CONSIDERATIONS FOR THE SM OOTH TESTS

Velocity profiles were measured at the test section in the centre o f the channel. The glass bed was used as the measurement datum. The LDA system was

employed and great amount o f care was taken to produce sensitive results. The velocity profiles for the three flow rates used are plotted in Fig 5.6.

5.4.2.1 W ALL DISTANCE ORIGIN

Laser Doppler anemometry has been used to obtain the velocity measurements in this experiment. In this method there is an inherent problem with the exact location o f the control volume position.

Two methods have been used to locate the control volume independently, in order to add to the certainty o f its position. A piece o f brass with the exact thickness o f 1cm was placed on the flat glass bed and, in the case o f rough wall test, on the downstream glass plate section which was used as datum. Then, visually, the intersection o f the laser beams forming a cross was located on the brass plate, and the vertical micrometer locating the position o f the control volume was adjusted accordingly. The position o f the control volume was further checked using a similar method to that described by Raven (1977). A razor blade was positioned vertically 1mm above the bed at the exact lateral position o f the control volume. The beams were then raised gradually and the reading on the dial gauge, attached to the milling machine base equipment mount, was noted just as the control volume first touched the sharp edge o f the blade. A second reading was taken at the point when the beams became totally eclipsed by the razor blade, thereby locating the bottom of the control volume. It was thus possible to locate the centre o f the control volume relative to the glass datum by taking the mean o f the two dial gauge readings.

Notwithstanding the great degree o f care taken in locating the control volume, the fact remains that it has a diameter o f 0.4mm - so there will always remain some uncertainty about the exact point, within this volume, which relates to the measurement taken, especially near the boundary in the region o f high velocity gradient. Due to the large velocity gradient, and the consequently greater number

of particles passing through the upper section o f the control volume, there is a potential bias for the actual measurement position to be closer to the top o f the control volume. This inaccuracy could only be in the order o f 0.1-0.2mm, but might nevertheless be significant in the determination o f the near-the-bed velocity gradient. Such an error would also cause the near-the-bed (viscous region) velocity profile to deviate from a straight line. The velocity profiles near the bed are plotted in Fig 5.7 and it can be seen that in each case the profile falls on a straight line passing through the datum, and therefore the error can be disregarded. The size o f the control volume also imposes a practical limit as to how close to the bed measurements can be taken.

5.4.2.2 BED SHEAR STRESS DETERM INATION: SM OOTH

For the smooth tests the bed shear stress, Tq, could be obtained using two separate methods, both employing the experimental results. This was a great advantage as it increased the certainty in the value o f the bed shear stress obtained.

From the equations 3.8 and 3.9 it is known that;

T =Xo(l-y/D) 5.1

where;

x/p= -u'v' + v(dU/dy) 5.2

Near the smooth boundary in the viscous region u'v' tends to zero as y tends to zero, therefore;

Vp=v(dU/dy)y_^ 5.3

In the case o f the smooth tests, dU/dyy_^o can be deduced from the near-wall velocity profiles measured and plotted in Fig 5.7. The value o f the kinematic viscosity was also known, as the water temperature in each case had been measured. Therefore, for each smooth test the value o f bed shear stress, Tq» was

calculated in this way.

For each experiment a set o f Reynold stress (-u 'v ) results was also obtained as described in 4.5. At each measurement point the velocity gradient was likewise obtained from the measured velocity profiles, see Fig 5.6. Hence the total stress, x/p, was plotted against the position above the bed, y, for each o f the smooth tests (Fig 5.8). For each test using the value o f the Tq previously obtained from the

wall gradients, the straight line representing the total stress obtained from equation 5.2 is also drawn. There is a very close agreement between this line and the experimentally obtained total stress values plotted (see Fig 5.8), indicating the reliability o f both methods. In Fig 5.8 the Reynolds stresses at different heights above the bed for each test are also plotted. It can be seen that the Reynolds stress is the major contributing factor to the total stress, and that except for a small region near the wall, Reynolds stress is almost equal to the total stress for the majority o f the boundary layer.