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Wednesday, September 14, 2011

IMPACT OF A JET
Introduction
Water turbines are widely used throughout the world to generate power. In the type of water turbine referred to as a Pelton wheel, one or more water jets are directed tangentially on to vanes or buckets that are fastened to the rim of the turbine disc. The impact of the water on the vanes generates a torque on the wheel, causing it to rotate and to develop power. Although the concept is essentially simple, such as turbines can generate considerable output at high efficiency. Powers in excess of 100MW and hydraulic efficiencies greater than 95% are not uncommon. It may be noted that the Pelton wheel is best suited to conditions where the available head of water is great and the flow rate is comparatively small. For example with a head of 100m and a flow rate of 1m3/s, a Pelton wheel running at some 250rev/min could be used to develop about 900kW. The same water power would be available if the head were only 10m and flow rate were 10m3/s but a different type of turbine would then be needed.

 To predict the output of a Pelton wheel, and to determine its optimum rotational speed, we need to understand how the deflection of the jet generates a force on the buckets, and how the force is related to the rate of momentum flow in the jet. In this experiment, we measure the force generated by a jet of water striking a flat plate or a hemispherical cup, and compare the results with the computed momentum flow rate in the jet.

 Description of Apparatus
Figure shows the arrangement, in which water supplied from the Hydraulic Bench is fed to a vertical pipe terminating in a tapered nozzle. This produces a jet of water which impinges on a vane, in the form of a flat plate or a hemispherical cup.
The nozzle and vane are contained within a transparent cylinder, and at the base of the cylinder there is an outlet from which the flow is directed to the measuring tank of the bench. As indicated in figure, the vane is supported by a lever which carries a jockey weight, and which is restrained by a light spring. The lever may be set to a balanced position (as indicated by a tally supported from it) by placing the jockey weight at its zero position, and then adjusting 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 it has been restored to its original balanced position.


Theory of the Experiment

The equation of momentum is discussed. Consider how it applies to the case shown schematically, which shows a jet of fluid impinging on a symmetrical vane.


Sketch of jet impinging on a vane

Let the mass flow rate in the jet be m . Imagine a control volume V, bounded by a control surface S which encloses the vane as shown. The velocity with which the jet enters the control volume is u1, in the x-direction. The jet is deflected by its impingement on the vane, so that it leaves the control volume with velocity u2, inclined at an angle β2 to the x-direction. Now the pressure over the whole surface of the jet, apart from that part where it flows over the surface of the vane, is atmospheric. Therefore, neglecting the effect of gravity, the changed direction of the jet is due solely the force generated by pressure and shear stress at the vane's surface. If this force on the jet in the direction of x be denoted by Fj, then the momentum equation in the x-direction is
Fj = m(u2cos β2 − u1)

The force F on the vane is equal and opposite to this, namely

F = m ( u1 − u2 cosβ2 )
For the case of a flat plate, β2 = 90°, so that cos β2 = 0. It follows that
F = mu1

is the force on the flat plate, irrespective of the value of u2.
For the case of a hemispherical cup, we assume that β2 = 180°, so that cosβ2 = −1, and
F = m(u1 + u2)

If we neglect the effect of change of elevation on jet speed, and the loss of speed due to friction over the surface of the vane, then u1 = u2, so
F = 2 mu1
is the maximum possible value of force on the hemispherical cup. This is just twice the force on the flat plate.
Returning now to the rate at which momentum is entering the control volume is mu1. We may think of this as a rate of flow of momentum in the jet, and
denote this by the symbol J, where
J = mu1

For the flat plate, therefore, we see from Equation that
F = J

and for the hemispherical cup the maximum possible value of force is, from Equation

F = 2J

In the SI system the units of m and u are
M  [kg/s] and u [m/s]
In an equation such as (11.3), then, the units of force F are
F [kg/s].[m/s] or [kg m/s2] or [N]


EXPERIMENT
TWO

TITLE           
IMPACT OF JET

OBJECTIVE
1.      Study the relation between the force produced and the change of momentum when a jet strikes a vane.
2.      Compare between force exerted by a jet on a flat plate and on a hemispherical surface.

THEORY
In order to calculate the force caused by impact of a jet into a flat plate or curved vane, the change in momentum principle is applied;

Force = Rate of change in momentum

F = ρ Q ΔV

F = ρ Q (Vin – Vout)

Where; F: the force exerted by the jet on the plate.
ρ: the mass density of water (= 1000 kg/m3).
Q: volumetric rate of flow (m3/s).
ΔV: the change in velocity just after and before impact.

The volumetric flow rate in the equation 'Q' is calculated in the experiment by taking an amount of volume in a known period of time and then use;

Q = v / t
Vin is calculated in the experiment by first knowing the velocity at the nozzle and  then  using the motion equations.
Vnozzel is measured by know the diameter of the nozzle (dia = 10mm) and the volumetric flow rate 'Q' calculated previously,
Vnozzel = Q/ A
Then Vin is calculated by;
Vin2 = Vnozzel 2 – 2 g S
Where;
g: the gravitational acceleration (9.81 m/s2).
S: the distance between the jet and the plates (35mm)

Vout generally equals Vin cos θ, where θ represents the change in direction of the jet.

For the flat plat θ = 90◦, so that Vout = 0.0 .

For the Hemispherical cup θ = 180◦, so that Vout = -Vin

So the following relations are used for calculating the Predicted values of the force;

For the Cone cup: F = ρ Q Vin

For the Hemi spherical cup: F =2 ρ Q Vin
The measured force from the experiment is calculated by using the equilibrium of moment equation.
And the final relation for calculating the measured force is;
F = 4 * 9.81 * d

Where 'd' is the ruler reading for the jockey weight.

APPARATUS          

This apparatus is designed primarily for use on the TQ H1 or H1D Hydraulics Bench. By directly measuring the force exerted on the plates by the water jet, it allows the student to experimentally study the theoretical momentum laws used to solve jet impact problems.
An upper weigh beam is pivoted on precision bearings at one end and carries along its length the fixed test plate. The beam jockey and a scale are used to measure the jet force. An adjustable spring supports the lever and is used for setting the initial zero level of the beam. A hanging tally weight on the end of the beam is used to return the beam to horizontal each time a reading is required.
A high velocity jet is produced by the vertical tapered nozzle. For clear observation, both nozzle and test plate are contained in a transparent cylinder.
The apparatus is leveled for test using the plastic screwed ball feet provided on the base legs.
A drain tube, in the base of the cylinder vessel, is used to direct the water to the weigh tank of the H1 or H1D Bench where the flow can be accurately measured.

PROCEDURES       

1. The lever was set to is balanced position with the jockey weight is at its zero position.
2. The water valve was opened to it max, and the jockey was repositioned so that the lever is back to its balanced position.
3. The water tank was emptied of water and the refilled to take reading of time versus volume which was used to calculate the volumetric rate of flow.
4. A series of reading for the similar procedures was taken for the cone cup with reducing the rate of flow in each reading by using the valve.
5. The same steps were then repeated by using the hemispherical cup instead of the flat plate.

ANALYSIS
Nozzle diameter          :           10mm / 0.01m
Flow rate                     :           Volume/time
Area                            :           п(D/2)2
                                    :           п(0.01/2)2
                                    :           7.854x10-5 m2
Velocity                      :           Flow rate / Area
Cone cup                     :           Flow rate x ρ x velocity x (1 + cos2d)

CALCULATIONS



DATA COLLECTIONS
Force (N)
Volume, m3
Time, s
Flow rate, m3/s
Velocity, m/s
Calculate Force, N2
0.5





1





2





3





5







DISCUSSIONS
1.      Discussion differences obtained from the experiment as compared to theoretical calculation.
A theoretical said that to hold impact surface stationary is obtained by applying yhr integral forms of the continuity and momentum equations. The details of the model depend on whether or not the fluid stream leaving the impact surface is symmetric relative to the vertical axis of the surface however from the experiment we can see there is a bit differences from theoretical that is more accurate rather than theoretical calculation.
2.      Discuss possible factors influencing the results of the experiment.
a.       Error when taking readings
b.      Parallax error occur reading
c.       Vibration occurs when the reading is being taken to influence the meter reading on the equipment.
d.      Damage to pointer screw.
3.   Give examples of uses of water jet momentum in civil engineering
a. To release water in the drain by using water jet pump
b. To pump water from the water source when needed in construction.


CONCLUSIONS

From the results obtained and the plots graphed, the following points were concluded:
• As the volumetric rate of flow 'Q' increased, the force resulted from the impact of the jet on both the flat plate and the hemispherical cup, is increased to for the predicted 'F1' and the measured 'F2' values of the force. This relation can be seen clearly from the four plots accompanied with this report. This result was already predicted from the change in momentum equation of calculating the force.
• The predicted value of the Jet force showed larger values than the measured one. This might be occurred for the following reasons:
o Errors in taking the reading.
o Losses in the experiment apparatus.