Concept explainers
Consider water flow in the range of 10 to 15 m3/s through a horizontal section of a 5-m-de rectangular channel. A rectangular or triangular thin-plate weir is to be installed to measure the flow rate. If the water depth is to remain under 2 m at all times, specify the type and dimensions of an appropriate was. What uid your response be if the flow range were 0 to15 m3/s?
The appropriate dimension for the rectangular weir for the varying flow rate.
The appropriate dimension for the triangular weir for the varying flow rate.
Answer to Problem 167P
The appropriate dimensions for the rectangular weir are
The appropriate dimensions for the triangular weir are
Explanation of Solution
Given Information:
The water flow rate range is
Write the expression for the weir head.
Here, the flow depth at upstream is
Write the expression for the discharge coefficient of the weir.
Write the expression for the water flow rate of the channel per meter width.
Here, the width of the channel is
Calculation:
Substitute
Substitute
Case I.
Substitute
The head of the weir plate for the different values of the volume flow rate is shown in below Table 1.
Table-1
S.No. | ||
1 | ||
2 | ||
3 | ||
4 | ||
5 | ||
6 |
Case II.
Substitute
The head of the weir plate for the different values of the volume flow rate is shown in below Table 2.
Table-2
S.No. | ||
1 | ||
2 | ||
3 | ||
4 | ||
5 | ||
6 | ||
7 | ||
8 | ||
9 | ||
10 | ||
11 | ||
12 | ||
13 | ||
14 | ||
15 | ||
16 |
The Table 2 shows that the height of the weir plate is increase with increase in the flow rate of the water. Therefore, consider the maximum height of the weir plate which is suitable for all volume flow rate varying from
The rectangular weir of
The triangular weir of
Conclusion:
The appropriate dimensions for the rectangular weir are
The appropriate dimensions for the triangular weir are
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Chapter 13 Solutions
Fluid Mechanics: Fundamentals and Applications
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