Orifice and Jet Flow
Sec(Tuesday)
Name ID
Hamad Almutlaq 219029524
Abdelhadi Almrri 219021375
Rashed Alrasheed 219007812
Anas Alnaim 219017296
Rakan Alsaleh 219032046
Instructor:Dr. Amer Aljaber
Experiment # 05: Orifice & Jet Flow
Table of contents
V. Orifice and jet flow.........................................................................................................................1
Objective:....................................................................................................................................................1
Theory:........................................................................................................................................................1
Co-efficient of velocity:........................................................................................................................3
Co-efficient of discharge:.....................................................................................................................3
Co-efficient of contradiction:..............................................................................................................3
Orifice and nozzles:..............................................................................................................................4
Theoretical trajectory path:................................................................................................................4
Apparatus:..................................................................................................................................................4
Procedure:...................................................................................................................................................5
Calculations & Results:..............................................................................................................................6
Discussion....................................................................................................................................................7
References...................................................................................................................................................9
List of Figures
Figure 1 Flow through an orifice, showing jet trajectory.............................................................................1
Figure 2 Determination of jet trajectory through probes by X and Y...........................................................2
Figure 3 Details of orifices and nozzles........................................................................................................4
Figure 4 Water Jet apparatus (Detailed)......................................................................................................5
Figure 5 Water Jet apparatus (Experimental)..............................................................................................5
Figure 6 Actual Trajectory of jet..................................................................................................................5
Figure 7 Determination of actual co-efficient of velocity............................................................................7
List of Tables
Table 1 Determination of actual co-efficient of velocity, contraction.........................................................6
Table 2 Difference between experimental and theoretical trajectory values..............................................8
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Experiment # 05: Orifice & Jet Flow
Orifice and jet flow
Objective:
The objective of this lab is to study the behavior of flow as it passes through the orifice and
determination of velocity and discharge co-efficient, and profile of the flow.
Theory:
Flow through an orifice is critical in many of the flows. In ideal cases, Bernoulli equation are
used to determine the flow. Consider the tank containing the water, as shown in figure 1 below.
Surface water is at the level of H from the orifice. If the orifice of the cylinder is open, flow
comes out of it with the velocity of V, which can be calculated using the equation below:
V = √ 2 gH
Where, H is the surface water height from the orifice and g is the gravitational pull.
Figure 1 Flow through an orifice, showing jet trajectory
Considering this into the Cartesian coordinates. When flow comes out of orifice, there are two
main components of flow, which vary across its path i.e. V x (Horizontal component) and Vy.
(Vertical component). At the instant, when flow starts from orifice, its vertical component is zero
and horizontal component is maximum. Eliminating the effects of air resistance, this could be
taken as constant velocity V. As the initial velocity of the flow is zero. It increases from to zero
as it comes out. Its component V y is dependent on the gravitational pull and can be calculated
using the equation below:
Vy = Vyo + gt
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Experiment # 05: Orifice & Jet Flow
As initial component is zero. So Vyo = 0. Above equation becomes:
Vy = gt
Where, g is gravitational pull and t is time. Considering the origin at the center of orifice, vertical
distance at any point can be calculated using the below equation:
Y = Yo + Vyo + 1/2gt2.
Origin is marked on the paper behind the needles, as shown in the figure 2 below:
Figure 2 Determination of jet trajectory through probes by X and Y
From the above figure, the horizontal distance from origin to first needed i.e. 0 to 1 = X1
Similarly, distance from 0 to 2 = X2
Vertical distance from origin to the bottom of first needle i.e. 0 to 1 = Y1
In the similar way, distance from 0 to 2 = Y2
Such values continue till X10 and Y10.
As the initial point is at the origin and initial velocity of the system is also zero. So, Y o and Vyo
become equal to zero and the equation becomes:
Y = 1/2gt2
Solving for the value of t:
t=
√ 2Y
g
Also considering the figure shown above:
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Experiment # 05: Orifice & Jet Flow
X = Vx t
Which leads to t = X/Vx
Solving for both equations containing t on left hand side:
X
Vx =
√ 2Y
g
Now, velocity of the flow can be determined if we know the values of X and Y. Y can be
calculated on the graph, with the help of tips of all probes. With knowing the value of X, we can
easily calculate the actual velocity of jet.
Co-efficient of velocity:
This co-efficient is used when there is difference between theoretical and actual velocity of the
system [1]. Mathematically, it is the ratio of actual to theoretical velocity and can be determined
using the equation below:
Actual velocity
Co-efficient of velocity = Cv =
Theoretical velocity
X
X
Cv =
√ 2 Y (2 gH ) =
g
2 √YH
Co-efficient of discharge:
As, we are measuring the flow using the measuring bench. Talking of the theoretical flow rate, it
is calculated using the formula below [2]:
Q = VA
Where, V is velocity of flow and A is the cross-directional area of orifice.
π 2
If d is diameter of orifice, area is measured as A = d
4
After that discharge co-efficient is calculated using the equation below:
Actual flow rate
Co-efficient of discharge = Cd =
Theoretical flow rate
QA
2
CD = π
d √ 2 gH
4
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Experiment # 05: Orifice & Jet Flow
Co-efficient of contradiction:
It is the ratio of discharge co-efficient to co-efficient of velocity. By definition, it is ratio of
cross-sectional area to the area of discharge aperture [3]. It is determined using the formula
below:
Discharge co−efficient C
Co-efficient of contradiction = CC = = D
Velocity co−efficient CV
Orifice and nozzles:
Orifice and nozzles are mostly faced by many flows. When placed in the flow path, they cause
much changes in the behavior of the flows. There will be change in pressure and velocity of
incompressible, as it passes through them. This change is dependent on size and configuration of
nozzles and orifice. For, this above mentioned co-efficients are introduced in flows, which also
tells the difference between actual and theoretical flow. Some of the detailed configurations of
orifices and nozzles are shown in the figure below:
Figure 3 Details of orifices and nozzles
Theoretical trajectory path:
As we have calculated earlier that:
t = X/Vx and Y = ½ gt2
Comparing both of the values, we get:
2
1 gX
Y= 2
2V X
Mentioned earlier that the theoretical velocity of the flow is √ 2 gH . Putting in the above
equation:
2
X
Y=
4H
Apparatus:
Instruments and machines utilized in this experiment are:
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Experiment # 05: Orifice & Jet Flow
Hydraulic bench to provide the water
Orifice in the tank
Mounting to measure level of water
4 nozzles
Side entry frame to observe the trajectory of flow
Depth gauge pins
Figure 4 Water Jet apparatus (Detailed) Figure 5 Water Jet apparatus (Experimental)
Procedure:
1. Apparatus is set as shown in the figure above. Orifice is also adjusted on the tank.
2. After that, overflow pipe is adjusted to maintain the level of water inside the tank.
3. Next, water supply is adjusted in such a way that constant steady flow of water is
achieved with minimized overflowing of water.
4. After the achievement of uniform and smooth flow of jet, probes tip are adjusted in such
a way that their tip has touched the flow.
5. After that, using the stopwatch and amount of collected water is measured. Using this,
flow rate of water is calculated.
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Experiment # 05: Orifice & Jet Flow
Figure 6 Actual Trajectory of jet
Calculations & Results:
First the calculations are performed for single case:
Water level measured = H = 380 mm = 0.38 m
Water collected = 15 L = 0.015 m3
Time = 43.975 s
Flow rate = QA = 0.000341
π
Area = (0.013)2 = 0.000133 m2
4
0.000341
Discharge co-efficient = Cd = = 0.941649
(0.000133) √ 2(9.8)(0.38)
At value of X = 200 mm = 0.200 m
Y = 30 mm = 0.03 m
200
Co-efficient of velocity = = 0.9368
2 √(30)(380)
From that, contraction co-efficient comes out to be:
0.941649
Co-efficient of contradiction = CC =
0.9368
= 1.005
For all other values of X and corresponding Y, results are shown in the table below:
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Experiment # 05: Orifice & Jet Flow
X (mm) Y (mm) 2√ YH (mm) Cv Cc
X1 40 Y1 2 87.17798 0.458831 2.052276
X2 80 Y2 5 123.2883 0.648886 1.451178
X3 120 Y3 11 150.9967 0.794719 1.184882
X4 160 Y4 18 194.9359 0.820783 1.147257
X5 200 Y5 28 213.5416 0.936586 1.005406
X6 240 Y6 40 261.5339 0.917663 1.026138
X7 280 Y7 55 301.9934 0.927173 1.015613
X8 320 Y8 73 348.7119 0.917663 1.026138
X9 360 Y9 94 389.8718 0.923381 1.019784
X10 400 Y10 115 435.8899 0.917663 1.026138
Table 1 Determination of actual co-efficient of velocity, contraction
We have also utilized the values given in the table above to confirm the trend of velocity co-
efficient on the overall flow. For that we have graph plotted between X and 2 √ YH and trend is
shown in the figure below:
Co-efficient of velocity
450
400
350
300
2(YH)^0.5
250
200
150
100
50
0
50 100 150 200 250 300 350 400 450 500
X (mm)
Cv Linear (Cv)
Figure 7 Determination of actual co-efficient of velocity
From the above graph, it has been seen that there is nearly linear trend between, it means slope of
the graph is nearly constant. From this, co-efficient of velocity is determined, whose values are
shown in the table 1.
Discussion
To begin with, let’s check the difference between the theoretical and actual flow rate. It is seen
that actual flow rate obtained is 0.0003411 m 3/s and theoretical one is 0.00036224. There is no
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Experiment # 05: Orifice & Jet Flow
much difference between both of the approaches as co-efficient of discharge comes out to be
0.9416. In some cases, this difference is much considerable because of area and configuration of
the orifice, but in our case, this difference is not much.
Talking of co-efficient of discharge and velocity, in our experiment they are 0.94 and 0.8263
(average). As, co-efficient of velocity, is dependent on the values of X and Y, which varies
across the flow. In our experiment, its value varies from 0.4588 to 0.9177 throughout the flow.
Based on the literature values, values of discharge co-efficient 0.61 to 0.65 and velocity co-
efficient is 0.95 to 0.99 [4]. Less value of discharge co-efficient in case of orifice plate is due to
sudden pressure reduction and flow restriction. As in our case, its value is 0.94. It means, there is
not much pressure reduction by orifice so there is not much difference between theoretical and
actual value of flow rate. Furthermore, there is not much difference the experimental and
literature value of the co-efficient of velocity.
Last one is the co-efficient of contraction. This co-efficient exist because of sudden contraction
in flows due to presence of orifice or nozzles in their path. As we have seen it is the ratio of
discharge and velocity co-efficient. In case of orifice, its value is mostly less than one, due to
sudden decrement in pressure as flow passes through the orifice. But in our case, as their no
considerable change is pressure or flow rate, contraction co-efficient is also mostly around 1.
Even the average of all values of contraction co-efficient that we have obtained is 1.13, which
means that there is not much effect of contraction seen here. Note that, this value is majorly
dependent on size and shape of the orifice.
In order the compare the theoretical and experimental values of trajectory values Y, we have
shown results in the table below:
X Y experimental Y theoretical
(mm) (mm) (mm)
X1 40 Y1 5 1.05
X2 80 Y2 10 4.21
X3 120 Y3 15 9.47
X4 160 Y4 25 16.84
X5 200 Y5 30 26.32
X6 240 Y6 45 37.89
X7 280 Y7 60 51.58
X8 320 Y8 80 67.37
X9 360 Y9 100 85.26
X10 400 Y10 125 105.26
Table 2 Difference between experimental and theoretical trajectory values
From the values obtained in the table above, it can be seen that initially, there is much difference
between theoretical and experimental value at the start. But as the flow proceeds, difference
between them begins to decrease. At the end of trajectory, there is much less difference
compared to trajectories values obtained at the start.
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Experiment # 05: Orifice & Jet Flow
Height does have the effect on the values of X and Y. As we know that H is the height level of
water from the orifice. More height leads to more pressure energy stored, which convert to
kinetic energy and comes out of the orifice. If the H is increased, flow coming out of orifice will
also have more energy stored, due to which effect of gravity on it will decrease. Due to which
value of Y, for similar value of X, will decrease. To summarize, keeping same value of X,
increase the value of H will decrease the value of H. This can also be seen in the equation of
theoretical trajectory Y theoretical.
References
[1] "Coefficient of Velocity," The constructor, 2021. [Online]. Available:
https://theconstructor.org/practical-guide/orifice-hydraulic-coefficients/2029/.
[2] "Coefficient of discharge," The constructor, 2021. [Online]. Available:
https://theconstructor.org/practical-guide/orifice-hydraulic-coefficients/2029/.
[3] "Definition of coefficient of contraction," Meriam Webster, 2021. [Online]. Available:
https://www.merriam-webster.com/dictionary/coefficient%20of%20contraction.
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