Aydin *et al.* introduced the weir velocity concept in 2011 for discharge measurement in contracted rectangular sharp-crested weirs. Gharahjeh *et al.* further reinforced this formula in 2015 to allow discharge to be computed using only weir velocity and crest width. These newly introduced expressions are tested and demonstrated to determine surface water yield of Tapah River in Sarawak. Aydin and Gharahjeh's formula is found to perform similarly to the improved discharge coefficient developed by French in 1986, but is simpler and easier to use. Exploring Aydin and Gharahjeh's formula through theoretical, experimental, and field approaches, it has been found that the formula performs well in a controlled environment. Discharge computations based on field data were determined to have been formerly underestimated, with the reason as yet undetermined.

## INTRODUCTION

### River safe yield

Safe yield, in the context of water storage, is a term generally used to describe the utmost quantity of water which can be guaranteed during a critical dry period (Linsley & Franzini 1979). The New Jersey (USA) Water Supply Authority (2000) defines safe yield from surface sources as the maintainable yield of a water system continuously throughout a repetition of the most severe drought of record. Safe yield estimates may be either simple or complex. The Commonwealth of Virginia USA (2016) divides the safe yield of a source into two systems: (i) simple intake (free flowing stream); or (ii) complex intake (impoundments in conjunction with streams). For the purposes of this study, Tapah/Beratok WTP has adopted complex intake with impoundment by a weir at the point of water supply intake in the Tapah River.

This study analyzes river water safe yield, specifically focusing on low flow events of the selected Tapah/Beratok WTP under the jurisdiction of JKR Sarawak^{1} to secure long term water supply. However, no records of water level readings or rainfall readings specific to the associated water supply catchment area are available. Thus, based on the problems identified, this study has the following objectives: (i) to analyze the safe yield of Tapah River in terms of the availability of water based on limited data and site restrictions; and (ii) to produce a design chart to enable estimation of a river safe yield for the Tapah River.

### A weir as a discharge measurement device

A weir may be defined as a barrier or fence which is designed across a river to alter the flow characteristics by raising the water level, diverting the water, or controlling its flow. This study focuses on determining the open channel flow rate of weir. A weir is simple to utilize in measuring the volumetric flow rate in a medium-sized river such as the Tapah River. Since the geometry of the top of the weir is known and all water flows over the weir, the depth of the water behind the weir can be converted to a rate of flow.

Using a weir as standard gauging device, the relationship between stage and flow can be studied. The flow is diverted through the structure, creating critical flow conditions and producing a unique relationship between the discharge and stage. Discharge measurement can be as simple as observing the stage of water just upstream of the device, while a simple associated equation may be used to compute discharge (Meals & Dressing 2008).

### Discharge equations

*Q*is discharge over the weir (m

^{3}/s);

*H*is head on weir (m);

*b*is crest width (m);

*g*is gravity acceleration and

*C*is the discharge coefficient for rectangular weir.

_{d}*C*(Arvanaghi & Oskuei 2013). Analysis and calibration tests have been performed by many researchers over many years to determine

_{d}*C*. After an experimental study conducted on a rectangular weir by Francis in 1850, it was concluded

_{d}*C*is a function of head

_{d}*H*, and height of weir crest

*P*. Furthermore, Rehbock (1929) considered the effects of Reynolds and Weber values to be negligible in most practical situations, such that the following correlation may be used:

*H/P*for full range of weir contraction

*b/B*. Furthermore, based on data from Kindsvater and Carter, French (1986) proposed an expression for

*C*as:

_{d}*H*. So, the effective length of weir crest is given by:where

*b*is effective width of the weir crest (m);

_{e}*b*is crest width (m);

*H*is head on the weir (m); and

*n*is number of end contractions.

Bos (1989) distinguished rectangular sharp-crested weirs into three types: fully contracted, partially contracted, or full width weirs, depending on the crest width *b* in relatively to the channel width *B*. sharp-crested rectangular weirs can be divided into two parts as contracted weirs (partially and full width) at the range of 0.3 ≤ *b/B* ≤ 1, and slit weirs (fully contracted) with *b/B* ≤ 0.25 (Sisman 2009; Aydin *et al.* 2011). The existing weir at Tapah/Beratok WTP has two lateral contractions giving the effect of sides shrinking on the emerging nappe. It is categorized as a partially contracted weir with weir width ratio falling between intervals of 0.3 ≤ *b/B* ≤ 1.

*et al.*(2011) introduced the weir velocity concept. According to their study, applying weir velocity instead of discharge coefficient

*C*will contribute to a more realistic and accurate calculation of discharge in rectangular contracted sharp-crested weirs. The suggested discharge relationship in terms of weir velocity

_{d}*V*is simplified and presented as follows:where

_{w}*Q*is discharge over the weir (m

^{3}/s);

*V*is weir velocity (m/s);

_{w}*b*is crest width (m); and

*H*is head on weir (m).

*et al.*(2012) further investigated possible expressions based on the weir velocity concept for a more compact discharge relationship. Based on their latest findings, weir velocity appears to be more suitable, with functions' best fit characteristics leading to a more precise empirical estimation (Gharahjeh

*et al.*2015). Then, discharge depends on weir velocity and crest width. Thus, the weir velocity can be expressed as:where the coefficient

*c*for contracted weir for

*b/B*≥ 0.3 is:

## METHODS

### Description of the study area

The Tapah River catchment area map provided by JKR Sarawak has been overlaid with spot satellite imagery to produce a geographical informative map that helps to visualize, analyze, and interpret data to understand relationships, patterns, and trends of the catchment topography. Observation of the satellite imagery indicates that the water supply catchment is healthy in its rural environment. Urbanization happens at the end of the catchment, brought about by the Kuching-Serian Highway. It is not threating the water source at the moment. This examination was followed by mapping and cataloging of the catchments, contours, and its associated land uses. ArcView, a geographic information systems software tool, is used to delineate the water supply catchment bounded by the Tapah/Beratok WTP and water intake point.

A pumping station is located about 25 m upstream of the weir. An old drawing dated 1971 had documented this weir. The research team was told the weir was upgraded to raise the to its current state in early 2000. Unfortunately, no further records of the weir or any hydrological study related to this weir or upstream catchment have been found. The dimensions of the weir, such as crest length *B*, crest width *b*, weir height *P,* and weir thickness *t* were measured using an open reel measuring tape and a leveling rod. In addition, the concrete dividing wall at the middle of the weir, acting as the supporting pier for the walk path, is also determined. Water level or head on the weir was measured using a leveling rod. A staff gauge affixed beside the pump station was used to verify the depth visually. The flow velocity of the Tapah River was measured using a probe meter. The primary probe device used for the field works was calibrated and validated using another probe of same model. Additionally, rainfall data was collected daily.

### Methodology

There are two conventional methods of determining river safe yield: long term or short term gauge records. Availability of long term gauge records is the most straightforward solution to determine the yield. With comprehensive and full database such as low flow over a period of 30–40 years, statistical analysis for drought recurrent year can be directly conducted to establish the safe yield chart.

The facts are: (i) Tapah River is an ungauged river, and (ii) the river is no longer a naturally free flowing but regulated by a weir. Therefore, it can be said that long term hydrological data is not available. Besides, drought of records and its return periods remain unknown for Tapah River. A different approach is required in this case.

Short term records for stream are a preferable method to determine river safe yield. This technique can be implemented with the existing storage facility, in this case the sharp-crested weir which impounds at the intake point of Tapah/Beratok WTP. Apart from that, adequate data collection methods for hydraulic parameters such as stream-flow, velocity, water level, and daily rainfall are required. Therefore, as explained in previous section, the weir is useful in analyzing Tapah River for safe yield with the fluctuation of water level (head) to flow relationships.

Site visits could provide the necessary data. As indicated in an interview with the plant attendant of Tapah/Beratok WTP, the lowest water level ever observed at the intake point may fall below the crest weir. This happened twice in March and September 2015. Flow measurement at weir may not represent the extreme low. However, low water level at weir could be measured. Site visits were carried out since September 2015, at the onset of tropical monsoon season over this region. Site visits that follow have been able to trace the high flow events and gradually transitioning to low flow events. Extrapolating from this range, it could give the extreme high or extreme low events. Although the extremes may not be accurate, they provide an indicator for reference.

### Laboratory set up

Field measurement data may be verified with laboratory experiments. Using the principle of similitude, a downscaled weir is placed at a flow channel and subjected to scaled flow events. With that, a range of discharges could be plotted for low water heads at weir. Similitude is widely applied in hydraulic engineering to test fluid flow conditions with scale models (Heller 2011). This laboratory experiment was carried out to compare and verify, both the onsite and offsite discharge values of the weir. Prior to experimental work, the similitude concept was applied.

## RESULTS AND DISCUSSION

### Theoretical flows over weir

As mentioned in previous section, there are several equations of a rectangular weir that may be used to determine the discharge value. Using two discharge coefficients of Rehbock (1929) (Equation (2)) and French (1986) (Equation (3)) substituted into Henderson formula (Equation (1)), two different sets of flow data are produced, respectively. Apart from that, using Aydin formula (Equation (5)) by substituting Gharahjeh's expression of weir velocity and coefficient of contracted weir (Equations (6) and (7)), another set of flow data was computed. Additionally, expression of end contraction (Equation (4)) incorporating the effect of contractions is applied in the three cases above. Out of these three sets of flow data, after comparing is done, the most suitable theoretical equation is then selected to be applied in this case study of Tapah River.

*H*to discharge

*Q*is plotted in Figure 3. All three flow curves display slightly deviations from each other. The correlation between these three lines give a statistical value of 0.9, suggesting that they are strongly related.

Comparing the substitution of discharge coefficient *C _{d}* into the Henderson formula, the flow curves for both Rehbock and French start to turn away from each other after

*H*= 0.3 m. Yet, from the theoretical perspective, this phenomenon happens may be due to accuracy of results with the consideration of the viscous and surface tension effects. Also, a combination of Rehbock's discharge coefficient with Henderson formula has been proven to be valid and suitable for application to a rectangular suppressed weir, where the crest length is equal to the width of the channel.

In contradiction, the flow curve from French is similar to that of Aydin and Gharahjeh, as both curves are closely aligned. This shows that the flow calculation using *C _{d}* expression proposed by French is not much different than the weir velocity concept. Thus, it is acceptable to apply weir velocity concept in this study as it is simple and easy to use.

### Field data collection

The height of water flowing over the weir, or head *H*, was measured from time to time over a six-month period. Data collection activity was initiated in November 2015. According to the Malaysian Meteorological Department (2015), the area is generally expected to experience hot and dry weather with a low amount of rain around March/April after the tropical monsoon that peaks in December/January. Thus, field work was expected until the end of April 2016. Table 1 shows the data records for the Tapah River arranged in chronological order.

No. . | Date . | Measured H (m) . | Measured V (m/s) . | Computed Q (m^{3}/s) from Aydin & Gharahjeh
. |
---|---|---|---|---|

1 | November 04, 2015 | 0.45 | 1.231 | 2.892 |

2 | November 26, 2015 | 0.23 | 0.882 | 1.077 |

3 | January 07, 2016 | 0.17 | 0.759 | 0.688 |

4 | January 26, 2016 | 0.28 | 0.973 | 1.441 |

5 | February 02, 2016 | 0.43 | 1.204 | 2.706 |

6 | February 25, 2016 | 0.36 | 1.102 | 2.086 |

7 | March 14, 2016 | 0.44 | 1.218 | 2.799 |

8 | March 24, 2016 | 0.16 | 0.736 | 0.629 |

9 | April 13, 2016 | 0.11 | 0.611 | 0.360 |

No. . | Date . | Measured H (m) . | Measured V (m/s) . | Computed Q (m^{3}/s) from Aydin & Gharahjeh
. |
---|---|---|---|---|

1 | November 04, 2015 | 0.45 | 1.231 | 2.892 |

2 | November 26, 2015 | 0.23 | 0.882 | 1.077 |

3 | January 07, 2016 | 0.17 | 0.759 | 0.688 |

4 | January 26, 2016 | 0.28 | 0.973 | 1.441 |

5 | February 02, 2016 | 0.43 | 1.204 | 2.706 |

6 | February 25, 2016 | 0.36 | 1.102 | 2.086 |

7 | March 14, 2016 | 0.44 | 1.218 | 2.799 |

8 | March 24, 2016 | 0.16 | 0.736 | 0.629 |

9 | April 13, 2016 | 0.11 | 0.611 | 0.360 |

There are three corresponding high flows which exceed 2.5 m^{3}/s. The maximum flow of 2.892 m^{3}/s could be traced back to the date of 4th November 2015. Additionally, low flow records below 1.0 m^{3}/s were also recorded as many as three times, respectively. The minimum flow was recorded at 0.360 m^{3}/s on 13^{rd} April 2016.

### Results

*H*from the weir crest at Tapah River is 0.8 m high, which is expected after the level overflow and submergence of the whole structure. If the value is scaled down, the maximum head in experimental test gives 0.2 m. Thus, extrapolation of the experimental flow curve is extended until the maximum head level of 0.2 m. The chart shows that sufficient data (11 points) are obtained from the experiment.

Both theoretical and experimental curves are almost perfectly matched. However, the field data is deflected apart from the two curves. The correlation gives a value of 0.98 for the three curves indicating close relationship of them. Such deviation may be due some unidentified uncertainties of field conditions. Factors such as sediment accumulation at the wall of upstream weir crest, or tree branches stuck in front of the weir, may alter the flow and affect the recording of field data.

It is found that the abstraction rate of Tapah/Beratok WTP is 0.14 m^{3}/s (12.0 MLD). It is a normal practice to limit abstraction not lower than 40% of safe yield. Thus, a 40% of increment from the abstraction rate is proposed as the safe yield of Tapah River. With that, the proposed safe yield has a value of 0.20 m^{3}/s (17.3 MLD). Corresponding to this safe yield, the head is estimated at 0.07 m. Taking into account uncertainties of the site, it should extend also to head of 0.16 m.

If the total amount of proposed future withdrawals is greater than the safe yield of the river, then the water is not being sustainably used. This indicates a need to reduce the amount of withdrawals or identify new water sources. On the other hand, if the safe yield is greater than the amount of abstraction rate of pump, water resources are being sustainably managed given the identified amount of acceptable risk.

## CONCLUSIONS

The recently reported weir velocity concept has been applied as the discharge formula for the contracted rectangular sharp-crested weir in finding the safe yield for Tapah River. Although there are some unavoidable conditions such as limited data and site restriction, the study was carried out successfully. Experimental results almost perfectly matched with the theoretical formulation. However, field data seemed to be underestimated, fluctuating from theoretical and laboratory findings. This is due to the uncertainties of site conditions that affect the water flow over the weir. A design chart has been produced to enable estimation of river safe yield. From the analysis, the safe yield of Tapah River is proposed to be 0.2 m^{3}/s based on the 40% increment of 0.14 m^{3}/s abstraction rate. With these particular findings, a corresponding head of 0.07–0.16 m has been determined. Maintaining the head in the identified range will assist JKR Sarawak in securing the availability of a long-term water supply and provide an initial outlook for global use.

The ownership of Tapah/Beratok WTP was under JKR Sarawak when this project was first started. Starting from 1 September 2015, rural water supplies came under the jurisdiction of Jabatan Bekalan Air Luar Bandar Sarawak.