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Critical slope is the minimum slope in which maximum discharge shall occur without requiring the box culvert to flow full. For box culverts with slope less than critical slope, at low headwater it tends to flow full and eventually requires a higher headwater depth to convey the same amount of water required for culverts with slopes greater than critical slope.
The headwater level and tailwater level of culverts are important parameters in hydraulic design. The headwater level cannot be set too large, otherwise flooding upstream may occur leading to the loss of life and properties. On the other hand, the tailwater level of culverts has to comply with the following requirements:
(i) For low tailwater levels at the outlet of culverts, the small depths of flow may cause significant erosion of downstream channels.
Supercritical flow involves shallow water flowing in high velocity. The shallow water depth results in higher velocity head when compared with subcritical flow. The fast flow of water causes erosion to channel linings and beddings. When the channel slope becomes flat, the flow can become subcritical causing the formation of hydraulic jump which further causes erosion to channel bed.
The best hydraulic section of an open channel is characterized by provision of maximum discharge with a given cross sectional area. As such, channels with circular shape is the best hydraulic sections while a rectangular channel with channel width being equal to two times the height of channel is the best hydraulic section among all rectangular sections.
For checking of self-cleansing velocity for pipes, there is another criterion to check design flow Q to full bore flow Qfull> 0.5. If this criterion is met, it can be deduced that the design flow is always greater than self-cleansing velocity.
In the design of gravity drainage pipes, full bore flow capacity is normally adopted to check against the design runoff. However, one should note that the maximum flow rate does not occur under full bore conditions. The maximum discharge occurs when the water depth in circular pipes reaches 93.8% of the pipe diameter. Therefore, the use of full bore discharge is on the conservative side though the pipe’s maximum capacity is not utilized.
Darcy-Weisbach equation combined with the Moody Diagram is the accepted method to calculate energy losses resulting from fluid motion in pipes and other closed conduits. However, the Moody Diagram may not be suitable for usage in some conditions.
Manning’s formula was proposed by Robert Manning (an Irish engineer) to calculate uniform flow in open channel. It is probably the most widely used uniform-flow formula around the world. Its extensive usage is due to the following reasons:
(i) The majority of open channel flows lies in rough turbulent region;
(ii) It is simple in form and the formula is well proven by much practical
experience.
Manning’s Equation is commonly used for rough turbulent flow while Colebrook-White Equation is adopted for transition between rough and smooth turbulent flow.
Rational Method is suitable for small catchments only because the time of concentration of small catchments is small. In Rational Method the peak runoff is calculated based on the assumption that the time of concentration is equal to the rainfall duration. For small catchments, this assumption may hold true in most circumstances. One of the assumptions of Rational Method is that rainfall intensity over the entire catchment remains constant during the storm duration. However, in case of a large catchment it stands a high probability that rainfall intensity varies in various part of the large catchment. In addition, for long duration of rainfall, it is rare that the rainfall intensity remains constant over the entire rainstorm and a shorter duration but a more intense rainfall could produce a higher peak runoff. Moreover, a reduction of peak runoff is also brought about by the temporary storage of stormwater like channels within the catchment.
