relatively narrow radii. This is because it applies to perfect flow, not
turbulent flow. At higher pressures, longer lengths or with wider bores,
turbulence sets in.Despite this, I have found clear relationships.? I found that the rate of water flow is
inversely proportional to the length of the tube.? This is because the volume per second of the water flowing
out of the tube (rate), is determined by the forces acting upon it.? The pressure force pushes the fluid through
the pipe against the resistance of the viscous force.? A longer glass tube creates more force opposing the movement of
water (the force directly proportional to the length) and therefore produces a
slower rate.During the course of
the investigation, I also discovered that the rate of flow is proportional to
the radius squared.? Since the cross
sectional area which the water flows through is given by πr2,
you would expect less resistance with a larger area of cross section of tube,
because less of the volume of water is in contact with the sides of the tube. Although limited by the
time available for this investigation, the effect of viscosity of the fluid
could also have been measured.? For
example, dilutions of a glycerol solution could have been created and the effect
on the rate of flow measured.? Errors and improvements There were many sources of error in this investigation,
that may account for any anomalous results or discrepancies in the results and
that could be improved in any future experiments. ·
Measurement of length – The measurement of length is
accurate to ± 1mm because each reading is accurate to ± 0.5mm.? This would probably only have contributed a
small error in the investigation. ·
Measurement of radius ? The measurement of radius is
accurate to ± 0.1mm because each reading is accurate to ± 0.05mm.? However, because the measurement of radius
involves reading the difference on the vernier scale between the two cross hair
positions, the errors must be added.?
This means that the radius measurement is accurate to ± 0.2mm. This
means that the smallest radius measurement had an error of 0.2/0.4 x 100 = 50%
whereas the largest radius measurement had an error of 0.2/4.0 x 100 = 5
%.? Therefore the radius is a
significant source of error in this investigation. ·
Measurement of time – Digital stopwatches can give
reading precise to within ±0.01seconds.?
But human error makes readouts accurate to only around ±0.1s.? ·
Measurement of volume ? The measurement of volume was
accurate to ± 1ml.? This meant that for
example a volume reading of 200ml had an error of 0.5%.? However, volume readings such as that of
30ml had an error of 3 1/3 %.? Therefore
readings where the rate of water flow was lowest i.e. less water was collected
had higher inaccuracies associated with them.?
This could be prevented in a future investigation by collecting a
relatively constant volume of water each time and measuring the time taken for
it to reach that level.? The rate could
then be calculated in the same way (by dividing the precise volume by the reading
on the stop watch).? This would mean
that there would be a constant low error with each measurement. ·
Flow of water out of tube – Steady,
laminar flow that obbeys Poiseuille’s equation is only created by liquid flow
at low pressure, in relatively short tubes with relatively narrow radii. In
order to create steady, laminar flow in a future investigation, capillary tubes
with a low water pressure should be used. ·
Temperature ? Temperature affects the viscosity of a
fluid and therefore the rate of flow. ?The temperature of the water, since it came directly out of a tap,
was impossible to control and did vary from day to day.? However, readings for one variable were
taken one after another and therefore significant variations in temperature
were unlikely. ??Therefore, the
temperature of the water is unlikely to be a significant source of error in
this investigation. ·
Error bars ? Error bars have been plotted on all of the
graphs of the results.? However, due to
very consistent measurements being taken, the errors are very small.? Therefore it is likely that relationships
and conclusions drawn in this investigation, are correct.Bibliography 1.
Physics, Duncan T, 2nd edition, 1993, P235 2.
A laboratory manual of physics, Tyler F, 2nd
edition, 1964, P63