CHARLES DARWIN UNIVERSITY

ENG243 – REACTION FORCE FROM A WATER JET

1. Introduction

Moving streams of water carry momentum. In order to change a direction or velocity of a water

flow it is necessary to apply a force with an equal an opposite force applied to the object redirecting

the stream of water. In this experiment, the force of a water jet on a flat plate and a hemispherical

cup will be determined by experimentation and compared with the expected result determined by

the application of the Reynolds transport theorem.

2. Apparatus and analysis of momentum transfer

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.

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 Fcv on the water in the control volume can be written as

( )inoutcv uumFrr

&r

−= (1)

where m& is the mass flow rate, and uout and uin are the velocities of the outgoing and incoming

water streams. The force of the vane is equal and opposite to the force on 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 velocity of the jet of water

as it strikes the vane is less than the velocity of the jet as it leaves the nozzle due to the effect of

gravity. This reduction in velocity can be determined using Bernoulli's equation,

hguu nozzleplate ∆−= 222

(2)

In this expression, g = 9.783 m/s2 is the local value of the gravitational acceleration while ∆h is the

distance between the nozzle outlet and the plate. The nozzle velocity is determined from the mass

flow rate as

2

4

d

mu nozzle

ρπ

&=

(3)

Where ρ is the water density and d is the nozzle diameter.

Question 1. Derive equation (2) using Bernoulli;s equation.

The analysis can be is simplified by assuming the change in velocity of the water jet is 90° in the

case of the flat plate, and 180° in the case of 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 counter

weight. The lever arm is orientated in a horizontal position by moving the counterweight until the

tally weight is in the correct position. Then the water jet is started, and the counter weight adjusted

until lever arm is again 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

L

xMgF

∆= (4)

where M is the mass of the counterweight, ∆x is the distance the counterweight is moved and L is

the distance from the pivot to the jet axis.

Question 2. Derive equation (4) from first principles by looking at the apparatus and examining its

functions.

The geometry of the apparatus

Nozzle Diameter 10mm

Jockey Weight 0.600 kg

Distance from pivot to jet axis 150mm

Height of vane above nozzle 35mm

3. Procedure and Analysis

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 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 centralize the water jet

on the vane using the adjusting screws on the legs of the apparatus.

Open the delivery valve completely. Adjust the position of the counterweight 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 20.0 kg of water in the weighing tank of the hydraulic bench.

Take a series of six readings at reducing water flow rates, such that the counterweight is 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. It is possible for the plate or cup to 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 six 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.

1. Determine the force of the water striking the vane from the position of the jockey weight,

and plot the force against the square of the flow rate. (Plot the results for the flat plate on a separate

graph from the results for the hemispherical cup.) The easiest way to do the calculations is to set

up a spreadsheet.

2. 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 frce 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?

3. On the same graph, plot the ratio of the actual Force divided by the theoretical Force as a

function of flow rate.

4. 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.

5. Lecturer/Technician Notes

I want them to use the edge not the middle to determine the position of the counterweight.

E Markland, A first course in Hydraulics, (Long Eaton, England : Tecequipment, 1976.)

621.2078.

Two stopwatches needed