Developing the practical
The apparatus consists of a transparent cylindrical chamber with a water nozzle in the middle.
Water from the nozzle is directed upwards where it strikes either a flat plate or a hemispherical cup, which disturbs the equilibrium on a lever arm, thus permitting the force of the water jet to be measured. A photograph and a schematic diagram of the apparatus are shown below.
(a)
(b)
Figure 1: Water jet experimental set up. Figure a show the actual apparatus used in the lab while figure b shows the schematic of it.
The magnitude of the force acting on a fluid when it strikes a surface (such as a vane) is given by the rate of change of momentum of the fluid stream. Using the Reynolds transport theorem, the force on the water in the control volume can be written as
where is the mass flow rate, and out and in are the velocities of the outgoing and incoming water streams. The force of the vane is equal and opposite to the force on the water jet. Positioning the water jet to strike the vane in its centre will mean that it will only be necessary to consider water velocities and forces acting in the vertical direction. Note that the jet of water’s velocity as it strikes the vane is less than the jet’s velocity as it leaves the nozzle due to the effect of gravity. This reduction in velocity can be determined using Bernoulli’s equation,
in this expression, is the local value of the gravitational acceleration while is the distance between the nozzle outlet and the plate. The nozzle velocity is determined from the mass flow rate as
Where is the water density and d is the nozzle diameter.
Some tips about the method.
With the flat plate in place and the counterweight in the zero position, balance the lever arm using the supporting spring weight so that the middle of the tally-weight is level with the lever arm. Make sure you record the position of the right-hand side of the counterweight.
With the delivery valve closed, start the pump. Open the valve slightly and centralise the water jet on the vane using the adjusting screws on the apparatus’s legs.
Open the delivery valve completely. Adjust the counterweight position on the lever arm so that the tally returns to its original position. Measure the flow rate by noting the time it takes to collect about 15.0 kg of water in the hydraulic bench’s weighing tank. The amount of water is not absolutely fixed, the goal being to measure over sufficiently large times, so the answer is not sensitive to timing errors or fluctuations in the flow rate.
Take a series of seven readings at reducing water flow rates, such that the counterweight is placed in approximately equally spaced positions. Note the counterweight position and flow-rate in each case. Close the delivery valve and turn the pump off to swap the vanes.
Remove the jockey weight, replace the flat plate with the hemispherical cup and repeat the procedure. This should be done by a laboratory technician. The plate or cup can fall into the chamber, and getting it out can be annoying.
Once the flat plate has been replaced by the hemispherical cup, take a set of seven measurements at equally spaced positions of the counterweight.
Theoretical considerations suggest that the force of the jet should be proportional to the square of the velocity.
Determine the water’s force striking the vane from the jockey weight position and plot the force against the square of the flow rate. (Plot the flat plate results on a separate graph from the results for the hemispherical cup.) The easiest way to do the calculations is to set up a spreadsheet.
For each flow rate, calculate the theoretical force on the vane. Plot the theoretical values on the same graph as the experimentally determined values. For each data point gradually work out what you need in a set of columns. The force exerted by the jet on each plate is expected to be roughly proportional to the square of the flow-rate. Is this supported by your data?
On the same graph, plot the ratio of the actual force divided by the theoretical force as a function of flow rate.
Attempt to explain any differences in the two sets of results. Observing the actual water flow while doing the experiment may help you achieve this.
Points to address in the discussion section
Derive equation (2) using Bernoulli’s equation.
The analysis can be simplified by assuming the change in velocity of the water jet is 90° in the case of the flat plate, and 180° in the hemispherical cup.
The test vane is supported by a lever, which is pivoted at one end and balanced by a supporting spring and a counterweight. The force on the plate is determined by the position of the counterweight. The lever arm is orientated in a horizontal position by moving the counterweight until the tally weight is correct. Then the water jet is started, and the counter weight-adjusted until the lever arm is horizontal (note, it is not crucial for the lever arm to be horizontal, merely for the lever arm orientation to be the same as when there was no water jet). Then the force of the jet on the vane is
where is the counterweight mass, is the distance the counterweight is moved, and is the distance from the pivot to the jet axis.
Derive equation (4) from first principles by looking at the apparatus and examining its functions.
The geometry of the apparatus. The geometric and physical properties of both apparatus are the same and tabulated below.
Nozzle Diameter 10mm Jockey
Weight 0.600 kg
Distance from pivot to jet axis 150mm
Height of vane above nozzle 35mm
