Derivation of discharge over rectangular weir

In summary, the derivation of discharge over a rectangular weir is important for determining the flow rate of water in open channels, and it can be calculated using the Francis formula or the weir equation. Assumptions made in the derivation include steady and uniform flow, negligible velocity approaching the weir, and a parallel water surface. The shape of the weir affects the discharge, with rectangular weirs having a higher discharge coefficient. However, there are limitations to using the derived discharge, as it is based on certain assumptions and may not accurately reflect real-world conditions or be applicable to non-standard weirs.
  • #1
Ravikant Rajan
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How does the velocity at an elemental height h equates to √(2gh)? My application of Bernoulli's equation is not yielding the result. Please show the process.

Thank you
 

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  • #2
So what is the difference between your handling of Bernoulli and, e.g., this one ?
 
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  • #3
BvU said:
So what is the difference between your handling of Bernoulli and, e.g., this one ?
Thank You so much.
The exiting fluid also experiences same atmospheric pressure as the top point.
 

1. What is the purpose of deriving the discharge over a rectangular weir?

The derivation of discharge over a rectangular weir is important for determining the flow rate of water in open channels. This information is useful for various engineering applications, such as designing irrigation systems or predicting flood levels.

2. How is the discharge over a rectangular weir calculated?

The discharge over a rectangular weir can be calculated using the Francis formula, which takes into account the dimensions of the weir, the head of water above the weir, and the gravitational constant. Alternatively, it can also be calculated using the more simplified weir equation, which only requires the head of water and the width of the weir.

3. What are the assumptions made in the derivation of discharge over a rectangular weir?

The derivation of discharge over a rectangular weir assumes that the flow is steady, uniform, and fully developed. It also assumes that the velocity of water approaching the weir is negligible and that the water surface is parallel to the crest of the weir.

4. How does the shape of the weir affect the discharge?

The shape of the weir plays a significant role in determining the discharge. A rectangular weir has a higher discharge coefficient compared to a V-notch weir, meaning that it can handle a larger flow rate for the same head of water. This is because the rectangular shape allows for a wider opening and a smoother transition of water over the weir crest.

5. What are the limitations of using the derived discharge over a rectangular weir?

The derived discharge over a rectangular weir is based on certain assumptions and may not accurately reflect real-world conditions. Factors such as changes in water level, debris accumulation, and roughness of the weir surface can affect the actual discharge. Additionally, the derived discharge may not be applicable for weirs with non-standard shapes or dimensions.

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