Fluid Dynamics - Free surface profiles in an open channel.

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Rubinder Singh Virdee

Fluid Dynamics Laboratory Investigation 2: Free Surface Profiles in an Open Channel.

Summary

The objectives of this laboratory experiment are to analyse the flow of water past a Sluice gate. Flow through a horizontal rectangular channel partially obstructed by a gate has been used to establish a hydraulic jump. Experimental measurements for upstream and downstream depths determining the free surface profile is compared to that predicted by theory for free surface profiles for the horizontal bed and Chezy’s roughness coefficient for the channel. This experiment enables design implications for many real civil engineering problems to be solved, or examined critically.

Introduction

Open channels are frequently encountered, “Natural Streams and rivers, artificial canals, irrigation ditches and flumes are obvious examples; but pipelines or tunnels which are not completely full of liquid also have essential features of open channels.” Predicting the free surface profile and the ability to control fluid levels especially the control of water levels and regulation of water discharge is necessary for purposes such as “irrigation, water conservation, food alleviation and inland navigation”.

This lab examines the rapid increase of depth from super-critical flow to sub-critical flow in a hydraulic jump. A hydraulic jump can occur downstream of a sluice gate (as will be the case in this lab), after a decrease in channel slope, due to an increase in roughness or channel width, or upstream of an obstacle located in a channel. It is an important energy-dissipating phenomenon; practical applications include the dissipation of energy below a spillway for the prevention of scouring farther downstream in the channel. The laboratory experiment not only has allowed visualisation but also made possible quantitative measurements of water depths, location of the jump and discharge rates.

The free surface profile shall be initially plotted using experimental measurements of the initial depths and the sequent depths. This shall then be compared to theoretical values.


Experimental Apparatus

The experiment has been carried out in the flumes of the Imperial College Fluid dynamics laboratory. The flow through a channel in which the sluice gate partially obstructs the flow has been used, (diagram I). The fluid flow is from left to right, with the supply to the flume being gravity driven. A weir at the downstream end of the flume controls the flow. The sluice gate is provided with stagnation tubes, facing directly upstream, these are filled with a colour dye such that the height of a column of water supported by pressure can be quantitatively measured (Diagram II, Appendix A).

The fluid in the upstream section builds up against the gate to a level Y1 and flows under the sluice gate at a height of Z. The fluid gains a higher velocity V2, and a shallower surface height Y2 downstream.

  • Once the flume had steady running water in the channel, it was adjusted such that the inflow rate Q was a low rate, and the upstream water depth was above the top stagnation tube on the gate.
  • Before any measurements were taken, a small amount of dye was placed upstream of the gate, allowing for a clear visualisation of streamlines.
  • The width of the flume and the height of the Sluice gate submerged were measured using a mm ruler.
  • Using a pointer gauge the upstream Y1 and downstream Y2 (see Diagram 1) water depths were measured.
  • The Discharge rate, Q (m3s-1) was measured. The flow was channelled into a tank of known cross sectional area, the time taken for a specific amount of fluid to discharge was measured, using a meter rule and a stopwatch.
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Results and Discussion

The discharge rate calculated experimentally is 8.744 x 10-3 m3s-1. The calculations have been illustrated in Appendix A. The theoretical value of discharge has also been calculated using the energy equation, (Appendix A, Part II) and is 9.235 x 10-3 m3s-1.

Although the two values are different, the discrepancy is 5.31%. The Experimental discharge is smaller than the theoretical discharge. A small error is expected, as the theoretical calculation does not take into account the friction between the water and the rough surface of the boundaries, which reduces the velocity of the flow. This justifies ...

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