Question
Download Solution PDFThe model of a spillway is to be built to a scale ratio 1:50 across a flume of 70 cm width. The prototype has a height of 16 m and expected maximum head is 1.6 m. Determine the head required for the model.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
For open channel flow over a spillway, the head is a length parameter and follows the law of geometric similarity in Froude model laws. So the scale ratio for head (H) is:
\( H_m = \frac{H_p}{\sqrt{L_r}} \)
Where:
- \(H_m\) = head in model
- \(H_p\) = head in prototype = 1.6 m
- \(L_r\) = length scale ratio = 50
Given:
- Prototype head = 1.6 m
- Model scale ratio = 1:50
Calculation:
As per Froude’s model law:
\( H_m = \frac{H_p}{L_r} = \frac{1.6}{50} = 0.032 \, \text{m} \)
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