measurements across the jet. Also compare all calculated coefficients
with values quoted in text books (say which). Does Cd vary with head of water? Comment. What
assumptions have been made in the experiment. Assess the experimental errors and the uncertainty they
imply in your results. What practical applications can you see for the results from this experiment.
This laboratory sheet should form the initial part of your report. Please ensure that you have read the
instructions for writing up experimental work (in the Blue Booklet) before completing your report.
A bullet-point style summary of the key outcomes of your report, each supported by the foregoing
discussion. This should include numerical values, their accuracy, and the reliability of the theory.
Proof-read through your report before submission.