**Exercise 5 - Rating Curve Development**

Develop and plot on the attached logarithmic graph paper a theoretical
rating for the channel shown below. Assume the sand bar forms a section
control. Also, assume that the weir equation applies for the sand bar
and that Manning's equation applies for the rest of the channel. When
channel control is in effect, the sand bar will be either drowned out or
will be washed out. Therefore, [the area and wetted perimeter of the
sand bar should be disregarded when using Manning's
equation]{.underline}.

+-----------------------------------+-----------------------------------+
| **Weir equation**:                | **Manning equation:**             |
|                                   |                                   |
| Q = CLH **^3/2^**                 | **Q = [1.486]{.underline} AR 2/3  |
|                                   | S 1/2**                           |
| where                             |                                   |
|                                   | **n**                             |
| C = 2.5,                          |                                   |
|                                   | **where:**                        |
| L = Top width, in feet            |                                   |
|                                   | **n = roughness coefficient**     |
| H = Average depth of flow, in     |                                   |
| feet                              | **A = cross sectional area**      |
|                                   |                                   |
|                                   | **R = Hydraulic Radius (A / WP)** |
|                                   |                                   |
|                                   | **S = Energy slope (assume to     |
|                                   | be**                              |
|                                   |                                   |
|                                   | **same as water surface slope)**  |
|                                   |                                   |
|                                   | **( = 0.0009)**                   |
+-----------------------------------+-----------------------------------+

**Schematic diagram of channel**

![](media/image1.png){width="8.996527777777779in"
height="3.6194444444444445in"}

A. Use the weir equation to complete the table below:

  ----------------- ----------------- ----------------- -----------------
  GH                L                 Ave. H            Q

  1                 0                 0                 0

  1.5               10                0.25              3.12

  2                 20                0.5               17.7

  **2.5**                                                

  **3**                                                  

  4                 40                2                 283

  5                 40                3                 520

  6                 40                4                 800
  ----------------- ----------------- ----------------- -----------------

B. Now use Manning's equation to complete this table:

  ---------- --------- -------- ---------- ------------- ---------- --------- ---------- ------------- --------------
  **G.H.**   **A**     **WP**   **R 2/3**  **Q(main)**   **A**      **WP**    **R 2/3**  **Q(over)**   **Q(Total)**

  **3**      **80**    **44**   **1.49**   **133**       ** **      ** **     ** **      ** **         **133**

  **4**      **120**   **46**   **1.9**    **253**       ** **      ** **     ** **      ** **         **253**

  **5**      ** **     ** **    ** **      ** **         ** **      ** **     ** **      ** **         ** **

  **6**      **200**   **50**   **2.52**   **562**       ** **      ** **     ** **      ** **         **562**

  **7**      **240**   **52**   **2.77**   **742**       ** **      ** **     ** **      ** **         **742**

  **8**      **280**   **54**   **3**      **935**       ** **      ** **     ** **      ** **         **935**

  **9**      **320**   **56**   **3.2**    **1140**      ** **      ** **     ** **      ** **         **1140**

  **11**     **400**   **58**   **3.62**   **1620**      **960**    **962**   **1.00**   **530**       **2150**

  **12**     ** **     ** **    ** **      ** **         ** **      ** **     ** **      ** **         ** **

  **14**     ** **     ** **    ** **      ** **         ** **      ** **     ** **      ** **         ** **

  **16**     **600**   **58**   **4.75**   **3180**      **5760**   **972**   **3.27**   **10500**     **13700**

  **18**     **680**   **58**   **5.16**   **3910**      **7680**   **976**   **3.96**   **16900**     **20800**

  **20**     **760**   **58**   **5.56**   **4710**      **9600**   **980**   **4.58**   **24500**     **29200**
  ---------- --------- -------- ---------- ------------- ---------- --------- ---------- ------------- --------------

C. Use the paper on the next page and the data in the tables above to
plot the rating

**Answers**

![](media/image2.wmf)

![](media/image3.wmf)

![](media/image4.wmf){width="7.251574803149606in" height="4.0in"}