Problem 1Stage and discharge measurements at a gauging station are given in the table below. We know thatthere is a power relationship between the stage and the discharge at a river cross-section as:Q = K(stage – a)bwhere Q: discharge (m/s)stage: water surface elevation (m)a: constants for the station where after this depth the real flow starts. (Assume that a=0.10 m)b: constant of the power equationK: constant of the power equationStage(m)Q (m³/s)0.30.40.50.70.91.11.72.12.695145170210225267348425487Using Excel, find the best fit equation of the rating curve between Q and (stage-a). Determinethe coefficients (K and b) from the equation best fit curve.Hint: (i) Plot (stage-a) vs Q as scatter plot. (ii) Right click on one of the points on the graph andselect “Add Trend Line". (iii) Select power equation and select to see the equation and R?value on the graph.b. Estimate the flood discharge for the given river stage of 2.3 meters.a.

Given: To find: Power relation Where,

Answered: Stage and discharge measurements at a…

Stage and discharge measurements at a gauging station are given in the table below. We know that there is a power relationship between the stage and the discharge at a river cross-section as:

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Problem 1
Stage and discharge measurements at a gauging station are given in the table below. We know that
there is a power relationship between the stage and the discharge at a river cross-section as:
Q = K(stage – a)b
where Q: discharge (m/s)
stage: water surface elevation (m)
a: constants for the station where after this depth the real flow starts. (Assume that a=0.10 m)
b: constant of the power equation
K: constant of the power equation
Stage(m)
Q (m³/s)
0.3
0.4
0.5
0.7
0.9
1.1
1.7
2.1
2.6
95
145
170
210
225
267
348
425
487
Using Excel, find the best fit equation of the rating curve between Q and (stage-a). Determine
the coefficients (K and b) from the equation best fit curve.
Hint: (i) Plot (stage-a) vs Q as scatter plot. (ii) Right click on one of the points on the graph and
select “Add Trend Line". (iii) Select power equation and select to see the equation and R?
value on the graph.
b. Estimate the flood discharge for the given river stage of 2.3 meters.
a.

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