MAPUA UNIVERSITY

HYDRAULICS DEPARTMENT

Name: Camacho, Paul Danielle C.

Subject & Section: CE142P-02 / A27 Date Performed:
Instructor: Engr. Arsenio Adriano Date Submitted:

EXPERIMENT NO. 6
ORIFICE & FREE JET FLOW
EXPERIMENT A
OBJECTIVE:
To determine the coefficient of velocity of two small orifices
EQUIPMENT:
Hydraulics Bench
Stopwatch Orifice and Jet Apparatus
 TECHNICAL DATA:
Diameter of small orifice 0.003m
Diameter of large orifice 0.006m
Surface Area of Reservoir Ag= 1.812 x 10-3 m2
PROCEDURE (EQUIPMENT SET-UP)
1. Position the reservoir across the channel on the top of the hydraulic bench and
level the reservoir by the adjustable feet using a spirit level on the base. Remove
orifice plate by releasing the knurled nuts and check the orifice diameter, take
care not to lose the O-ring seal. Replace the orifice and connect the reservoir
inflow tube to the bench flow connector. Position the overflow connecting tube
so.
2. That it will discharge into the volumetric tank; make sure that this tube will not
interfere with the trajectory of the jet flowing form the orifice.
3. Turn on the pump and open the bench valve gradually. As the water level rises
in the reservoir towards the top of the overflow tube, adjust the bench valve to
give a water level of 2 to 3 mm above the overflow level. This will ensure
constant head and produce a steady flow through the orifice.

EXERCISE 1
DETERMINATION OF THE COEFFICIENT OF VELOCITY FROM THE
TRAJECTORY OF A JET

Column
Heading Unit Nom. Type Description

Orifice Measured Orifice diameter. The diameter is measured in

Diameter m d mm. Convert to meters in calculation.
Head Measured Head in reservoir for which trajectory data has
m h been take. The head is entered in mm. Convert
to meters for calculation.
Horizontal Measured Distance from the orifice of the measuring
Distance m x needle. The value is entered in mm. Convert to
meter for the calculation.
Vertical Measured Distance the jet has fallen from the level of the
Distance m y orifice. The value is entered in mm. Convert to
meter for the calculation.
(yh)0.5 Calculated Allows the plotting of a straight line
m relationship between the coefficient of velocity
Cv, and the horizontal distance for the jet. A
 graph of x plotted against (yh)0.5 will have a
slope of 2Cv.
Slope S Calculated Slope of x vs (yh)0.5 for each point.
Velocity Calculated
Coefficient CV = Average Slope / 2
Cv

DERIVATION:
From the application of Bernoulli’s Equation (conservation of mechanical energy for a
steady, incompressible, frictionless flow).
The ideal orifice outflow velocity at the jet vena contracta (narrowest diameter) is
vi = (2gh)1/2
Where h is the height of fluid above the orifice
The actual velocity is
v = Cv (2gh)1/2 (1)
Cv is the coefficient of velocity, which allows the effects of viscosity and therefore Cv < 1
Cv can be determined from the trajectory of the jet using the following argument:
Neglecting the effect of air resistance, the horizontal component of the jet velocity can
be assumed to remain constant so that in time, t, the horizontal distance traveled,
x = vt (2)
Because of the action of gravity, the fluid also acquires a downward vertical (y-
direction) component of velocity. Hence, after the same time, t, (ie. After travelling a
distance x) the jet will have a y displacement given by
y = gt2 / 2
which can be arrange to give
t = (2y/g)1/2 (3)
Substitution for t from (3) into (2) and for v from (1) into (2) yield the result
CV = x / 2(yh)1/2
Hence for steady flow conditions, ie. Constant h, CV can be determine from the x,y
coordinates of the jet. A graph of x plotted against (yh)1/2 will have a slope of 2C.
PROCEDURE – DETERMINATION OF COEFFICIENT OF VELOCITY FROM THE
TRAJECTORY OF A JET
1. Position the overflow tube to give a high head. Note the value of the head. The
jet trajectory is obtained by using the needles mounted on the vertical backboard
to follow the profile of the jet. Release the securing screw for each needle in turn
and move the needle until its point is just immediately above the jet and re-
tighten the screw. Attach a sheet of paper to the backboard between the needle
and board and secure it in place with the clamp provided so that its upper edge
is horizontal. Mark the location of the top of each needle on the paper. Note the
horizontal distance from the place of the orifice. (taken as x=0) to the coordinate
point marking the position of the first needle. This first coordinate point should
be close enough to the orifice to treat it as having the value of y=0, thus y
experimental errors in each of the quantities measured.
2. Repeat this test for a low reservoir head,
3. Then repeat the above procedure for the second orifice.

Column
Heading Units Nom. Type Description
Orifice m d Measured Orifice diameter. The diameter is entered
Diameter in mm. Convert to meters for calculation
Head m h Measured Head in reservoir for which trajectory
data has been taken. The head is entered
in mm. Convert to meters for calculation.
Volume m3 V Measured Taken from scale on hydraulic bench.
The volume collected is measured in
liters. Convert to cubic meters for the
calculation.
Time s t Measured Time taken to collect the known volume
of water.
(h)0.5 (m)1/2 Calculated Allows the plotting of a straight line
relationship between coefficient of
velocity, Cv, and the flowrate of jet, Q.
Slope S Calculated Slop of flow rate vs (h)1/2 for each point.
Discharge Cd Calculated Cd = S / (A0)(2g)1/2
Coefficient, Cd
 Column Units Nom. Type Description
Heading
Orifice m d Measured Orifice diameter. The diameter is
Diameter entered in mm. Convert to meters for
the calculation.
Area of Orifice m2 A0 Calculated Orifice area, calculated from the
orifice diameter.
Area of m2 Ar Given Surface area of the reservoir
Reservoir including area of constant head tank
Head m h Measured Head in reservoir at time t. The head
is entered in mm. Convert to meter
for calculations
Head at Start m h1 Measured Head in reservoir at time = 0. The
head is entered in mm. Convert to
meters for calculations.
Time s t Measured Time since start of run
h0.5 Calculated Allows the plotting of a straight line
relationship between coefficient of
discharge Cd, and the head loss
Slope S Calculated Slope of t vs (h1)1/2 for each point
Discharge Cd Calculated 𝐴𝑟 2𝑆 1
𝐶𝑑 = ( )2
Coefficient Cd 𝐴𝑂 𝑔

For unsteady flow, the time t, for the head to drop from h1 to h is given by
𝐴𝑟 2 1 1 1
𝑡= ( )2 ((ℎ1 )2 − (ℎ2 )2 ))
𝐶𝑑 𝐴𝑜 𝑔
Where:
Ar is the cross-sectional area of the reservoir (including the secondary chamber)
PROCEDURE:
1. For flow under a varying head, the overflow pipe is raised to obtain the
maximum head, the header tank is filled to just below the top and the bench
flow control valve closed and the pump stopped. Start a stopwatch when the
level reaches the first convenient scale mark (noted as h1) You will need to take
reading of the falling head (h) at 20-second intervals. You may fined the easiest
way of doing this to attach a piece of masking tape immediately adjacent to the
scale on the reservoir and at 20 second intervals mark the position of the falling
level. At the end of this procedure, you can read off the head position
corresponding to the known time.
 FINAL DATA SHEET
NAME: Camacho, Paul Danielle C. DATE:
SUBJECT & SECTION: CE142P-2 / A27 GROUP NO:
SEAT NO.

A. COEFFICIENT OF VELOCITY (v) UNDER CONSTANT HEAD

Orifice Diameter Head Horizontal Distance Vertical Distance 𝑥

√𝑦ℎ
d h x y (m) √𝑦ℎ
(m) (m) (m) (m)
0.0135 0 0 0
0.0635 0.005 0.0420 1.5119
0.1135 0.0120 0.0651 1.7435
0.006 0.353 0.1635 0.0250 0.0939 1.7412
0.2135 0.0430 0.1232 1.8330
0.2635 0.0620 0.1479 1.7816
0.3135 0.0810 0.1691 1.8539
0.3635 0.1140 0.2006 1.8121
1.7396
Cv = 0.8698
B. COEFFICIENT OF DISCHARGE UNDER CONSTANT HEAD

Orifice Diameter Head Volume Time Flow rate 𝑄

d h V t Q √ℎ √ℎ
(m) (m) (m3) (sec) (m3/s)
0.339 0.001 21.89 4.5683 x 10-5 0.5822 7.8466 x 10-5
0.006 0.348 0.001 20.09 4.9776 x 10-5 0.5899 8.4380 x 10-5
0.353 0.001 20.03 4.9925 x 10-5 0.5941 8.4035 x 10-5
0.361 0.001 19.19 5.211 x 10-5 0.600 8.6850 x 10-5
8.3483 x 10-5

Cd = 0.666

C. COEFFICIENT OF DISCHARGE UNDER VARYING HEAD

Orifice Diameter Area of Reservoir Head Time √ℎ𝟏 − √ℎ𝟐 √ℎ𝟏 − √ℎ𝟐
d h t 𝑡
(m) (m) (sec)
0.320 0 0 -
0.313 2 0.00622 3.1100- x 10-3
0.006 0.001812 0.308 4 0.01071 2.6775 x 10-3
0.304 6 0.01432 2.3867 x 10-3
0.299 8 0.01888 2.3600 x 10-3
2.6336 x 10-3

Cd = 0.0762
SAMPLE CALCULATIONS:

A. COEFFICIENT OF VELOCITY UNDER CONSTANT HEAD

TRIAL 2:

Orifice Diameter, d = 0.006

Head, h = 0.353
Horizontal Distance, x = 0.0635
Vertical Distance, y = 0.005

• (yh)0.5

= √𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑥 𝐻𝑒𝑎𝑑

= √(0.005)(0.353)

= 𝟎. 𝟎𝟒𝟐𝟎 𝒎

• Slope, S

𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
=
√𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑥 𝐻𝑒𝑎𝑑

0.0635
=
0.0420

= 𝟏. 𝟓𝟏𝟏𝟗

Coefficient of Velocity, CV

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑆𝑙𝑜𝑝𝑒
=
2

1.7396
=
2

= 𝟎. 𝟖𝟔𝟗𝟔
B. COEFFICIENT OF DISCHARGE UNDER CONSTANT HEAD

TRIAL 1:
Orifice Diameter, d = 0.006
Head, h = 0.339
Volume, V = 0.001
Time, t = 21.89

• Flow Rate, Q

𝑉𝑜𝑙𝑢𝑚𝑒
𝑄=
𝑇𝑖𝑚𝑒

0.001
=
21.89

= 𝟒. 𝟓𝟔𝟖𝟑 × 𝟏𝟎−𝟓

• (h)0.5

= √0.339

= 𝟎. 𝟓𝟖𝟐𝟐

• Slope, S

𝐹𝑙𝑜𝑤 𝑅𝑎𝑡𝑒
𝑆=
√𝐻𝑒𝑎𝑑

4.5683 × 10−5
𝑆=
0.5822

= 𝟕. 𝟖𝟒𝟔𝟔 × 𝟏𝟎−𝟓

• Coefficient of Discharge, Cd

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑆𝑙𝑜𝑝𝑒
=
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑂𝑟𝑖𝑓𝑖𝑐𝑒 𝑥 √2𝑔

8.3483 × 10−5
=
2.8274 × 10−5 × √2(9.81)

= 0.666
C. COEFFICIENT OF DISCHARGE UNDER VARYING HEAD

Orifice Diameter, d = 0.006

Area of Reservoir Ar = 0.001812
First Head, H1 = 0.320
Second Head, H2 = 0.313
Time t, = 2

• √𝒉𝟏 − √𝒉𝟐

= √0.320 − √0.313

= 𝟎. 𝟎𝟎𝟔𝟐𝟐

• Slope, S

√ℎ1 − √ℎ2
𝑆=
𝑡

0.00622
=
2

= 3.11 × 10−3

• Coefficient of Discharge, Cd

𝐴𝑟𝑒𝑎 𝑜𝑓 𝑅𝑒𝑠𝑒𝑟𝑣𝑜𝑖𝑟 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑜𝑓 𝑆𝑙𝑜𝑝𝑒(2)

𝐶𝒅 = ×√
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑂𝑟𝑖𝑓𝑖𝑐𝑒 𝑔

0.001812 2.6336 × 10−3 (2)

= × √
2.8274 × 10−5 9.81

= 𝟎. 𝟎𝟕𝟔𝟐