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# ENGINEERING MATHEMATICS AND FLUIDS - Speech or Presentation Example

## Extract of sample ENGINEERING MATHEMATICS AND FLUIDS

that the plot of flow rate against depth of flow is a smoother curve with the theoretical flow rate in l/s, as compared to the curve with the observed flow rate. The same observation was noted in Figures 3 and 4 when the flow rates are expressed in m3/s. The curves in Figures 1 and 3 are smoother and the flow rates tend to increase as the depth of flow increases. The curves in Figures 2 and 4 have slight outliers from the typical pattern of the curve. However, like in Figures 1 and 3, the flow rates also tend to increase with the depth of flow.
Figures 5 and 6 present a plot of the theoretical flow rate and the observed flow rate, respectively, against the depth of flow, when the flow rate is in liters/sec. Similarly, Figures 7 and 8 show the same data when the flow rate is expressed in cubic meters per second.
It will be noted that Figure 6 is exactly the same as Figure 2, since the same observed values were used for both the rectangular weir and the V-notch weir. It was observed from Figures 5 and 6 that the plot of flow rate against depth of flow in the rectangular weir is a smoother curve with the theoretical flow rate in l/s, as compared to the curve with the observed flow rate, and that the flow rates tend to increase with the depth of flow. The same observation was noted in Figures 7 and 8 when the flow rates are expressed in m3/s. The curves in Figures 7 and 8 are smoother and the flow rates tend to increase as the depth of flow increases. The curves in Figures 6 and 8 have slight outliers from the typical pattern of the curve.
c). Plot a graph of log Q vertical against log H horizontal, and obtain the gradient of the best straight line of fit (estimated by eye). Comment on this value compared to the theoretical value expected.
Figure 9 presents the plot of the theoretical flow rate in liters per second against the depth of flow. As shown the plot almost defines a straight line, with a slope of the gradient line at about 49.

## Summary

Carry out an investigation to establish the relationship between depth of flow and discharge rate of water over both a “V” and a rectangular notch weir. You are to compare the discharge results against the given theoretical formulae.
Figures 1 and 2 present a plot…
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