Experiment (9)

Impact of a Water Jet

Introduction
Over the years, engineers have found ways to utilize the force that can be imparted by a
jet of fluid on a surface diverting the flow. For example, the pelton wheel has been used
to make flour. Furthermore, the impulse turbine is still used in the first and sometimes the
second stage of a stream turbine. Firemen make use of the kinetic energy stored in a jet to
deliver water above the level of the nozzle to extinguish fires in high-rise building. Fluid
jets are also used in industry for cutting metals and debarring. Many other applications of
fluid jets can be cited which reveals their technological importance.
One way of producing mechanical work from fluid under pressure is to use the pressure
to accelerate the fluid to a high velocity in a jet. When directed on to the vanes of a
turbine wheel, the force of the jet rotates the turbine. The force generated is due to the
momentum change or ‘impulse’ that takes place as the jet strikes the vanes. Water
turbines working on this impulse principle have been constructed with outputs of the
order of 100000 kW and with efficiencies greater than 90%.

Objectives
This experiment aims to:
1- Determine the force produced by a water jet when it strikes a flat vane and a
hemispherical cup.
2- Compare the results measured with the theoretical values calculated from the
momentum flux in the jet.

Apparatus
Figure (1) shows a more detailed drawing of the apparatus. The unit fits onto a hydraulic
bench, which supply water and measure flow.
The main part is a transparent cylindrical tank held between a top and bottom plate by
three threaded bars. The whole assembly sits on three adjustable legs.
The water enters the tank through a vertical inlet pipe that ends in a tapered nozzle inside
the tank. This produces a jet of water which hits the vane in the form of a Flat Plate and
Hemispherical Cup. The water leaves the tank through a drain pipe to allow you to direct
it back into the hydraulic bench.
The vane (hemispherical cup or the flat plate) supported by a pivoted beam, restrained by
a light spring. The beam carries a jockey weight. Adjusting the jockey weight sets the
beam to a balanced position (as indicated by the tally) along with adjustment of the
knurled nut above the spring. Any force generated by impact of the jet on the vane may
now be measured by moving the jockey weight along the lever until the tally shows that
the lever is back at its original balanced position.

1|Page Lab. Supervisor: Eng. Walaa Araydah

 Figure 1: General layout of the apparatus
Theory
Consider a vane symmetrical about the x-axis as shown in figure (2). A jet of fluid
flowing at the rate of 𝑚̇ along the x-axis with the velocity 𝑢0 strikes the vane and is
deflected by it through angle 𝛽, so that the fluid leaves the vane with the velocity 𝑢1
inclined at an angle to the x-axis. Note that this ignores changes in elevation and in
piezometric pressure in the jet from striking the vane to leaving it.
Momentum enters the system in the x-direction at a rate of:
𝑚̇𝑢0 [𝑘𝑔. 𝑚. 𝑠 −2 ] − − − − − − − −(1)

After being deflected through an angle 𝛽, the momentum leaves the system in the same
direction at a rate of:
𝑚̇ 𝑢1 cos(𝛽) [𝑘𝑔. 𝑚. 𝑠 −2 ] − − − − − − − −(2)

The force on the vane in the x-direction is equal to the rate of change of momentum
change. Therefore:

2|Page Lab. Supervisor: Eng. Walaa Araydah

 𝐹 = 𝑚̇(𝑢0 − 𝑢1 cos(𝛽)) [𝑁] − − − − − − − −(3)

Ideally, jets are of constant velocity, so that 𝑢0 = 𝑢1 . Therefore:

𝐹 = 𝑚̇𝑢0 (1 − cos(𝛽)) [𝑁] − − − − − − − −(4)

Figure 2: Vertical Jet of Fluid Striking a Symmetrical Vane

Now in the case of a flat plate, figure (3a), 𝛽 = 90° . So cos(𝛽) = 0 and equation (4)
reduces to:

𝐹 = 𝑚̇𝑢0 [𝑁] − − − − − − − −(5)

For a hemispherical cup, figure (3b), 𝛽 = 180° . So cos(𝛽) = −1 and equation (4)
reduces to:

𝐹 = 2𝑚̇𝑢0 [𝑁] − − − − − − − −(6)

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 Figure 3: Force Against Flat and Hemispherical Vanes
Fluid mass flow is equal to the product of its density, the area of the flow and the
velocity:
𝑚̇ = 𝜌𝐴𝑢 [𝑘𝑔/𝑠] − − − − − − − −(6)
From this, if you know the fluid (water) density, the cross-sectional area through which it
passes (the nozzle in this equipment) and the mass flow (from the hydraulic bench), then
you may find the velocity. Assuming that the density of the water is 1000 kg.m-3, and the
area of the nozzle is 78.54 mm2:
𝑚̇
𝑢= = 12.76𝑚̇ − − − − − − − −(7)
1000 × 0.00007854
The velocity u 0 of the jet as it is deflected by the vane is less than the velocity, u, at exit
from the nozzle because of the deceleration due to gravity. You can find the velocity u 0
at the vane using:

𝑢02 = 𝑢2 − 2𝑔𝑠 − − − − − − − −(8)

Where: s is the nominal distance from the nozzle tip to impact point on vane (35 mm).

𝑢02 = 𝑢2 − 2 × 9.81 × 0.035 → 𝑢0 = �𝑢2 − 0.6867

In order to calculate the force on the vane due to the jet we taken moment about the pivot
of the weighing beam. The weight beam forms a lever, pivoted at one end, with the jet
force upwards at a distance of 150 mm from the pivot. The mass of the jockey weight and
gravity are an opposing force downwards. At initial balance, you cancel out the mass of
the weigh beam itself using the balance spring, see figure (4). Substitute known values
into the equation we get:

𝐹 × 0.15 = 𝑀𝑔𝑦 − − − − − − − −(9)

Where: M is the mas of the Jockey weight is 0.6 kg, then:

4|Page Lab. Supervisor: Eng. Walaa Araydah

 𝐹 × 0.15 = 0.6 × 9.81 × 𝑦 → 𝐹 = 39.24𝑦

Figure 4: The balancing arm attached to the vane

Experimental Procedures

Part 1: Impact of a Water Jet

1) Fit the flat plate to the apparatus. If the cup is fitted, remove it by undoing the
retaining screw and lifting it out, complete with loose cove plate. Take care not to
drop the cup in the plastic cylinder.
2) Fit the cove plate over the stem of the flat plate fitting and hold it in position below
the beam. Screw in the retaining screw and tighten it.
3) Set the weigh-beam to its datum position. First, set the jockey weight on the beam
so that the datum groove is at zero on the scale, figure (5). Turn the adjusting nut,
above the spring, until the grooves on the tally are in line with the top plate as
shown in figure (6). This indicates the datum position to witch the beam must be
returned, during the experiment, to measure the force produced by the jet.
4) Start the hydraulic bench and set to maximum flow.
5) Move the jockey weight until the beam balances again. Note the distance y from
the zero position. Record it in table (1).
6) Record the flow rate by measuring the time required to collect 15 Liter of water in
the hydraulic bench.
7) Move the jockey weight inwards by 15 mm and reduce the flow rate until the
beam is approximately level. Record the scale reading in table (1).
8) Repeat step (6) to measure the flow rate.
9) Repeat steps (7) and (8) until you have about 6 sets if readings over the range
flow. Take the last set of readings at about 10 mm from the zero position.

5|Page Lab. Supervisor: Eng. Walaa Araydah

 10) Switch off the hydraulic bench pump and fit the hemispherical cup to the
apparatus using the method in steps (1) and (2). Repeat step (3) to check the
datum setting.
11) Repeat steps (4) to (9), but this time move the jockey in steps of about 25 mm and
take the last set of readings at about 20 mm from the zero position. Record the
data in table (2).

Figure 5: Jockey in datum position

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 Figure 6: Tally in datum position

Table 1: Raw data - Flat Vane

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8|Page Lab. Supervisor: Eng. Walaa Araydah
 Table 2: Raw data - Hemispherical Vane

Discussion and Conclusions

1) Plot F against 𝑚̇𝑢0 for the two vanes, and, for the two values of F, the theoretical
and the experimental.
2) How well do your results compare with the theory?

9|Page Lab. Supervisor: Eng. Walaa Araydah