Impact of jet

6 June 2016

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. The jet is directed on to the vanes of a turbine wheel, which is rotated by the force generated on the vanes due to the momentum change or impulse which takes place as the jet strikes the vanes. Water turbines working on this impulse principle have been constructed with outputs of the order of 100,000 kW and with efficiencies greater than 90%.

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In this experiment, the force generated by a jet of water as it strikes a flat plate, conical plate, and hemispherical cup may be measured and compared with the momentum flow rate in the jet.

2. DESCRIPTION OF APPARATUS
The Jet Impact Apparatus, H8, has been designed for use with the Hydraulic Bench, H1. This provides the necessary water supply and flow measurement facility. Figure 1 shows the arrangement in which the bench supply is led to a vertical pipe terminating in a tapered nozzle. This produces a jet of water which impinges on the vane in the form of a Flat Plate, Conical Plate, or Hemispherical Cup. The nozzle and vane are contained within a transparent cylinder; at the base of the cylinder there is an outlet by which the flow may be directed to the weighing tank.

As indicted in Fig. 1, 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 the tally suspended 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 the lever has been restored to its original balanced position.

Figure 1. Diagrammatic Arrangement of Apparatus.

3. BACKGROUND
Consider a vane symmetrical about the x-axis as shown in Fig. 2. A jet of fluid flowing at the rate of EMBED Equation.3 (kg/s) along the x-axis with the velocity uo (m/s) strikes the vane and is deflected by it through an angleβ, so that the fluid leaves the vane with the velocity u1 (m/s) inclined at an angle β to the x-axis. Changes in elevation and in piezometric pressure in the jet from striking the vane to leaving it are neglected. Figure 2. Vane symmetrical about x-axis.

Momentum enters the system in the x direction at a rate of:
EMBED Equation.3
Momentum leaves the system in the same direction at a rate of: EMBED Equation.3
The force on the vane in the x direction is equal to the rate of change of momentum change.
Therefore:
EMBED Equation.3
(newtons)
Ideally, jets are “isotachtic”, or constant velocity so that uo = u1. Therefore: EMBED Equation.3
(newtons)
Table 1 shows vanes of various shapes, the deflection angle, and the theoretical calculations of the force developed on the vanes.

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