Abstract

The lab was fairly successful in demonstrating the impact of jets and how various
surface angles affect the resulting forces. Working with the fluids equipment gave a
direct understanding of how the high momentum of a jet flow is transferred to different
shapes, depending on how the fluid reacts on impact. While the jet angles at 90 and
120 yielded predictable results, the data found for 180 was not as expected. The
outcomes achieved followed the known principles of fluid statics, but discrepancies and
re-runs occurred during the experimentation which could have affected results. Overall,
a smaller angle resulted in less of a momentum shift of the fluid, requiring a higher flow
to sustain the weight applied opposite to the jet.
Introduction
A jet flow is any fluid flow coming from an opening of some sort. This typically
results in concentrated stream of fluid at high speeds, which has the ability to carry high
momentum and therefore can be used to do work. Energy can be extracted from a jet
by changing its direction upon a surface, and the objective of this lab is to analyze how
different redirections of flow affect the forces exerted on said surface.
Procedure
1) Experimenters attached a 90 impact head to the spring / weight apparatus
2) A 20 g weight was placed on top of the weight pan by an experimenter
3) Another experimenter controlled the flow of water hitting the impact head by
using a valve
4) Another experimenter observed the weight pan until its centre was lined up with
the level gauge
5) Another experimenter observed the volume of water used on a meter that read
out volume, the change in volume used was kept at a constant 5 litres throughout
the whole experiment
6) Another experimenter timed how long it took for the gauge to reach a change in
volume of 5 litres, the time keeper started when the volume reading experimenter
called out to start and the time keeper stopped when the volume reading
experimenter called out to stop
7) The times were recorded in a data table by an experimenter
8) Steps 1-7 were repeated when the impact heads were changed to 120 and 180
where the 20 g, 40 g, and 60 g weights were used for all 3 impact heads

Apparatus

Figure 1: Hydraulic Bench Apparatus

Figure 2: Water Jet and Impact Head Apparatus

Figure 3: Various Weights that were used on Weight Pan (20 g, 40g, and 60g)

Figure 4: Impact Heads (Includes 90, 120, and 180)

Figure 6: Volume Measurement Apparatus and Flow Control Valve

Figure 7: Volume Holding Container

Figure 8: Full Testing Apparatus (Includes jet, impact head, weight pan, level gauge,
knurled nuts, adjustable feet, air vents, and spring)

Figure 9: Full Testing Apparatus Schematic [1]

Observations
Diameter of nozzle = 8 mm = 0.008m
Table 1: Using an impact angle of 90
Weight (g)
Force due to
Volume (L)
weight (N)
20
0.1962
5
40
0.3924
5
60
0.5886
5
Table 2: Using an impact angle of 120
Weight (g)
Force due to
Volume (L)
weight (N)
20
0.1962
5
40
0.3924
5
60
0.5886
5
Table 3: Using an impact angle of 180
Weight (g)
Force due to
Volume (L)
weight (N)
20
0.1962
5
40
0.3924
5
60
0.5886
5
The force equation given for the jet is:

Since

and that

Where:

, the equation becomes:

(
(

is the fluid density

Q is the volume flow rate
A is the jet cross-sectional area
is the jet redirected angle

Time (sec)

Q (m3/s)

50.13
35.26
29.4

Time (sec)

Q (m3/s)

52.3
40.76
34.05

Time (sec)
55
48
43

Q (m3/s)

Since the fluid is water the density will be 998 kg/m3

The volumetric flow rate can be calculated using the formula:
Using the values from table 1 at 20g,
(

)(

For an impact angle of 90:

For an impact angle of 120:

For an impact angle of 180:

Sample calculation for impact angle 90 at 20 g:

)
(

)
)

Table 4: Using an impact angle of 90

Weight (g)
Force due to weight (N)
20
0.1962
40
0.3924
60
0.5886

Impact force (N)

Table 5: Using an impact angle of 120

Weight (g)
Force due to weight (N)
20
0.1962
40
0.3924
60
0.5886

Table 3: Using an impact angle of 180

Weight (g)
Force due to weight (N)
20
0.1962
40
0.3924
60
0.5886

Impact force (N)

Impact force (N)

The predicted results are small and show that the system is not in equilibrium as the
impact force is significantly smaller compared to the force due the weight.

Graph 1: Jet Impact Force VS Weight

Discussion of Results
With regards to the experiment, 3 different weights corresponding with 3 different
angles yielded 9 experimental results. In each situation, the volumetric flow rate (Q)
was calculated, essential for finding the impact forces.

Theoretically speaking, the flow rate of the liquid (in this particular case, water)
divided by the cross-sectional nozzle area of the travelling reservoir would result
in finding the velocity at which the water travels. By the process of dimensional
analysis:
,

Where Vw is the velocity of the water

, Q is the volumetric flow rate
, and A is the cross sectional area.
These 3 variables are composed of their own corresponding dimensions that
ultimately define their units of measurement. {L} represents the principle
dimension of length, and {T} represents the principle dimension of time. Dividing
the area by the volumetric flow rate will result in the velocity of water, as shown
by the dimensional analysis.

The horizontal distance between the jet and the target is small. As a result,
deceleration of the moving liquid is little to negligible. In classic kinematics, the
projectile motion of a mass is determined by its initial velocity, final velocity,
distance travelled, time it travelled, and the vertical acceleration of gravity. When
combining the effects of both vertical and horizontal components of the mass, the
velocity at which the mass hits the ground is ultimately determined by the
horizontal distance travelled. The horizontal speed will always be constant
throughout the motion. Since in this particular case, the velocity at which the
water hit the target was almost entirely equal to the initial velocity, gravity had
negligible effects due to the small distance travelled.

Based on the theoretical predictions, it was assumed that the force would
increase with the impact angle. While the forces increased with weight as
predicted, when comparing to other impact angles, the impact force did not have
an effectively linear relationship. Observing Graph 1, it can be seen that the jet
at 180 started with a greater force at less weight, but increased at a lower
gradual pace than the other angles.

Sources of error
o The density of water was assumed to be 998kg/m3, however this value
corresponds to a temperature of 20C. The observed temperature
approximated to 24.13C which ultimately may have affected the
theoretical density. Since the density of water is inversely proportional to
the ambient temperature, the density was smaller than actually predicted,
resulting in a smaller impact force. To improve this, the actual density at
this temperature should have been used. The temperature should have
also been recorded after every test due to fluctuation.
o Human error due to parallax and coordination is probable. As the volume
was increasing, students were assigned to manually observe the change
in volume, while timing the overall rate of change. Parallax is a factor
because the observation angle may have given an incorrect result. The
timer may have also stopped at an incorrect time. To improve upon this,
multiple students should observe the rate of change at a 180 angle to the
volumetric pipette. There should also be more than one timer in order to
reduce responsive error.

Conclusion
The results obtained from the experiment were quite different than originally
predicted. While the jet angles at 90 and 120 yielded fair results, the data found for
180 was not as predicted. As the weight increased, the slope of the angle decreased
in retrospect with the other angles. As a result, the final weight yielded a smaller thrust
force compared to the other angles recorded. Our initial predictions said otherwise;
where the overall thrust force would keep increasing as the angle increased. This
suggests that at a horizontal angle, a maximum convergence occurs, where angles
greater than 180 result in a smaller thrust force.
References
1) MEC 516 - Fluid Mechanics I Laboratory Department of Mechanical Engineering.
Toronto: Ryerson U. 13. Print.