# Test Data AC3-10

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# Combining/dividing flow in Y junction

## Overview of Tests

Experimental investigations of the flow in a ‘Y’ junction with an included angle of 50 degrees were carried out, with various distributions of flow in the minor branches, under both converging and diverging situations. The flow rates through the main branch were chosen to give nominal Reynolds numbers of (5, 7, 9 and 12) x ${\displaystyle 10^{5}}$.

Schematic diagrams of the rig arrangement for convergent and divergent tests are shown in Figures 1 and 2 respectively. Figures 3 and 4 are photographs showing the ‘Y’ junction in the convergent arrangement. The ‘Y’ junction was manufactured from Perspex, and its internal geometry is shown in Figure 5.

Each tapping plane had 4 equispaced taps around the circumference and these were connected via a ‘triple-tee’ piezometer ring (Reference 1) to an Orkney differential piston manometer. This presented an average of the pressures at the individual tappings in each plane to the manometer. The connections into the manometer were valved such that the pressures into the high and low sides of the manometer could be reversed, thus allowing the measurement of ‘negative’ differential pressures which arose at certain flow rate ratios through the branches.

Water was pumped from a sump to a constant-head tank, from which it entered the suction side of a 34 bar, 335 kW (450 hp) pump. The water then discharged into a 6-inch diameter high-pressure line containing a ‘T-section’. One arm of this section led to the test-line containing the ‘Y’ junction pipework arrangement and the other acted as a bypass line to the sump. Initial flow rates and pressures were set by adjusting two matched globe valves on the arms of this ‘T-section’. Finer control of the flow rates through the two branches was achieved using the 3-inch NB valves shown in Figures 1 and 2. In the case of the converging tests, a further valve at the downstream end of the test section was also used, to ensure enough back pressure to prevent cavitation.

3-inch turbine meters were installed in branches 2 and 3 to measure the flow rates, and a third 6-inch NB turbine meter was installed upstream of the installation to ease the setting up of the flow in branch 1. Prior to installation, these turbine meters were calibrated to give mean meter factors (and hence flow rates) with an uncertainty within 0.25 per cent for the 3-inch turbine meters and 0.4 per cent for the 6-inch meter over the required flow ranges.

Most of the pipework, and in particular the pipes adjacent to the ‘Y’ junction containing the tapping planes, were made of thermoplastic having smooth internal surfaces.

The internal diameters of the pipes adjacent to the ‘Y’ junction were supplied by Durapipe Ltd, the pipe manufacturers, and were as follows:

Branch 1 ${\displaystyle {(D_{1})}}$ = 72.3 mm

Branch 2 ${\displaystyle {(D_{2})}}$ = 54.4 mm

Branch 3 ${\displaystyle {(D_{3})}}$ = 54.4 mm

The following equation, given by the manufacturers, which is based on the modified Lamont S3 formula, was used to calculate the pressure losses between the tapping planes and the eye of the ‘Y’ junction for each branch:

${\displaystyle G=\mathrm {K} d^{n}h^{m}}$ (4)

Where G = flow rate (litres/sec)

K = 4.5 x ${\displaystyle 10^{-4}}$

d = internal diameter of pipe (mm)

h = pressure loss (m head of water/m length of pipe)

n = 2.6935

m = 0.5645

The distance from the tapping plane to the eye of the ‘Y’ junction for all branches was 0.457 m (18 inches). Hence the values of h from equation (5) were multiplied by 44.82 to convert the pressure loss to mbar for the 0.457 metre lengths.

From Reference 2, the junction head loss coefficient ${\displaystyle k_{ij}}$ for both convergent and divergent flows is defined as the ratio of the total head loss between branches i and j to the mean velocity head in the branch carrying the total flow. Hence, in this report, taking into account the pressure losses between the tapping planes and the eye of the junction, the following equations have been used:

For convergent tests:

${\displaystyle k_{2,1}={(\Delta P_{2,1}+1/2\rho _{w}V_{2}^{2}-1/2\rho _{w}V_{1}^{2}-h_{1}-h_{2})}/{(1/2\rho _{w}V_{1}^{2})}}$ (5)

${\displaystyle k_{3,1}={(\Delta P_{3,1}+1/2\rho _{w}V_{3}^{2}-1/2\rho _{w}V_{1}^{2}-h_{1}-h_{3})}/{(1/2\rho _{w}V_{1}^{2})}}$ (6)

For divergent tests:

${\displaystyle k_{1,2}={(\Delta P_{1,2}+1/2\rho _{w}V_{1}^{2}-1/2\rho _{w}V_{2}^{2}-h_{1}-h_{2})}/{(1/2\rho _{w}V_{1}^{2})}}$ (7)

${\displaystyle k_{1,3}={(\Delta P_{1,3}+1/2\rho _{w}V_{1}^{2}-1/2\rho _{w}V_{3}^{2}-h_{1}-h_{3})}/{(1/2\rho _{w}V_{1}^{2})}}$ (8)

## Test Cases

All the results are given in Tables 1 to 8, as listed below:

Table 1 Convergent flow, nominal ${\displaystyle Re_{D}=5x10^{5}}$

Table 2 Convergent flow, nominal ${\displaystyle Re_{D}=7x10^{5}}$

Table 3 Convergent flow, nominal ${\displaystyle Re_{D}=9x10^{5}}$

Table 4 Convergent flow, nominal ${\displaystyle Re_{D}=1.2x10^{6}}$

Table 5 Divergent flow, nominal ${\displaystyle Re_{D}=5x10^{5}}$

Table 6 Divergent flow, nominal ${\displaystyle Re_{D}=7x10^{5}}$

Table 7 Divergent flow, nominal ${\displaystyle Re_{D}=9x10^{5}}$

Table 8 Divergent flow, nominal ${\displaystyle Re_{D}=1.2x10^{6}}$

At certain flow ratios, it was apparent that pressures within the ‘Y’ junction were giving rise to ‘negative’ differential pressures, as indicated by the minus signs in the Tables.

## References

1. Blake, K. A. The design of piezometer rings. J. Fluid Mech., 1976, 78(2), pp 415-428

2. Miller, D. S. Internal Flow Systems. Published by BHRA Fluid Engineering, 1978, Ch. 13.

## Nomenclature

${\displaystyle D_{1},D_{2},D_{3}}$ Internal diameters of pipe branches 1, 2 and 3 m

${\displaystyle h_{1},h_{2},h_{3}}$ Pressure losses for lengths of pipe between the tapping

planes and ‘eye’ of junction for branches 1, 2 and 3 mbar

${\displaystyle k_{1,2}}$ Head loss coefficient between branches 1 and 2 for divergent test -

${\displaystyle k_{1,3}}$ Head loss coefficient between branches 1 and 3 for divergent test -

${\displaystyle k_{2,1}}$ Head loss coefficient between branches 2 and 1 for convergent test -

${\displaystyle k_{3,1}}$ Head loss coefficient between branches 3 and 1 for convergent test -

P Absolute pressure Pa

${\displaystyle \Delta P_{1,2}}$ Pressure difference between branches 1 and 2 for divergent test mbar

${\displaystyle \Delta P_{1,3}}$ Pressure difference between branches 1 and 3 for divergent test mbar

${\displaystyle \Delta P_{2,1}}$ Pressure difference between branches 2 and 1 for convergent test mbar

${\displaystyle \Delta P_{3,1}}$ Pressure difference between branches 3 and 1 for convergent test mbar

${\displaystyle Q_{1},Q_{2},Q_{3}}$ Flow rates through branches 1, 2 and 3 litre/s

${\displaystyle Re_{D}}$ Reynolds number, based on diameter of branch 1 -

t Temperature of water °C

${\displaystyle V_{1},V_{2},V_{3}}$ Mean velocities in branches 1, 2 and 3 m/s

${\displaystyle \mu _{w}}$ Dynamic viscosity of water Pa s

${\displaystyle \rho _{w}}$ Density of water kg/m3